Close
About
FAQ
Home
Collections
Login
USC Login
Register
0
Selected
Invert selection
Deselect all
Deselect all
Click here to refresh results
Click here to refresh results
USC
/
Digital Library
/
University of Southern California Dissertations and Theses
/
Managing functional coupling sequences to reduce complexity and increase modularity in conceptual design
(USC Thesis Other)
Managing functional coupling sequences to reduce complexity and increase modularity in conceptual design
PDF
Download
Share
Open document
Flip pages
Contact Us
Contact Us
Copy asset link
Request this asset
Transcript (if available)
Content
MANAGING FUNCTIONAL COUPLING SEQUENCES
TO REDUCE COMPLEXITY AND INCREASE MODULARITY
IN CONCEPTUAL DESIGN
by
Chu-Yi Wang
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirement for the Degree
DOCTOR OF PHILOSOPHY
(MECHANICAL ENGINEERING)
August 2018
Copyright 2018 Chu-Yi Wang
i
Acknowledgement
First and foremost, I would like to thank my Ph.D. advisor Dr. Stephen Lu, whose
continuing guidance helped me in achieving my goal.
I would like to acknowledge the members of my committee: Dr. Jin Yan, Dr. Yong
Chen, Dr. Geoffrey R. Shiflett, and Dr. Behrokh Khoshnevis. Their constructive
comments during my qualifying proposal helped me perfect my work and make it
more valuable.
Next, I would like to thank my senior labmate, Dr. Ang Liu for giving me advice on
this research and taking the time to work with me. I am thankful for the great
availability and diligence of Phil Chung who enabled me to carry out the case studies
described in this work in the best conditions possible.
Next, I would like to acknowledge the great financial support from Taiwan
Government and USC Viterbi School in these five years.
Finally, I would like to thank all my family and close friends for their support. My
parents and my sister always encouraged me and gave me positive mental support
despite the distance. Without their support with love, pursuing PhD would have not
been possible for me. I also want to thank my friend, Chung-Hau Wang and his
family, who gave me a lot of support and care. Finally yet importantly, I would like
to thank Aditya Shrivatri, whose love, care and attention helped me overcome my
health problem and surpass the goals I had set for myself and make me a better
person.
ii
Table of Contents
Acknowledgement ..................................................................................................... i
Table of Contents ...................................................................................................... ii
Abstract ...... ............................................................................................................. vi
List of Figures ............................................................................................................ x
List of Tables .......................................................................................................... xiii
Chapter 1.Introduction ............................................................................................... 1
1.1 Background and Motivations ................................................................ 1
1.2 Research Objectives .............................................................................. 7
1.3 Scope of works ...................................................................................... 7
1.4 Dissertation Organization ...................................................................... 8
Chapter 2.Background ............................................................................................. 11
2.1 Background for Conceptual Design .................................................... 11
2.1.1 Axiomatic Design Theory ............................................................13
2.1.2 Innovative Design Thinking .........................................................19
2.1.3 Reengineering for Concept Improvement ....................................23
2.1.4 Challenges of Applying Design Theory in Practice .....................25
2.2 Background for Modular Design.........................................................27
2.2.1 The Definition of Module .............................................................27
2.2.2 Representation of Modules ...........................................................28
2.2.3 The Benefits of Modularity ..........................................................28
2.2.4 The Challenge of Modularity .......................................................28
2.3 Background for Design Complexity ...................................................29
2.3.1 Time-Independent Design Complexities ......................................29
2.3.2 Design Matrix and Functional Coupling ......................................31
2.4 Background for Sequencing Algorithm ..............................................31
2.4.1 The Execution Sequence ..............................................................32
2.4.2 Complexity Reduction Framework ..............................................32
2.4.3 Suh’s DM Rearrangement ............................................................34
2.4.4 Benavides’ Extended Algorithm ...................................................36
2.4.5 Lee’s Optimal Strategy .................................................................38
2.4.6 Limitations of the above methods ................................................40
2.5 Challenges of Working with DM Directly ..........................................40
iii
2.5.1 Difficulties of rearranging DM directly .......................................40
2.5.2 Execution Sequence for Coupled Design .....................................44
2.5.3 Sequence Reading Limitation from DM ......................................45
2.6 Summary of the Chapter .....................................................................46
Chapter 3.Research Foundations .............................................................................48
3.1 Research Assumptions .........................................................................48
3.2 Research Hypotheses ...........................................................................48
3.2.1 Hypothesis I (H1): Generality ......................................................48
3.2.2 Hypothesis II: Uniqueness ............................................................50
3.3 Observation and Foundations for Execution Sequence ......................51
3.3.1 The Solution by Linear Algebra ...................................................51
3.3.2 The Coupling Loop from Lee’s Optimal Strategy .......................52
3.3.3 The rationale of Suh’s rearrangement algorithm .........................53
3.3.4 Research Foundation I: The Concept of Precedence ...................53
3.4 Rationales and Foundations for Modular Design ...............................55
3.4.1 Using Sets Rather than Direct Elimination ..................................55
3.4.2 The Sequence in Component Diagram .........................................56
3.4.3 Research Foundation II: Two Types of Functional Sets ...............57
Chapter 4.The Approach: Design Coupling Sequence ............................................58
4.1 Introduction of DCS and DCS Representation ...................................58
4.1.1 From DCS to The Acceptable Execution Sequences ...................60
4.1.2 From DCS to The Design Matrix Rearrangement .......................60
4.2 The Concept Improvement Strategies with DCS Sets ........................62
4.2.1 The Whole Design Concept Refinement ......................................62
4.2.2 The Design Change without DM Change ....................................62
4.2.3 The Design Change with DM Change .........................................63
4.3 The DCS Algorithm.............................................................................63
4.3.1 The Logic of the Algorithm ..........................................................63
4.3.2 The Notions in the Algorithm .......................................................64
4.3.3 The Procedure of the Algorithm ...................................................65
4.4 Summary of This Chapter ...................................................................67
Chapter 5.The Software Implementation .................................................................68
5.1 Objectives and Software Introduction .................................................68
5.1.1 Objectives .....................................................................................68
iv
5.1.2 The DM-DCS Converter ..............................................................68
5.1.3 System Architecture......................................................................69
5.2 Graphical User Interface and the Program Manipulation ...................71
5.2.1 The Database ................................................................................71
5.2.2 The Main Interface .......................................................................72
5.2.3 Design Matrix Importation ...........................................................74
5.2.4 DCS Sequence Exportation ..........................................................75
5.3 System Testing and DCS Algorithm Validation ..................................75
5.3.1 The Test Results of the Three typical types of DM ......................75
5.3.2 The Test Results of non-typical DM ............................................77
5.3.3 The Test Results of the non-ADT’s DM ......................................79
5.3.4 The Test Results of the Large DM with Mixed Design Types .....83
5.4 Discussion ...........................................................................................85
5.4.1 The Usability of the Software ......................................................85
5.4.2 System Scale and Limitations ......................................................86
5.5 Summary and Future Extensions.........................................................86
Chapter 6.Case Studies for DCS Validations ...........................................................87
6.1 A Simple Design Case: The Kitchen Faucet Design ...........................87
6.1.1 The Objectives of the Case Study and the Case Introduction ......87
6.1.2 The Problem Statement ................................................................88
6.1.3 The Improvement by Suh’s method .............................................89
6.1.4 The Improvement by DCS method ..............................................93
6.1.5 Discussions ...................................................................................95
6.1.6 Summary .......................................................................................96
6.2 A Re-Engineering Product Design Case: The Coffee Maker Design .97
6.2.1 The Case Introduction ..................................................................97
6.2.2 The Re-Engineering Results .........................................................98
6.2.3 The Conceptual Design with ADT and TRIZ ............................102
6.2.4 The Conceptual Design with DCS .............................................105
6.2.5 Discussions .................................................................................108
6.2.6 Summary .....................................................................................109
6.3 A Complex Design Case: The Product Development of PCR Tire ..109
6.3.1 The Objectives of the Case Study and the Case Introduction ....109
6.3.2 The Problem Statement .............................................................. 111
v
6.3.3 The Traditional Tire Improvement Method ................................ 112
6.3.4 The Application Results by DCS................................................ 114
6.3.5 The Application Results by the Traditional Method .................. 119
6.3.6 Discussions .................................................................................120
6.3.7 Summary .....................................................................................120
6.4 An Extended Application: Collision Avoidance Planning Strategy ..121
6.4.1 The Objectives of the Case Study and the Case Introduction ....121
6.4.2 The Problem Statement ..............................................................122
6.4.3 The Problem Formulation ..........................................................124
6.4.4 The Application Approach ..........................................................125
6.4.5 The Application Example and the Results .................................126
6.4.6 Summary .....................................................................................129
6.5 Conclusions, Limitations, and Future Extensions .............................129
Chapter 7.Summary, Contributions, and Future Works .........................................131
7.1 Summary ...........................................................................................131
7.2 Contributions .....................................................................................131
7.3 Future Works .....................................................................................132
Works cited .............................................................................................................133
vi
Abstract
According to the Axiomatic Design Theory (ADT), a design concept that can
satisfy the upstream objectives under downstream constraints with the minimal
relative complexity can lead to the most ideal design. As stated by Suh’s Complexity
Theory, the relative complexity of a design concept is caused by couplings between
functional requirements (FRs) and design parameters (DPs), and can be reduced by
strategically ordering the execution (i.e., implementation) sequence of DPs.
However, it is generally very difficult in the current design practice to obtain this
“execution sequence” with existing methods due to their inherent limitations and/or
many real-world restrictions. Meanwhile, many practical methods, such as the
modular design approach, have been widely used in industries to produce real-world
design results that don’t necessarily conform with the principles required by those
ideal design theories. As a result, from the perspectives of design theories, most real-
world designs are “not ideal” (i.e., having some relative complexities due to FR-DP
couplings) and therefore can (and should) be improved by better sequencing their
DPs. This is the motivation under which the Design Coupling Sequence (DCS)
method was developed in this thesis research. The DCS method can assist designers
to automatically obtain the “execution sequences,” in the forms of functional sets,
that can yield the minimal relative complexity, hence making a practical design
concept most ideal (i.e., as close to the ideal concept with the minimal relative
complexity as possible) while taking into practical considerations (such as increasing
the modularity to lower the production costs) in real-world conceptual designs.
vii
The DCS method defines the ‘precedence’ between ‘functional sets’ to manage
coupled design concepts to support the modular approach during conceptual design.
It identifies the ‘precedence’ by the level of functional coupling to determine the
proper sequencing order to minimize the overall complexity. Two types of functional
sets are defined in DCS as 1) the complete independently set U: the collection of all
the functionally dependent DPs in the system so that the set is independent to other
U sets, and 2) the indivisible coupled set C: the collection of coupled concepts that
can’t be decoupled by sequencing, so it prescribes the designer to consider the group
of DPs together as a set to match existing modules in the database. To handle the
real complexity of design concepts which require redesign, the DCS algorithm helps
to determine the proper execution sequence. To minimize the imaginary complexity,
which occurs when design concepts “appear” to be functionally coupled due to a
lack of understanding of the system structure, the DCS method provides a formula
to reveal the number of acceptable execution sequences that can lead to the simplest
design implementation. Compared with existing methods, the DCS method is
applicable for any design cases with known design matrices, including the square,
rectangular, zero-at-diagonal, large, and/or numerical matrices. In short, for all
practical design cases, DCS can organize functional-coupled design concepts as
“functional sets” with execution sequences of DPs that lead to the minimal
complexity of this design concept.
The foundation, hypothesis, algorithm and its usability of the DCS method are
validated by four case studies in this research. The faucet design case demonstrates
viii
how to apply the DCS method and shows the differences between ADT and DCS
results. The case of coffee maker design shows how the DCS method manages the
functional sets based on the design matrices reengineered from existing design
concepts. The vehicle tire design case demonstrates how different DCS strategies
within the Innovative Design Thinking (IDT framework during the conceptual
design stage can work in a real-world product development situation. The IDT
framework prescribes four consecutive steps: (1) following the top-down process to
ideate new design concepts that satisfy the principles/axioms suggested by the
design theory to reach a certain layer of details, (2) following the bottom-up process
to identify some existing design modules from available engineering database (or
catalogs) that can satisfy the functional requirements at this detail layer, (3)
constructing the design matrix that shows the couplings between FRs and DPs at this
detail layer, and (4) apply the DCS algorithm to determine the execution sequence
of DPs based on the above design matrix. This will yield a new design concept with
an execution sequence that is most creative (because it satisfies the design principles
at the top layers) and most practical (because it utilizes the existing modules at the
bottom layers). Finally, a case of collision avoidance planning presents one of the
possible extensions of the DCS algorithm.
The results of this research have significant impacts on both design theory and
design practice. Theoretically, the approach in this research 1) guides designers to
improve concepts not only organizing design matrix but also extract additional
coupling information to increase modularity and 2) is a more generalized approach
ix
than the previous methods that can be applied to any design cases with design matrix.
Practically, the research 1) demonstrates the usability of the DCS algorithm within
an executive program to generate the DCS functional sets automatically for large
design system and 2) allows the principle of functional dependency and the practice
of modular design to be considered simultaneously as much as possible during the
conceptual design stage. It is a fundamental contribution that demonstrates how the
ideal principles (or axioms) of design theories can be used together strategically with
practical design methods (or considerations) in industry practices to generate real-
world design results that are both most practical and creative. For future research,
there would be three aspects- DCS algorithm, DCS sets, and DCS strategies. Number
one, DCS algorithm would be further revised to extend to software design or
machine learning with functional sets in terms of a component diagram. Number two,
with DCS sets, the three-dimensional design matrix could be studied further.
Number three, DCS strategies would be investigated further for applying on detailed
design cases.
As a recap, the research prescribes a functional coupling managing algorithm
with functional sets for suggesting acceptable execution sequences in conceptual
design. It not only helps designers with complexity reduction but also bridges the
ideal design theory to practical modules. The designer can create better designs that
are most creative and yet practical by using the DCS strategies.
x
List of Figures
Figure 2.1 IDEF0 Model of Conceptual Design. .......................................................................... 12
Figure 2.2 Two Phases in Conceptual Design Stage. .................................................................... 12
Figure 2.3 Four Domains in Axiomatic Design. ........................................................................... 14
Figure 2.4 Zigzagging Reasoning Pattern in ADT. ....................................................................... 15
Figure 2.5 DM (a) with no functional coupling and (b) with a coupling term at DM21. ............. 17
Figure 2.6 (a) Uncoupled design, (b) decoupled design, and (c) coupled design. ........................ 17
Figure 2.7 Coupling types of design matrix and their complexity. ............................................... 17
Figure 2.8 An Example DM of a Decoupled Design. ................................................................... 18
Figure 2.9 The big-circle reasoning pattern in ATC. .................................................................... 20
Figure 2.10 The fractal co-evolution reasoning pattern in IDT. ................................................... 21
Figure 2.11 A pair of FR-DP triads. .............................................................................................. 22
Figure 2.12 Reengineering. ........................................................................................................... 23
Figure 2.13 The DSM and DMM in HoQ ..................................................................................... 24
Figure 2.14 Two examples of more functional couplings at the lower layer ................................ 26
Figure 2.15 Two examples of more functional couplings at the upper layer. ............................... 26
Figure 2.16 Two examples of unequal numbers of FR and DP .................................................... 26
Figure 2.17 The roadmap of complexity reduction framework .................................................... 34
Figure 2.18 An Example of the Implementation of the Suh’s Method ......................................... 35
Figure 2.19 An Example of the Implementation of the EA’s Phase 1 .......................................... 37
Figure 2.20 An Example of the Implementation of the EA’s Phase 2 .......................................... 37
Figure 2.21 An evidence of showing EA is not an optimal method ............................................. 38
Figure 2.22 An Example of the Implementation of the Lee’s Method ......................................... 39
Figure 2.23 A 4x4 design matrix ................................................................................................... 41
Figure 2.24 A possible process of DM rearrangement for a decoupled design case. ................... 41
Figure 2.25 A 9x9 Design Matrix ................................................................................................. 42
Figure 2.26 The 9x9 DM rearrangement by Suh’s method .......................................................... 43
Figure 2.27 An example of coupled DM ...................................................................................... 45
Figure 2.28 Another design matrix example ................................................................................. 46
Figure 3.1 Linear equation solving sequence ............................................................................... 51
Figure 3.2 The procedure of finding the coupling in a sample DM with coupling ...................... 52
Figure 3.3 The procedure of finding the coupling in a sample DM without coupling ................. 52
Figure 3.4 Another design matrix example ................................................................................... 54
xi
Figure 3.5 Encapsulation reveals modularity................................................................................ 56
Figure 3.6 An example for functional set...................................................................................... 57
Figure 4.1 An example design matrix for explaining DCS representation ................................... 59
Figure 4.2 An example of the result of DCS ................................................................................. 59
Figure 4.3 Design matrix rearrangement by DCS ........................................................................ 61
Figure 4.4 Design matrix rearrangement by DCS ........................................................................ 61
Figure 4.5 Three-dimensional design matrix ................................................................................ 61
Figure 4.6 The flow chart of DCS algorithm ................................................................................ 65
Figure 5.1 The use case diagram ................................................................................................... 69
Figure 5.2 The component diagram .............................................................................................. 71
Figure 5.3 The DM in Excel ......................................................................................................... 72
Figure 5.4 The main window ........................................................................................................ 73
Figure 5.5 The DM imported into the DM data panel .................................................................. 73
Figure 5.6 The DCS showed in the DCS results textbox .............................................................. 74
Figure 5.7 The file import interface .............................................................................................. 74
Figure 5.8 The textbox copy ......................................................................................................... 75
Figure 5.9 The result of the uncoupled design .............................................................................. 76
Figure 5.10 The result of the decoupled design ............................................................................ 76
Figure 5.11 The result of the coupled design ................................................................................ 77
Figure 5.12 The result of the partially decoupled DM .................................................................. 78
Figure 5.13 The result of the partial coupled DM......................................................................... 78
Figure 5.14 A rectangular DM example ........................................................................................ 79
Figure 5.15 The result of the example rectangular DM ................................................................ 79
Figure 5.16 The DCS result of the rectangular DM from EA method .......................................... 80
Figure 5.17 The working DM with zero at diagonal .................................................................... 81
Figure 5.18 The result of the 9×9 DM .......................................................................................... 81
Figure 5.19 The numerical DM sample from tire design case in section 6.3 ............................... 82
Figure 5.20 The result of the numerical DM ................................................................................ 82
Figure 5.21 The result of the binary DM ...................................................................................... 83
Figure 5.22 The result of the 9×9 DM .......................................................................................... 84
Figure 5.23 The 9×9 DM and its DCS sets ................................................................................... 84
Figure 5.24 The DM rearrangement result from the DCS result .................................................. 85
Figure 5.25 A 3-D DM was built according to the above results .................................................. 85
Figure 6.1 (a) A common kitchen faucet (b) its DM ..................................................................... 88
xii
Figure 6.2 A shower faucet example. ............................................................................................ 88
Figure 6.3 The design that needs to be improved and its DM ...................................................... 89
Figure 6.4 The DM rearrangement result for the faucet design by Suh’s method ........................ 90
Figure 6.5 The improved design from Suh’s method ................................................................... 90
Figure 6.6 Five possible options of DP4. ...................................................................................... 91
Figure 6.7 Three possible options of DP3 .................................................................................... 91
Figure 6.8 The final improved design from Suh’s method ........................................................... 93
Figure 6.9 The DCS’s sequence .................................................................................................... 93
Figure 6.10 The process of the DCS’s improvement. ................................................................... 94
Figure 6.11 Four possible options of the module of DP1 and DP2 .............................................. 95
Figure 6.12 The final improved design from DCS method. ......................................................... 95
Figure 6.13 The DP hierarchy of a coffee maker design from layer 0 to 2 .................................. 97
Figure 6.14 The DP hierarchy of DP1 and the FRs at layer 4 ...................................................... 98
Figure 6.15 The DP hierarchy of DP2 and the FRs at layer 4 ...................................................... 99
Figure 6.16 The DP hierarchy of DP3 and the FRs at layer 4 ...................................................... 99
Figure 6.17 The design matrix of the coffee maker at layer 4 .................................................... 100
Figure 6.18 The design matrix of the coffee maker at layer 3 .................................................... 101
Figure 6.19 The design matrix of the coffee maker at layer 2 .................................................... 101
Figure 6.20 The design matrix of the coffee maker at layer 1 .................................................... 102
Figure 6.21 The design matrix of the coffee maker at layer 1 .................................................... 103
Figure 6.22 The extra coupled FR-DP in the coffee maker design at layer 4 ............................. 103
Figure 6.23 The improved coffee maker by extra coupling elimination .................................... 104
Figure 6.24 The design matrix at layer 1 of the original and improved coffee maker ............... 104
Figure 6.25 The DCS sets in the coffee maker design ................................................................ 105
Figure 6.26 The DM rearrangement with modular clusters by DCS in the coffee maker case .. 106
Figure 6.27 One of the execution sequence for the coffee maker case. ...................................... 106
Figure 6.28 The options for DP2222 swivel filter cup design. ................................................... 107
Figure 6.29 The options for DP2116 heating plate design.......................................................... 107
Figure 6.30 The design result by DCS approach ........................................................................ 107
Figure 6.31 The design of the coffee maker with two mugs ....................................................... 108
Figure 6.32 Different coffee makers with similar design improvement for using mug .............. 108
Figure 6.33 Tire Performance Compromises Under Wet Breaking Conditions ..........................110
Figure 6.34 The reengineering process of PCR tires ...................................................................115
Figure 6.35 The numerical DM for RR design ............................................................................117
xiii
Figure 6.36 Tire construction .......................................................................................................117
Figure 6.37 A Low Rolling Resistance Tire Design Result from Hankook (2009) .....................118
Figure 6.38 The design matrix for RR + WET design .................................................................118
Figure 6.39 Test result ..................................................................................................................119
Figure 6.40 The FR hierarchy ..................................................................................................... 124
Figure 6.41 The DP hierarchy ..................................................................................................... 125
Figure 6.42 The flow chart of the planning strategy ................................................................... 126
Figure 6.43 The design matrix of the avoidance situation .......................................................... 127
List of Tables
Table 2.1 Time-Independent design complexity ........................................................................... 31
Table 6.1 The design range of the kitchen faucet ......................................................................... 89
Table 6.2 The list of PVs, DPs, and FRs ......................................................................................116
Table 6.3 The new FRs and new and changed DPs .....................................................................118
Table 6.4 Predictive behaviors of O ............................................................................................ 127
Table 6.5 Functional requirements of X. .................................................................................... 127
Table 6.6 The constraints corresponding to the design matrix elements .................................... 128
Table 6.7 The decisions for the DP. ............................................................................................ 129
1
Chapter 1. Introduction
1.1 Background and Motivations
There has always been a major struggle between theory and practice in the
engineering design community. Researchers working in design theories generally
favor a view that the quality of design results can be improved by some universal
principles and basic laws. Due to the subjective nature of human decisions which
make it difficult to develop normative theories, some researchers have focused on
developing prescriptive design principles and processes instead. A good example of
such is the Axiomatic Design Theory (ADT) proposed by N.P. Suh in 1980s’. ADT
prescribes two fundamental design axioms with a strict zigzagging design process
to achieve the most ideal design with the least (or no) relative complexity. However,
notwithstanding the fact that many research papers with demonstration cases have
been published to validate ADT’s practical uses, engineers working in design
practices still found it very cumbersome, if not impossible, to use the theory in many
real-world design tasks. One reason for this difficult is the large gap between the
practical restrictions and hands-on considerations that engineers face in real-world
design cases and the idealized assumptions (or preconditions) upon which design
theories are developed. Unfortunately, rather than finding ways to bridge the gap
between theory and practice, many industrial practitioners have turned to a rather
pessimistic view toward engineering design research, which hinders the progresses
in both design theories and design practices. This challenge is the main motivation
behind our decade-long research in developing the Innovative Design Thinking (IDT)
2
framework that bridges the gaps between theoretical principles and practical
considerations to support real-world design tasks. The Design Coupling Sequence
(DCS) method developed in this these research is a continuing effort under our IDT
framework.
As a background to understand IDT and DCS researches, let’s use the two-
dimensional conceptual framework of ADT to define some terminologies to explain
the gaps between theory and practice in engineering design. The horizontal axis
represents types of design decisions in different domains, ranging from customer
need (CN) at the “upstream,” to functional requirement (FR), design parameter (DP),
and parametric value (PV) at the “downstream.” The vertical axis represents levels
of details of these decisions at different abstraction layers, ranging from the most
abstract ones at the “top,” to the most specific ones at the “bottom.” According to
ADT, when designers make decisions horizontally from upstream to downstream
domains, it is call “mapping”; when they make a vertical decision from top to bottom
layers, it is called “decomposition.”
Using this two-dimensional framework, ADT suggests a strict “zigzagging”
decision process, which uses “zig” operations first to horizontally map from
upstream to downstream domains at a single abstraction layer from the top. It is then
followed by a “zag” operation that diagonally moves back from downstream to
upstream domains with vertical decompositions at subsequent abstraction layers
toward the bottom. In theory, this breath-first, top-down, zigzagging reasoning
process can lead to a completely new design from top-layer customer needs at the
upstream domain without considering (or taking advantage of) any known product
architectures and existing modular or production constraints at the downstream. In
3
other words, engineers can only follow through the ADT design process, if they are
given the complete freedom with no regard to practical constraints to pursue first-
of-its-kind and most innovative designs with brand new product architectures and
specifications. Unfortunately, most industrial scenarios do not fit well with this ideal
situation, and consequently, rather than following design theories, more practical
methods, such as Analytic Target Cascading (ATC), are commonly used by engineers
in their design practices, especially during routine redesign, modifications or
improvements of existing products.
ATC uses a depth-first reasoning process to make design decisions in functional
and physical domains. First, it consecutively decomposes abstract decisions at top
layers to more detailed ones at bottom layers in the FR domain, then horizontally
maps these detailed FRs to corresponding DPs in the DP domain at the bottom
specific layer, before composing all detailed DPs upwards to more abstract ones at
top abstraction layers to complete the design. Rather than freely “thinking-outside-
the-box” without any mental references, designers can rely on some known existing
product architectures to guide their top-down decomposition and bottom-up
composition tasks in functional and physical domains respectively. As well, since
horizontal mapping tasks from FRs to DPs are performed at more detailed layers,
engineers can often take advantage of those already-available physical modules from
similar products or supplier catalogues to achieve modular designs to reduce the
overall development costs. However, while ATC is convenient for practical and
routine designs, it often falls short to generate good new designs with creative
architectures that are truly innovative to lead to breakthrough products.
4
While ADT is ideal in theory, ATC is useful in practice. Rather than choosing
one at the expense of the other, the IDT framework balances the power of theories
(such as ADT) with that of practices (such as ATC) to support real-world design tasks
that can yield new design results that are as ideal and practical as possible. In our
previous research, we developed a new design process which is the hybrid between
the ADT and ATC processes (need a figure here!). The IDT process treats design
decisions as systematic “proposition-making” in which, according to the formal
definitions of propositional logics, an analytic proposition is made when the resulted
predict is a part of the subject, and a synthetic proposition is made when the resulted
predict is NOT a part of the subject. Operationally speaking, analytic propositions
in IDT are called “specification” operations and performed vertically same as
compositions in ADT; whereas synthetic propositions in IDT are called “ideation”
operations and carried out horizontally like mappings in ADT. At any time, IDT
performs a cycle of specification, ideation, and validation operations between any
two consecutive abstraction layers. Specifically, it first uses an analytic proposition
to specify a given FR with more detailed FRs at a lower abstraction layer. Then, it
uses synthetic propositions to ideate corresponding DPs for these decomposed FRs.
Finally, it validates the logic feasibility of resulting DPs by composing them back to
an abstract DP which must be valid with respect to the original FR at the top layer.
Such a close-loop reasoning cycle in IDT not only combines the depth-first ATC
process with the breath-first ADT process, but more importantly, confirms the logic
feasibility of all FR and DP decisions at each cycle (across two ADT abstraction
layers). In short, the IDT framework enables engineers to generate designs that are
as ideal and practical as possible.
5
Although IDT combines ADT and ATC to result in a new “design process” that
balances theory with practice, engineers still often find the application of those
idealized “design principles” (i.e., axioms) in design practice very difficult. For
example, one of the design axioms of ADT is the Independence Axiom, which
suggests “maintain the independence of functional requirements (FR).” However, in
industry practices, it is extremely difficult for designers to maintain functional
independence between each design parameter (DP) thoroughly (i.e. an uncoupled
design) under real-world restrictions and considerations. For those decoupled
designs whose design matrix can be rearranged into triangular matrix, Suh (2005)
suggests an “execution sequence” to minimize the relative complexity, which is
caused by functional couplings. Nevertheless, most of real-world design cases are
neither uncoupled nor decoupled completely. This is the main motivation behind the
development of DCS as part of our IDT framework.
One solution is to eliminate the extra functional couplings. Some applications
have demonstrated the feasibility and the benefits of ADT by eliminating couplings
to make the coupled design at least decoupled (Kim and Suh, 1991; Gabala and Suh,
1992). However, in practice, either the system is usually not as simple as those
examples or the coupling is indivisible in real world (such as to increase friction and
to reduce energy loss ). Some studies have shown that there are many
implementation limitations and practical considerations that prevent designers from
following ADT completely (Chen et al, 1994; Bi and Zhang, 2001).
In previous work (Suh, 2005; Lee, 2006; Benavides, 2011), some methods have
been suggested to strategically order the execution (i.e., implementation) sequence
of FRs-DPs pairs to reduce the imaginary complexity of design concepts. But these
6
existing methods are generally hard to apply in design practices due to their inherent
limitations and/or many real-world restrictions. As a result, although there are design
theories and sequencing methods that can suggest how to obtain idealized design
concepts in theory, most real-world designs are still “not ideal” (i.e., still having
some relative complexities due to FR-DP couplings), and therefore can (and should)
be improved by better ordering the FRs-DPs sequences.
To managing functional couplings in practice, module-by-function is commonly
used (Ulrich and Eppinger, 2004). The benefits of the modularity include the
flexibility in function management and the feasibility of physical component change
as well as the cost reduction such as time, labor, and design cycle costs (Gershenson
et al, 2003). Nevertheless, modular design is feasible in practice but not ideal in
theory— i.e., the relative complexity of the design is usually overlooked. Although
Jung (2017) proposed a new clustering method using Design Structure Matrix (DSM)
and modularity indices to examine the physical interactions between each DPs, the
issue of the functional coupling remains unresolved.
Based on the IDT framework and motivated by the modular design, this thesis
research developed the Design Coupling Sequence (DCS) approach, to strategically
manage functional coupling sequences with functional sets. By using DCS strategies
during conceptual design, ADT is bridged to modular design to help improve the
relative complexity with functional sets in order to assist designers to create the
design practically as ideal as possible.
7
1.2 Research Objectives
Based on the background and motivations discussed in Section 1.1, the main
goal of this research is to develop a theoretically sound practical approach to reduce
relative complexity on one hand and to increase modularity on the other hand in the
conceptual design stage. In order to achieve the goal, a set of objectives in the
research are listed as following:
For the complexity reduction, 1) the structure of the functional coupling
relationship between FRs and DPs (i.e. the design matrix) and the sequencing
methods were studied; 2) the algorithm to arrange DPs into (an) execution
sequence(s) for any design case with known design matrix was developed. For the
modularity enhancement, 1) the similarity and compatibility between conceptual
design and modular design were investigated; 2) the functional sets were defined
and the strategies of using those functional sets as the execution sequence in various
design scenarios were proposed and validated. For the usability enhancement of the
DCS approach, a software program was developed to implement DCS algorithm by
computer.
1.3 Scope of works
Although this research approach (i.e. DCS) is able to handle any design case, its
application scope is limited to the followings:
The availability of a design matrix. Building the sequence from the DCS
method requires a design matrix that clearly indicates dependency
relationships between FRs and DPs. This design matrix can be the direct
8
result from the conceptual design stage if designers follow the ADT process
carefully. Otherwise, it must be reconstructed (or reengineered) from an
existing artifact previously designed by other methods. Such an
reengineering task is often difficult and time-consuming.
The meaninglessness of the DCS sequences. The execution sequence is
obvious for the fully-coupled, the fully-decoupled, and the uncoupled
designs. For the fully-coupled design, the sequence is impossible because
there is no acceptable sequence to be found as each FR is satisfied by all
DPs. For the fully-decoupled design, the sequence is self-evident because
there is only one acceptable sequence, which follows the order of DP
corresponding to the triangular design matrix. For the uncoupled design, the
sequence is unnecessary because the sequence can be any order of DP as
each FR is only satisfied by one DP. Although the DCS method is able to
represent these extreme design cases, the solutions become unnecessary.
1.4 Dissertation Organization
This dissertation consists of seven chapters that are organized as following:
Chapter 2. Background
Chapter 2 introduces the related works including four topics and one issue.
The four topics are 1) conceptual design, 2) modular design, 3) design
complexity, and 4) sequencing algorithm. The issue is talking about the
challenges that designers may face on when working with design matrix
directly for obtain the execution sequence.
9
Chapter 3. Research Foundations
The research assumptions, hypotheses, and foundations are presented in this
chapter. With the hypothesis of generality, DCS should be applicable for
any design cases. With the hypothesis of uniqueness, DCS should manage
functional coupled design into the execution sequences of DP by functional
sets. In the research foundations, the ‘precedence’ and ‘functional sets’ were
defined in DCS to manage the coupled design concepts in order to support
the modularity of the design concepts.
Chapter 4. The Approach: Design Coupling Sequence
Basing on the foundations, the representation, the algorithm logic, and
procedures were illustrated in this chapter. The strategies for different
concept improvement tasks are also elaborated in this chapter.
Chapter 5. The Software Implementation
A DM-DCS converter was generated according to the DCS algorithm; the
system functions, architecture, user interfaces, and software demonstration
are presented in Chapter 5. It helps examine the DCS algorithm for the
validation of the generality hypothesis and obtain the DCS sequences by the
automated procedures with the user friendly designs under the Windows OS.
Chapter 6. Case Studies for DCS Validations
The applications of the DCS approach in four design cases are presented in
this chapter for validating the foundation, hypothesis, algorithm and its
feasibility and capability of the DCS method in different design manners:
one simple design improvement case, two reengineering design cases, and
an extended application.
10
Chapter 7. Summary, Contributions, and Future Works
Chapter 7 concludes the research with a summary of our current results. The
contributions of this research and its future works are also presented in this
chapter.
11
Chapter 2. Background
2.1 Background for Conceptual Design
Conceptual design is commonly understood as an early stage design activity
before the detailed technical design (Blanchard and Fabrycky, 1990; Hsu and Woon,
1998; Wang et al., 2002). It is the transformation stage between market requirements
(i.e., the design objective) and technical specifications of artifacts being developed.
However, in different design theories, there are different definitions of conceptual
design. Ulrich and Seering (1988) stated that it is a process from the functional or
behavioral requirements to the structural descriptions or concepts. Finger and Dixon
(1989) regarded that it commences with the functional requirements and proceeds
with the physical embodiment or configuration. Pahl and Beitz (1996) understood
that it begins with functions, and then forms a working principle structure. McNeill
et al. (1998) indicated that it starts from high-level descriptions of requirements and
ends with a high-level description of a solution. In Suh’s ADT (2001), it is described
as a mapping (i.e., decision-making) process from the functional requirements (FRs)
in the functional domain to the design parameters (DPs) in the physical domain. In
Innovative Design Thinking (IDT) (Liu and Lu, 2014; Wang and Lu, 2014),
conceptual design is also described as the mapping process from FR to DP.
In general, conceptual design can be described by an IDEF0 model with an input
of functional requirements in the function domain, and then an output of design
concepts (or parameters, proposed solutions) in the physical domain (Figure 2.1). In
this research, the definition of conceptual design basically follows the definition of
12
ADT and IDT as the basic design foundations used here are based on these two.
According to IDT, there are the concept generation phase and concept improvement
phase in conceptual design. The concept generation phase is a top-down process to
generate DPs from FRs with logical reasonings. The concept improvement phase is
a back-forth process to improve the DPs according to the relationship between FRs
and DPs (Figure 2.2).
Figure 2.1 IDEF0 Model of Conceptual Design.
Figure 2.2 Two Phases in Conceptual Design Stage.
For the concept generation phase, the two relevant theories, ADT and IDT, are
introduced in Section 2.1.1 to Section 2.1.2. These sections focus on the concept
generation process and what they suggest to lead to the ideal/good enough design
concept for a new product development.
13
For the concept improvement phase, the premise of moving into this phase is
that the designer has design concepts. The design concepts are either from the
concept generation phase or from reengineering. The basic information of
reengineering is introduced in Section 2.1.3 to realize how the relationship between
FRs and DPs is obtained.
2.1.1 Axiomatic Design Theory
ADT developed by Suh (1990, 2001) has several features: the domain structure,
the zigzagging process, the design matrix, and the two axioms (the Independence
Axiom and the Information Axiom).
The notion of “domain” in ADT refers to the different types of design decisions
in a design space (Suh, 2001). For the design of physical artifacts, Suh classified all
decisions in the design space into four different domains: the customer domain, the
functional domain, the physical domain, and the process domain. A typical
engineering design process starts from the customer needs (CNs) in the customer
domain at the upstream (i.e., the market), followed by choosing the functional
requirements (FRs) in the functional domain to satisfy CNs. And then after the
conceptual design process, the design parameters (DPs) in the physical domain are
generated to satisfy FRs. Finally, the process variables (PVs) in the process domain
are specified during parametric design (or called technical design) to realize DPs and
guide the product manufacturing process (Figure 2.3).
14
Figure 2.3 Four Domains in Axiomatic Design.
Suh especially discussed the stage from FRs to DPs, (i.e. the conceptual design
stage). Based on the FRs chosen by designers, multiple DPs are proposed in the
physical domain to satisfy FRs and describe parametric requirements of a proposed
design solution. Suh uses two separate “hierarchies” to manage the dependency
relationships between elements in FR and DP domains respectively. They indicate
the vertical inherent relationships of the FR and its sub-FRs which are in the upper
and lower “layers” within a hierarchy, and the horizontal mapping relationships of
the FRs (and sub-FRs) and their corresponding DPs (and sub-DPs) between two
hierarchies. They also show the zigzagging ideation process (Figure 2.4) that is used
to create the latter.
The zigzagging approach is the reasoning pattern of ADT conceptual design to
generate the FR and DP hierarchies by alternating between the function domain and
the physical domain (Figure 2.4). Simply put, the procedure is the iteration of the
ideation (“zig”) from the FR hierarchy to the DP hierarchy, and the decomposition
of FR into the next layer based on DP (“zag”) from the DP hierarchy back to the FR
CNs
.
.
.
FRs
.
.
.
DPs
.
.
.
PVs
.
.
.
Customer
Domain
Function
Domain
Physical
Domain
Process
Domain
15
hierarchy. DP as a solution to satisfy the same-layer FR, and the next-layer FRs are
the required functions of the upper-layer DP.
Figure 2.4 Zigzagging Reasoning Pattern in ADT.
The layer-by-layer zigzagging process in ADT is useful when a completely new
design concept is generated, for example, in an original design scenario. In this case,
ADT can create both the mapping architecture and the design parameters
simultaneously of a completely new design. It gives most rooms for design creativity
by experienced designers, but it is hard to follow in practice by typical engineers.
The two design axioms in ADT play the important roles in generating and
selecting FRs and DPs during the conceptual design stage. The first axiom is called
the Independence Axiom which suggests “maintain the independence of functional
requirements”, and the second axioms is called the Information Axiom, which
suggests “minimize information contents.” These decision-making rules (criteria)
16
are based on subjective “axioms” which Suh derived from his long design
experiences. To apply the Independence Axiom during conceptual design, the design
matrix (DM) is introduced to represent the dependency relationships between FRs
and DPs in two separate hierarchies. Also, the three types of the design matrix
represent different design concepts with different complexity levels of the design,
including coupled, decoupled, and uncoupled designs, are defined in ADT.
According to Axiomatic Design Theory (ADT), the design complexity is
defined as a measure of uncertainty in achieving specified functional requirements
(FRs), and the functional couplings, defined as the dependency relationships of FRs
between each design parameter (DP), can be depicted in the design matrix (DM). A
design without functional couplings (i.e., the minimal complexity) results in a
diagonal DM (Figure 2.5a), and the “off-diagonal” terms in a DM indicate the extra
functional couplings (or complexity) which must be reduced and/or managed (Figure
2.5b). In other words, a design concept comprises extra functional couplings when
more than one DP satisfies an FR. When those couplings exist, changing one DP
may consequently alter another DPs; causing difficulties in implementing this design
concept. The design complexity of changing DPs caused by extra functional
couplings is called the “real complexity,” which will be further explained in Section
2.3. Because of these functional couplings, unless designers are able to follow the
correct sequence to manage the design concepts, the resulted complexity would
make the iteration of concept improvement steps very difficult.
17
Figure 2.5 DM (a) with no functional coupling and (b) with a coupling term at DM21.
Suh (1995) defined three types of design in accordance with their design
complexity: uncoupled design, decoupled design, and coupled design (Figure 2.6).
In Figure 2.7, for example, the uncoupled design with a diagonal DM has zero design
complexity, with every FR having only a one-to-one mapping relationship with
every DP. The decoupled design, whose design matrix can be rearranged into a
triangular DM, has design complexity that can be minimized by only changing the
DPs in the specific order of the DP sequence depicted in the triangular DM. The
latter one is more complex than the former one. All other designs are coupled designs,
and the complexity can be infinite when the design involves a full DM.
Figure 2.6 (a) Uncoupled design, (b) decoupled design, and (c) coupled design.
Figure 2.7 Coupling types of design matrix and their complexity.
18
Suh (1995) explained that if the designer can follow the two ADT axioms
completely, then the design result should be an uncoupled design, and it is the
simplest design (i.e. the most ideal design). On the other hand, if the designer fails
to do so and ends up with a coupled design, then he or she needs to redesign by
proposing a different design concept (with a simpler FR-DP relationships). Suh
further indicated that there exists a special case, the design with either upper- or
lower- triangular matrix (i.e. the decoupled design), which is acceptable if the
designer specifies the DPs in a “sequence” strategically guided by the DM to yield
the minimum information content (i.e., satisfy the Information Axiom). The
sequence is so-called “execution sequence” talked through this dissertation. This is
because the execution of DPs in this order decouples the functional dependencies
between the DPs. For example, considering the lower-triangular matrix case in
Figure 2.8, the proper sequence of the execution order that yield the minimal design
complexity is DP
1
DP
2
DP
3
(it can be read directly from the DP sequence in the
triangular DM). This sequence motivates us to find the execution sequence for other
design types such as the coupled designs or the designs with numerical design matrix
because it would turn those designs into acceptable through concept improvement.
Figure 2.8 An Example DM of a Decoupled Design.
19
2.1.2 Innovative Design Thinking
Innovative Design Thinking (IDT) was developed by Lu based on theoretical
investigations in design theory, design cognition, logic reasoning, and collaborative
engineering (Lu et al., 2007; Lu and Liu, 2012, 2013). This design framework was
first introduced as a reasoning approach based on logic propositions (Liu and Lu,
2014), and then the detail of its reasoning pattern comparing with ADT and Analytic
Target Cascading (ATC) was presented (Wang and Lu, 2014). According to
experiment results to date, IDT has demonstrated its ability to enable the designer to
generate a logically feasible DPs to satisfy each FR by going through a structured
process and a systematic reasoning to support early stage engineering design (Liu
and Lu, 2014).
The IDT framework follows the theoretical foundations of ADT that uses the
domain and the layer representations in a hierarchical manner, but the reasoning
pattern is different from that of ADT. It is a hybrid reasoning pattern between ADT
and ATC.
Different from the reasoning process of ADT, that of ATC is more straight
forward. Kim, et al. (2001, 2003) introduced Analytic Target Cascading (ATC),
which is a methodology for the design of large and complex engineering systems at
the early product development stages. Together with optimization algorithms, this
approach is widely used in many engineering fields in parametric (or technical)
design of complex systems (Allison, 2004; Liu, 2006). In industrial practice,
however, ATC is not often used in the conceptual design stage when numerical
parameters are to be generated. Instead, it is most commonly used in design
20
improvement or redesign tasks of existing artifacts. Nevertheless, conceptually
speaking, ATC can be used in the conceptual design by interpreting the design
process as a “big-circle” reasoning pattern between FR and DP hierarchies, the circle
of decomposition ideation composition verification (Figure 2.9).
Specifically, designers decompose the given FR as much as possible to the detail
leaf-level of the FR hierarchy, and then ideates from the FR hierarchy to sub-DPs at
the leaf-level of the DP hierarchy, and finally composes the sub-DPs progressively
upward into the DP at the top layer, following by verifications that the resultant DP
indeed can satisfy the given FR. The decision making of the leaf-level DPs is the
key of ATC to improve the design, but the DPs are usually functionally coupled
because they are not required to satisfy the Independence Axiom of ADT. Therefore,
managing the functional coupling to reduce the design complexity in ATC is rather
difficult in practice. Nevertheless, the ATC decomposition-composition process can
aid designers to redesign or to improve concepts of an existing design with a known
architecture. However, it cannot yield a completely new design with a different
architecture.
Figure 2.9 The big-circle reasoning pattern in ATC.
21
Taking the advantages of both zigzagging across each layer as in ADT and a big
decomposition-and-composition cycle across multiple layers as in ATC into account,
IDT prescribes a fractal co-evolution pattern, which can be viewed as a hybrid
between ADT and ATC (Figure 2.10).
Figure 2.10 The fractal co-evolution reasoning pattern in IDT.
Each pair of the FR-DP triad in the hierarchies is constructed by the process
shown in Figure 2.11, and this “circle-like” process is the same as the process in
ATC (decomposition ideation composition verification). However, unlike
ATC which constructs an FR hierarchy first and then constructing a DP hierarchy,
the IDT process is carried out by zigzagging these coevolving pairs of FR-DP triads
into progressively more detailed pairs of layers. Designers can iterates this way to
get a dual-hierarchical structure with further details until the design resources (such
as time) is exhausted. Because the IDT reasoning is a hybrid between ADT (for the
most creative new designs) and ATC (for the most routine redesigns), it is more
22
useful in industrial practices when typical design tasks are in between these two
extreme situations.
Figure 2.11 A pair of FR-DP triads.
As with the two design Axioms in ADT, the concepts are recommended but not
strictly required (or forced) to be independent and/or with minimal information
content in IDT. Therefore, the “execution sequence” introduced in ADT can also be
used in IDT during concept improvement.
Previously, the IDT framework has prescribed three consecutive steps: (1)
following the top-down process to ideate new design concepts that satisfy the
principles/axioms suggested by the design theory to reach a certain layer of details,
(2) following the bottom-up process to identify some existing design modules from
available engineering database (or catalogs) that can satisfy the functional
requirements at this detail layer, and (3) constructing the design matrix that shows
the couplings between FRs and DPs at this detail layer. In this research, the fourth
step of IDT: (4) apply the DCS algorithm to determine the execution sequence of
DPs based on the above design matrix was further developed to complete the
framework in the goal of bringing the conceptual design within both the (ideally)
top-down and (practically) bottom-up manner. This will yield a new design concept
with an execution sequence that is most creative (because it satisfies the design
23
principles at the top layers) and most practical (because it utilizes the existing
modules at the bottom layers).
2.1.3 Reengineering for Concept Improvement
Re-engineering in design is to examine the finished product and build a better
one. As shown in Figure 2.12, there are two major phases in re-engineering: reverse
engineering and forward engineering (Chikofsky and Cross, 1990). Reverse
engineering is a process of analyzing the finished product including identifying the
system’s components and their interrelationships and creating representations of the
system (from downstream to upstream). Forward engineering is a process from the
high-level abstractions to the physical design and then to the design implementation
(from upstream to downstream). Therefore, implementing reengineering in
conceptual design is exactly in the concept improvement phase where the reverse
engineering from a finished product is backward and the forward engineering with
the known system structure is forward referred to Figure 2.2.
Figure 2.12 Reengineering.
24
During reverse engineering, matrix is commonly used to representing the
interrelationships of the system components such as Design Structure Matrix (DSM)
(Bartolomei, et al., 2007), or Domain Mapping Matrix (DMM) (Danilovic and
Brown, 2007). DSM is a square matrix capturing dependency relationships between
system elements of the same kind within a single domain, whereas DMM is a
rectangular matrix representing dependency relationships between system elements
of different kinds in two different domains. For example, the matrix at the “roof” in
the “house of quality (HoQ)” representing the relationships between the “HOWs”
themselves is a kind of DSM, and the matrix at the “living room” in the HoQ
representing the relationships between “WHATs” and “HOWs” is a kind of DMM
(Figure 2.13). The design matrix (DM) of ADT is a kind of DMM that depicts the
dependency relationships between FRs and DPs. In this research, the DM is taken as
the input of the DCS algorithm to further extract the information of functional
couplings in the terms of functional sets so that designers can obtain the execution
sequence to improve the design concept with minimal real complexity.
Figure 2.13 The DSM and DMM in HoQ.
25
2.1.4 Challenges of Applying Design Theory in Practice
Some studies have shown that there are many implementation limitations and
practical considerations that prevent designers from following ADT completely,
although they all admitted that it is better if one could apply ADT completely (Chen
et al, 1994; Bi and Zhang, 2001). Chen et al. pointed out that the relationship between
FR and DP becomes difficult to track when the system is complex. Bi and Zhang
found out that the FR and DP numbers are usually different in reengineered design
cases so that applying ADT would be challenged.
Similar challenges were shown in some design exercises with engineering
students. While teaching design theories to engineering students in the graduate-
level course for many years, the authors have found out that it is very difficult for
people to follow the Independence Axiom to decompose FRs and DPs all the way
down to the bottom layer even the people have engineering background. It appeared
in many design results from the design exercises that the design looked like
uncoupled when it was decomposed at the abstract layers (such as layer 1 and layer
2; it depends on the system scale as well as how it is decomposed), but the functional
couplings revealed in the lower layers corresponding to the coupled relationship in
the upper layers (Figure 2.14), or vice versa (Figure 2.15). Besides, in many cases,
the numbers of FR and DP are hardly to be equal, and it is also difficult to decompose
till very end by following the complete, minimal, and independent principles (Figure
2.16).
26
Figure 2.14 Two examples of more functional couplings at the lower layer.
Figure 2.15 Two examples of more functional couplings at the upper layer.
Figure 2.16 Two examples of unequal numbers of FR and DP.
27
As a short conclusion in this section, ADT is ideal but only the designer who is
smart enough and has sufficient knowledge and experiences on the subject is able to
really follow the process. For the practical design cases, a strategic approach to
implement design theories is needed.
2.2 Background for Modular Design
Modular design is a design method that is widely used for complex systems.
Although it has many advantages in the practical cases, it is rarely to be near ideal
(i.e. uncoupled or decoupled design) because and the real complexity (caused by
functional couplings) is usually overlooked.
2.2.1 The Definition of Module
There are various definitions of a module (Gershenson, 2003), but it is generally
regarded as a collection or a set of components that are independent or isolated from
others in the system. The less interactions between the set and other components, the
higher modularity of the set is. In modular design, there are three types of modules
in general- function module, physical module, and process module. Function module
is a set of components that grouped by function. Similarly, physical module is a set
of components that physically independent from others. The process module is a set
of components that is supposed to manufacture each component in the same process.
By mapping to the design process, in the conceptual design stage, the interaction can
be regarded as functional coupling as the relationship between FR and DP. Also,
since the geometry of the product hasn’t been defined yet in conceptual design stage,
to group the module by its function is the most appropriate and the most important
way when applying modular design method in conceptual design stage.
28
2.2.2 Representation of Modules
There are several presentations for modules as long as it separates the parts in
groups. As it is defined as a “set,” it would be represented by the symbol of braces,
{}, or a circle in a diagram in mathematics. In software design, block grouping such
as the component diagram or the class in object-oriented program (OOP). In
conceptual design, clusters in DSM, blocks, and hierarchies are commonly used
(Jung, 2017; Bi and Zhang, 2001). In this dissertation, we use “U-set” and “C-set”
to name different types of the group of DPs, and the C-set is represented in braces
and the U-set is linked by arrows.
2.2.3 The Benefits of Modularity
Basically, the benefits of modularity are the flexibility in function management,
and the feasibility of physical component change as well as the cost reduction such
as time, labor, and design cycle costs (Gershenson et al, 2003). Besides, when doing
design with modules, designer can look up the module database, which contains a
lot of empirical well-designed or good modules, so designer could save time to
repeat the design iterations. Therefore, practically, modular design is useful,
although the design results could not be ideal. In stead of giving up the design theory,
applying theoretical strategies to make the design as ideal as possible with modules
would be feasible and better.
2.2.4 The Challenge of Modularity
Modularity in conceptual design within ADT is challenged. For one hand, it is
hard to apply ADT for modularity to get a complete uncoupled design (i.e. ideal
design). Since there are ‘functional coupling,’ the design complexity is carried out.
29
For the other hand, when doing decomposition to create functionally independent
DPs, it is sometimes difficult to dissect components by functions which results that
some components overlapped in different modules (Yu et al, 2007; Helmer et al,
2010). Because overlapped using the same component for different function
purposes, there are functional couplings between the modules. As stated before, the
functional coupling is usually overlooked, so managing functional couplings from
the perspective of modularity to reduce the design complexity could be the key to
combine ADT and modular design.
2.3 Background for Design Complexity
The complexity of a design concept is determined by many factors, some of
which, such as the complication of chosen objectives and the degree of given
constraints (Pahl et al., 2007), are beyond the control of designers, while others are
the direct consequence of their decisions made during conceptual design. The former
is called “inborn complexity” and the latter is named as “acquired complexity” (Lu
and Suh, 2009). It is especially important to strategically reduce the acquired
complexity in the early design stage because the acquired complexity can be
accumulated during design procedures.
In this research, the design complexity indicates the relative complexity
including real and imaginary complexities defined by Suh (2005).
2.3.1 Time-Independent Design Complexities
Suh (2005) categorized the acquired complexity into four types—real
complexity, imaginary complexity, combinatorial complexity, and periodical
30
complexity. The real and imaginary complexities are independent of time, whereas
the combinatorial and periodical complexities are time dependent (Table 2.1). Our
research focuses on the real and imaginary complexities.
The real complexity occurs when the designed systems do not satisfy targeted
functional requirements at all times. The desired target with the tolerance range
of achieving the functional requirements is the design range, and the uncertainty
in achieving functional requirements is represented by the system range. It can
be eliminated by bringing the system ranges back to the targeted design ranges,
or by redesigning the system to become functionally uncoupled or decoupled
according to the Axiomatic Design theory. If the DM of the design can be
rearranged into a triangular DM, the real complexity can be minimized by
shifting the system range of each DP to the design range in the sequence given
by its DM. In fact, such a sequence is what our research is seeking for.
The imaginary complexity occurs when design concepts appear to be
functionally coupled due to a lack of understanding of the system structure (i.e.,
the design matrix). It can be quantified in the formula (1) according to ADT
C
𝐼 = −𝑙𝑜𝑔 2
(
𝑧 𝑚 !
) (1)
where z is the number of acceptable sequences in carry out m design tasks, and
m! is the total number of sequences for the design with a m×m design matrix. It
can be reduced by increasing the z value such as eliminating coupling concepts
or by knowing the execution sequence such as satisfying multiple functional
requirements explicit in his/her design documentations in the correct sequence.
Therefore, the goal of our research is seeking to find the acceptable sequences
31
as many as possible of any type of design that leads to the largest value of z to
minimize the imaginary complexity of design concepts without changing the
fundamental design.
Table 2.1 Time-Independent design complexity.
Real Complexity Imaginary Complexity
Uncoupled,
Multiple FRs (or single FR)
Designed systems do not
satisfy the FR at all times
Non-exist
Decoupled,
Multiple FRs Lack of understanding of the
system Coupled,
Multiple FRs
2.3.2 Design Matrix and Functional Coupling
As elaborated in Section 2.1.1, there are three typical types of DM that represent
different level of relative complexity. The uncoupled design has zero complexity, the
completely coupled design has a hundred percent complexity, and the complexity of
the decoupled design whose DM can be rearrange into triangular DM can be
minimized by the execution sequence. The off-diagonal terms are those non-zero
terms which is not in the diagonal. They were suggested to eliminated to minimize
the complexity, but the DCS research focuses on sequencing rather than simply
eliminating the off-diagonal term.
2.4 Background for Sequencing Algorithm
In order to develop the algorithm to find the execution sequence, the complexity
reduction methods were studied. Traditionally, the design is simplest (i.e. ideal)
32
when it is an uncoupled design, so it is unnecessary to reduce the complexity; it is
too complex to improve when the design is a coupled design; and it is acceptable
when the design is a decoupled design, and by following the order of DP in the
triangular DM the design complexity can be minimized. Other than these three types,
it is called partially coupled design. For those partially coupled design, elimination,
rearrangement, and sequence are the three major ways to reduce the complexity.
2.4.1 The Execution Sequence
As mentioned in Section 2.1.1, “Execution Sequence” is defined as a sequence
of DP that shows the “decoupling” order, which implies that following the order lead
to minimum complexity. So, if the designer follows the order to implement concept
decisions in conceptual design, that order is the execution sequence.
2.4.2 Complexity Reduction Framework
For the design which is not one of the typical designs (and this kind of design is
more common in fact), Suh suggested rearrangement to be more triangular, and then
elimination of the off-triangular terms, so then to obtain the sequence to decide the
design.
Arranging those methods into a framework, the roadmap shown in Figure 2.17
displays the prescription of the complexity reduction process including three major
reduction methods: rearrangement, elimination, and sequencing. When the design
matrix is not clear to show the design type, the DM rearrangement involves the
design case to obtain the most triangular DM for the execution sequence. When the
design is rearranged well but the extra functional couplings are still there, the
elimination involves removing the coupling so then reduce the complexity. For the
33
research approach, when the DM is none of the typical types, execution sequence
can be obtained by applying the DCS algorithm.
To describe the procedure in detail, as shown in Figure 2.17, the complexity
reduction framework starts from a DM generated from a new conceptual design or
reengineered from an existing product. If the DM is a diagonal DM (i.e. uncouple
design), then the design is already ideal. If not, with the DM, designers can employ
one of the following improvement strategies: (A) redesign, (B) rearrange DM into
the most triangular or the most diagonal DM, or (C) sequence the decoupling orders.
The strategy (A) is usually chosen when the design fails or is fully coupled. Then
the total redesign process is back to the previous step of concept generation with the
given FRs. In this situation, the designer is suggested to carefully follow one of the
conceptual design approaches such as ADT and IDT to generate a design with less
functional couplings. The strategy (B) is usually chosen when the design type is
unable to be identified quickly. Consequently, the execution sequence would be
obtained if the rearranged DM is triangular. If not, the process of eliminating off-
diagonal terms would be applied so then the execution sequence could be obtained
after the elimination. The strategy (C) is usually chosen when the DM is already
triangular. In addition, our approach provides an additional opportunity to choose
the strategy (C) even if the design type is unknown, and/or the fundamental change
of the original design is not allowed.
To further examine the framework, the design tasks all end up at execution
sequence. This means to obtain the execution directly is a more efficient way for
implementing complexity reduction.
34
Figure 2.17 The roadmap of complexity reduction framework.
2.4.3 Suh’s DM Rearrangement
The Suh’s Design Matrix Rearrangement (2005), in general, is a method moving
rows and columns by following specific rules. The result is an organized “triangular-
like” DM with reduced design complexity. It includes five steps:
1) Find a row which has only one non-zero element.
2) Rearrange the orders of FRs and DPs by moving the row and the column which
contain the non-zero element first.
3) Excluding the first row and column, then find the row which contains one non-
zero element.
35
4) Rearrange the components of FRs and DPs by moving the row and column which
contain the non-zero element second.
5) Repeat the above procedure until there are no more submatrices to analyze further.
An example of the Suh’s design matrix rearrangement method is shown in
Figure 2.18. As the result demonstrates, the design in the example becomes a
decoupled design, which was not obvious judging from the original design matrix.
According to ADT, the designer can follow the order of DP
2
DP
4
DP
1
DP
4
(i.e.
the sequence of DP given in the resulted triangular DM) to improve the design with
the minimal real complexity. In addition, here in the example, the acceptable
sequence is only one (i.e. z=1, refer to Equation 1). The imaginary complexity C
I
of
this design is about 4.58 (= -log
2
(1/4!)). However, if the sequence is unknown, C
I
would be infinity due to z is 0 (C
I
= -log
2
(0/4!) = -log
2
0 = infinity).
Figure 2.18 An Example of the Implementation of the Suh’s Method.
Suh’s method works well when there are a few non-zero terms in each row of
the given design matrix; but it has possibilities of not finding the best rearrangement
36
(Suh, 2005). Besides, the given design matrix should be square for this method to
work at all. If the DM is not square, it requires the designer being knowledgeable
enough to pick up certain FRs and DPs from the original DM (i.e., forming square
matrices) to apply this method (Suh, 2005).
2.4.4 Benavides’ Extended Algorithm
The Extended Algorithm (EA) by Benavides (2011) is a halfway between Suh’s
and Lee’s methods. It works well for large and strongly coupled design matrices,
and can find the most triangular and most diagonal matrix. It can deal with
rectangular matrices, and the main diagonal terms of a square matrix can be zero.
This method is divided into two phases:
Phase 1. Rearranges the given design matrix to obtain the most triangular one,
and
Phase 2. For rectangular matrices, it selects the best DPs or FRs to be eliminated
and obtains the most diagonal matrix.
In other words, the design matrix can be reorganized into the most triangular matrix
by the method in Phase 1, but only the rectangular matrix can be rearranged into the
most diagonal matrix by eliminated some terms using the method in Phase 2. The
steps are as followed:
Phase 1 (Figure 2.19):
1) Find the row with the minimum number of non-zero elements.
2) Extract the associated columns of the row, and calculate the numbers of the non-
zero terms of their lower parts. Among the columns selected above, take one with
the greatest value.
37
3) If there are more than one columns with the greatest value, calculate the numbers
of the non-zero terms of their upper parts. Among the columns selected above,
take the one with the lowest value.
4) Put the row and the column first in the matrix.
5) Excluding the first row and column, repeat the above steps 1 to 4 over the
resultant sub-matrix until there are no more submatrices to be analyzed.
Phase 2 (Figure 2.20):
1) Check if one of the extra columns can reduce the non-zero term number at the
lower part of any column that belongs to the square part of the matrix.
2) Permute columns that fulfill the anterior condition.
Figure 2.19 An Example of the Implementation of the EA’s Phase 1.
Figure 2.20 An Example of the Implementation of the EA’s Phase 2.
38
EA makes the rearrangement of the design matrix more possible to be used in
the concept improvement for the existing products. However, EA is not an optimal
method because the rearrangement results may not be the most triangular one. For
example, there are only two off-diagonal terms in Figure 2.21c, but there are three
off-diagonal terms in Figure 2.21b. Besides, EA only suggests the elimination of the
coupling concepts, and it doesn’t provide any alternatives if the elimination is not
allowed.
a) The original DM (b) Arranged DM by EA (c) Arranged DM by Optimal Strategy
Figure 2.21 An evidence of showing EA is not an optimal method.
2.4.5 Lee’s Optimal Strategy
Lee (2006) introduced the optimal strategy of eliminating off-diagonal terms in
DM to manage the functional couplings. Lee uses adjacency matrix, incidence
matrix, and the cycle matrix to find the “cycles” of dependencies, which are the extra
off-diagonal terms after matrix rearrangement, and then suggests to eliminate them.
The processes of making those matrices were developed based on the Graph Theory
(Figure 2.22). It can be simply summarized in the four steps:
1) Construct the Adjacency Matrix A from the original matrix, DM
i,j
where A =
DM
T
-I, and draw a digraph according to the elements in A to determine the extent
of coupling.
39
2) If there are cycles in the digraph, construct an Incidence Matrix B from the
digraph. It follows the rules:
If the corresponded arrow j of the off-diagonal term in the digraph is directed
away from the pair of FR
i
-DP
i
, B(i,j) = 1; if it is directed towards from the pair
of FR
i
-DP
i
, B(i,j) = -1; otherwise, B(i,j) = 0.
3) Construct the Cycle Matrix C by following the below rules:
If cycle Z
i
of the digraph contains arc j directed in the same way as the orientation
of Z
i
, C(i,j) = 1; if it is opposite way, C(i,j) = -1; otherwise, C(i,j) = 0.
4) Determine terms that can be eliminated:
a) Search the combinations of the columns to find the 1st set of columns with
non-zero entries when summed up
b) Combination of columns found in the previous step indicates the minimum
set of off-diagonal terms that can decouple the design matrix DM
i,j
Figure 2.22 An Example of the Implementation of the Lee’s Method.
Although it is the “optimal” strategy for eliminating coupling terms from a given
design matrix, Lee’s method will fail when the design matrix is rectangular or square
with 0 on its main diagonal (Lee, 2006). In addition, it doesn’t provide the strategy
for the situation when the designer is unable to eliminate the coupling terms.
40
2.4.6 Limitations of the above methods
There are many limitations in the above three algorithms. For the Suh’s and the
Lee’s algorithm, the square matrix is a premise. The Lee’s method even requires all
the terms on diagonal are non-zero. Also, Lee’s method is using a complex method
to reduce the design complexity, so it would not be useful. For the EA method, it is
not optimal although it can be applied to the design case with rectangular DM. Those
methods all suggest elimination rather than directly solve it under current situation.
In addition to the limitations of the methods, we also need to emphasize that there
are also many challenges of working with the process of DM rearrangement to the
elimination then obtain the execution sequence. These are presented in Section 2.5.
2.5 Challenges of Working with DM Directly
The DM captures the functional coupling information between DPs, but there
are two challenges when designers try to find the execution sequence via DM: 1) the
matrix rearrangement is complicated; 2) the execution sequence is not always
accurate.
2.5.1 Difficulties of rearranging DM directly
The DM rearrangement is generally difficult, and designers cannot easily judge
the type of the design until the DM is well-organized (i.e. the most triangular or the
most diagonal). For example, even as simple as a 4-by-4 matrix shown in Figure
2.23, the designer may mistakenly judge the design as a coupled design at the first
glance because the designer is unclear of how to rearrange it into a triangular matrix.
41
In fact, this concept is a decoupled design if the designer is able to rearrange the
order of the FRs and DPs. Without using the methods of DM rearrangement, the
designer often must rely on try-and-error to rearrange the matrix and then find the
sequence for decoupling. Even if the designer can rearrange the matrix like that
demonstrates in Figure 2.24 without any mistake, it is still rather complicated when
he/she tries to implement such a matrix rearrangement to achieve a triangular one.
[
𝐹𝑅
1
𝐹𝑅
2
𝐹𝑅
3
𝐹𝑅
4
]=[
𝑋 𝑋 𝑂 𝑋 𝑂 𝑋 𝑂 𝑂 𝑋 𝑋 𝑂 𝑋 𝑋 𝑋 𝑂 𝑋 ][
𝐷𝑃
1
𝐷𝑃
2
𝐷𝑃
3
𝐷𝑃
4
]
Figure 2.23 A 4x4 design matrix.
Figure 2.24 A possible process of DM rearrangement for a decoupled design case.
By applying Lee’s optimal strategy, the designer can only know it is a decoupled
design because there is no loop in the graph extracted from the adjacency matrix.
Furthermore, the designer still need to rearrange the matrix by himself/herself in
order to find the execution sequence. By applying Suh’s or EA method, the designer
can obtain a triangular-like DM, but the process requires a lot of matrix drawing,
and the designer may get lost easily.
42
The difficulty increases exponentially when the DM becomes larger. For
example, in case of a larger DM such as 9-by-9 (Figure 2.25), the task of matrix
rearrangement becomes very time-consuming and complicated as shown in Figure
2.26. It requires many times of the risky decision-making when the number of the
non-zero elements are the same in the different rows. Like the problem illustrated in
the Benavides’ paper (2011), the Suh’s and Benavides’ methods are not optimal. If
the result is not a perfect triangular matrix, the designer may need to trace back to
see whether another row with the same number of the non-zero element should be
picked at that time, and tries it again and again until a triangular DM is obtained or
all the possible options are exhausted to make sure that it is a coupled design.
Unfortunately, there’s no strategy to obtain the execution sequence in the existing
methods if the result shows that it is a coupled design— the only strategy suggested
by the existing methods is to redo the whole design or to eliminate all the off-
triangular DPs to obtain the execution sequence. Like the result in Figure 2.26, after
trying all the possible options, the designer could conclude that it is a coupled design.
This means that the designer should have tried 96 (2*2*3*2*2*2 = 96) times before
concluding “redesign” or “elimination” strategy.
[
𝐹𝑅
11
𝐹𝑅
12
𝐹𝑅
13
𝐹𝑅
21
𝐹𝑅
22
𝐹𝑅
23
𝐹𝑅
31
𝐹𝑅
32
𝐹𝑅
33
]
=
[
𝑋 𝑂 𝑂 𝑂 𝑋 𝑂 𝑂 𝑂 𝑋 𝑂 𝑋 𝑂 𝑂 𝑋 𝑂 𝑂 𝑂 𝑂 𝑋 𝑂 𝑂 𝑂 𝑂 𝑂 𝑂 𝑋 𝑂 𝑂 𝑋 𝑂 𝑂 𝑂 𝑂 𝑋 𝑋 𝑂 𝑋 𝑋 𝑂 𝑂 𝑋 𝑂 𝑂 𝑂 𝑋 𝑂 𝑂 𝑂 𝑂 𝑂 𝑂 𝑂 𝑂 𝑂 𝑂 𝑋 𝑂 𝑂 𝑂 𝑋 𝑂 𝑂 𝑂 𝑂 𝑋 𝑂 𝑂 𝑂 𝑂 𝑂 𝑂 𝑂 𝑋 𝑂 𝑂 𝑂 𝑋 𝑂 𝑂 𝑂 𝑋 ]
[
𝐷𝑃
11
𝐷𝑃
12
𝐷𝑃
13
𝐷𝑃
21
𝐷𝑃
22
𝐷𝑃
23
𝐷𝑃
31
𝐷𝑃
32
𝐷𝑃
33
]
Figure 2.25 A 9x9 Design Matrix.
43
Figure 2.26 The 9x9 DM rearrangement by Suh’s method.
44
A better way is to apply Lee’s optimal strategy after the result of applying Suh’s
or EA method is not a perfect triangular DM, but still, there’s no way to obtain the
execution sequence unless the designer eliminates all the coupling DPs. Even after
getting the execution sequence via the well-organized DM, the designer still needs
to follow the sequence carefully to adjust the DPs to reach the minimal information
point (i.e., with the minimal complexity). Therefore, the DM rearrangement is
complicated, and it requires the designer to be a “smart” or “lucky” decision maker
because there is no straight way in the existing methods to lead the designer to obtain
the execution sequence.
Moreover, when the DM is rectangular, there is no strategy of obtaining the
execution sequence directly in the existing method. Although the EA method
provides the strategy for handling the rectangular DM, it is only for the DM
rearrangement, not sequencing. As a result, when the designer follows the EA
method to obtain an organized rectangular DM, he/she still needs to eliminate the
DPs which are outside of the square part to obtain a square matrix and execution
sequence. Hence, it is not useful to use DM rearrangement methods to obtain the
execution sequence.
2.5.2 Execution Sequence for Coupled Design
DM Rearrangement is complicated, but the trouble in obtaining the sequence
from a rearranged DM may be even bigger. The sequence is not always accurate.
Firstly, Suh (1999) stated that it is meaningless to find the execution sequences of
changing DPs for minimizing the design complexity for coupled design cases
45
because when one of the DPs is changed, the entire set of DPs must be taken into
consideration. Consequently, the existing methods suggest designers to give up
improving the part of the design and then completely redesign or to change the
fundamental design by eliminating the off-triangular DPs. These methods should
work well when the process of redoing the design is quick and easy or when the
elimination is acceptable and the amount of the off-triangular terms are less.
However, Suh’s statement is not always true. When one of the DPs is changed in a
coupled design, sometimes it only requires a part of DPs to be taken into
consideration. That is, a coupled design should have at least one meaningful
execution sequence. Using the DM in Figure 2.27 as an example, the system range
of the DP
1
and DP
2
can be determined sequentially for FR
1
and FR
2
. And then, the
remaining part of the design (i.e. DP
3
and DP
4
) could be considered as a module so
that one could obtain the execution sequence as “DP
1
DP
2
{DP
3
, DP
4
}.” In other
words, if the designer could adjust the system range of DP
3
and DP
4
to match the
design range for FR
3
and FR
4
, then the fundamental design won’t change but would
be improved.
[
𝐹𝑅
1
𝐹𝑅
2
𝐹𝑅
3
𝐹𝑅
4
]=[
𝑋 𝑂 𝑋 𝑋 𝑂 𝑂 𝑂 𝑂 𝑋 𝑋 𝑋 𝑋 𝑋 𝑋 𝑋 𝑋 ][
𝐷𝑃
1
𝐷𝑃
2
𝐷𝑃
3
𝐷𝑃
4
]
Figure 2.27 An example of coupled DM.
2.5.3 Sequence Reading Limitation from DM
There may be more than one acceptable sequence in a design. According to
Suh’s complexity theory, the imaginary complexity can be reduced if the acceptable
46
sequences increase. Unfortunately, there is always one sequence when the designer
obtains the sequence by using the order of DP in an organized DM. For example,
there are two acceptable sequences in the design shown in Figure 2.28. The designer
can obtain one of the sequences by reading from it as “DP
1
DP
2
DP
3
DP
4
.”
In fact, “DP
1
DP
2
DP
4
DP
3
” is also one of them because the DM remains
the same when the row 3 and 4 and column 3 and 4 are swapped. Another explanation
is that DP
4
doesn’t have to be decided after DP
3
because once DP
1
and DP
2
are
decided, DP
4
can be decided without knowing the DP
3
. In this case, the precedence
of the two are the same, so the best interpretation of the acceptable sequences should
be “DP
1
DP
2
DP
3
or DP
4
.” To reach the minimal imaginary complexity, all the
acceptable sequences should be found. Note that this example is quite simple, hence
the additional sequence is rather easy for the designer to notice. For a more complex
case, the task becomes more difficult. A clear strategy to resolve the similar cases is
required.
[
𝐹𝑅
1
𝐹𝑅
2
𝐹𝑅
3
𝐹𝑅
4
]=[
𝑋 𝑂 𝑋 𝑋 𝑂 𝑂 𝑂 𝑂 𝑋 𝑋 𝑋 𝑋 𝑋 𝑂 𝑂 𝑋 ][
𝐷𝑃
1
𝐷𝑃
2
𝐷𝑃
3
𝐷𝑃
4
]
Figure 2.28 Another design matrix example.
2.6 Summary of the Chapter
Conceptual design is an early design stage from functional requirement to
design parameters, and concept generation and concept improvement are the two
phases. In conceptual design, real and imaginary complexities are caused by the
functional couplings, which can be reduced by design matrix rearrangement,
47
coupling elimination, and execution sequence. There are many limitations in the
previous methods when implemented in practice. IDT provides a design framework
with the hybrid reasoning between ADT and ATC so that it could be applied in
practice. The dissertation research aims to extend the IDT framework to prescribe
functional coupling management strategies within execution sequences and
functional sets for matching module database, in order to bridge design theory to
support modularity for design practices.
48
Chapter 3. Research Foundations
Research foundations are elaborated in this chapter. It starts from the research
assumptions and two hypotheses to the foundations of the developed algorithm and
the concepts of “precedence” and “functional sets”.
3.1 Research Assumptions
According to conceptual design phases, the role of the research approach is
starting from the transition between the concept generation phase and concept
improvement phase. The research assumes that every design can be decomposed into
several DPs and can be traced back to several FRs. Also, the coupling relationship
between FRs and DPs can be accurately identified by the designer within a design
matrix (DM). In addition, it assumes that the impact of the physical geometry
interaction, material fabrication, and manufacturing process can be neglected in the
conceptual design stage.
3.2 Research Hypotheses
The hypotheses to be validated in our research are generality and uniqueness.
They are presented in the following sections.
3.2.1 Hypothesis I (H1): Generality
As there are many limitations mentioned in the chapter 2, the generality is one
of the major hypotheses of this research to seek out of the limitation boundary. It
states as
49
H1: the generality hypothesis:
The research approach is a general approach in any design case with DM.
The hypothesis includes
(1) The consistency of the typical design types. The research results is supposed
to be consistent with the results of uncoupled, decoupled, and coupled
designs in the design theory. The result of the uncoupled design in this
research should be concluded that the execution sequences are the sequence
of the DP in any order. The result of the decoupled design in this research
should be concluded as a sequence of DP by the order from the triangular
DM. The result of the complete coupled design should be concluded as no
execution sequence or the need of complete redesign.
(2) The existence of the execution sequence. There exists at least an execution
sequence in any design case with design matrix, and the execution sequence
can be obtained from the original DM without design matrix rearrangement
or design concept elimination.
(3) No matrix type limitations. The research algorithm can be applied to both
square and rectangular DM, both DM types with non-zero and zero at
diagonal, and both binary (i.e. Axiomatic Design Matrix annotated
relationship by ‘X’ and ‘O’) and numerical DM (i.e. the design matrix with
weighted values).
(4) The ability of DM rearrangement. Although the research approach is seeking
not to obtain the execution sequences through DM rearrangement, the
approach results are expected to rearrange DM to show the functional
schematics of the design.
50
3.2.2 Hypothesis II: Uniqueness
Several uniqueness features were hypothesized in this research. The overall
statement is as following
H2: the uniqueness hypothesis:
DCS can lead to a unique execution sequence of DPs that yields the least amount
of real and imaginary complexity with functional sets for a certain design.
The hypothesis includes
(1) The uniqueness of complexity reduction for coupled design. This is the first
execution sequence for the partially coupled design without concept
elimination.
(2) The uniqueness of functional sets and precedence for execution sequence.
This research approach defined the concept of precedence and two
functional sets for the execution sequence, which didn’t appear in any
previous studies on design matrix.
(3) The uniqueness of concept improvement strategies. The research identified
three common concept improvement scenarios and prescribed the strategies
for each scenario. In the past, the concept improvement tasks in design
theories were focused on concept refinement to approach the ideal design.
In practice, the concept improvement tasks would be assigned with some
conditions. For those design tasks, designers require not only knowing the
execution sequence but also having a strategic way to implement the
sequence.
51
Therefore, the research approach was developed based on the following
foundations: Sequencing algorithm and functional sets.
3.3 Observation and Foundations for Execution Sequence
Based on the assumptions and hypotheses, the following previous methods were
investigated. The DCS algorithm was then developed according to the following
foundations: “precedence” and “functional sets”.
3.3.1 The Solution by Linear Algebra
The execution sequence in the decoupled design case can be seen as the
executive linear equation solution order (Figure 3.1). In some simple design cases,
one can simply apply the solution way either with augmented matrix or elimination
by substitution to obtain the execution sequence. However, in most design cases, the
result of the execution sequence appears unclear or unsolvable. The unclear result
would be the system is rather large or multiple objectives, and the unsolvable result
would be unequal number of FR and DP or linear dependent (i.e. multiple couplings).
Figure 3.1 Linear equation solving sequence.
Although the equation solving sequence can’t be obtained directly, some rules
for executive priority can be observed from linear algebra: the most engaged
parameter (the most functionally coupled DP) among those equations may be the
best key parameter to substitute other parameters (i.e. to be determined first).
52
3.3.2 The Coupling Loop from Lee’s Optimal Strategy
Lee’s optimal strategy (2006) uses the graph theory to find the functional
couplings. The method is that: after creating an adjacency matrix, one can draw a
digraph according to the adjacency matrix. The “loop” in the digraph means the
coupling.
For example, with the given DM as the matrix in Figure 3.2a, one can create the
adjacency matrix A as shown in Figure 3.2b, where A is equal to DM
T
– I. A digraph
with m vertices and n arcs is equivalent to m FR-DP pairs and n off-diagonal terms,
so there are 4 vertices in the digraph, and the direction of the arc is from v
i
to v
j
when
the A
ij
is non-zero. As shown in Figure 3.2c, there are 3 loops in the digraph. Since
the loops cover all the vertices, all the DPs are functionally coupled. On the contrary,
for the sample matrix in Figure 3.3, the result reveals it is a decoupled design because
there is no loop in the digraph.
(a) (b) (c)
Figure 3.2 The procedure of finding the coupling in a sample DM with coupling.
(a) (b) (c)
Figure 3.3 The procedure of finding the coupling in a sample DM without coupling.
53
Since the research approach should be applicable on rectangular DM as well,
the vertices method that represents the FR-DP pairs would not work. Nevertheless,
based on the similar theoretical foundations, The unsolvable functional coupling can
be revealed by tracing the coupling connections crossing the DPs.
3.3.3 The rationale of Suh’s rearrangement algorithm
In Suh’s rearrangement algorithm, the FR which is controlled by the less DPs
has higher priority, and the DP which effects more FRs has higher priority. Although
the FR-DP swapping method does not work in rectangular matrix so that the
algorithm is confined, the information of the “precedence” for the DPs is implied in
his algorithm.
3.3.4 Research Foundation I: The Concept of Precedence
According to the above foundations, the concept, “precedence”, was defined in
this research approach as the level of functional coupling to determine the proper
sequencing order to minimize the overall complexity.
Here firstly introduces the concept of “precedence” in the formation of the
execution sequence. Precedence is the decision-making order of DP, and each DP
can be determined in a sequence for sure to achieve the FR because other DPs which
also the means of the FR are already determined or have less impact on the system
so that can be determined later. In general, the DPs that relate to the FR which has
the least sum of the numbers in its row is in the highest level of precedence because
the change of those DPs would affect the FR most. In addition, the most functionally
coupled DP (i.e. the largest sum of the numbers in its column) has the highest
precedence according to the ADT’s sequence for a fully-triangular DM. Like the
54
method of elimination by substitution on solving an algebra problem, the first key
parameter is usually chosen the most coupled one. In observing the sequence that
was read from a triangular DM, the conclusion is the same. Based on the above
description, we can define the “sensitivity” of the DP for the FR as follow:
The sensitivity of the DP for the FR
=
(Sum of the number of the DP)∗The change of the DP
(Sum of the numbers of the FR)
(2)
The Suh’s and the EA methods are not optimal because the “precedence” of the
DPs can’t be expressed clearly in a matrix. Like the example in Figure 3.4, the
precedence of DP
1
is higher than that of DP
2
, and that of DP
3
and DP
4
are equal.
That is because DP
1
couples with all the FRs (the first column is full.) With the
understanding of the precedence of DPs, their execution sequence can be arranged
without DM rearrangement.
[
𝐹𝑅
1
𝐹𝑅
2
𝐹𝑅
3
𝐹𝑅
4
]=[
𝑋 𝑂 𝑋 𝑋 𝑂 𝑂 𝑂 𝑂 𝑋 𝑋 𝑋 𝑋 𝑋 𝑂 𝑂 𝑋 ][
𝐷𝑃
1
𝐷𝑃
2
𝐷𝑃
3
𝐷𝑃
4
]
Figure 3.4 Another design matrix example.
To conclude, the DP that relate to the FR which has the less sum of the
correlation numbers in its row is in the higher level of precedence, and the more
functionally coupled DP (i.e. the larger sum of the numbers in its column) has the
higher precedence. When the above metrics are equal, the DPs have “equal
precedence.” If there are functional couplings between them, they would be the
unsolvable DPs (strongly coupled) and should be consider together. If not functional
coupled, the order of these DPs doesn’t matter (i.e. any of them can go first).
55
3.4 Rationales and Foundations for Modular Design
In the past, the design theories regarding the execution sequence for coupled
design focused on eliminating the extra functional coupling. The research provides
a new idea to managing the functional coupling. Rather than directly processing
elimination, the research approach employs functional sets to form the execution
sequence in design theory.
3.4.1 Using Sets Rather than Direct Elimination
The solution within the elimination changes the fundamental design. It could
cause creative designs, but because of the change, it consumes time and money to
embody the design into a real product. Therefore, the trade-off between practical
limitation and creative possibility is very important.
The basic idea of the algorithm is to capsule the coupled DPs so that the system
looks like uncoupled or decoupled (Figure 3.5). Since the coupling is covered by the
capsule, the coupling relationship can be resolved as long as designers can eliminate
the coupling among the DPs in the capsule with a creative design or can find a
feasible module to satisfy the FRs so that the tradeoff can be considered while doing
the conceptual design. For finding the feasible module to resolve the functional
coupling, using the matrices in Figure 3.5 as an example, as long as designers could
find a module that satisfies FR
4
, FR
5
, and FR
6
in the design ranges, no matter what
the details in the module are, the design is “good enough”. In this manner, the time
and money cost are hopefully reduced in practice.
56
Figure 3.5 Encapsulation reveals modularity.
To study “encapsulation”, software design is worthy of investigation. Software
design especially Object-Oriented Programming (OOP) nowadays became speedily
developed and one main feature is modularization. They use “class” to create the
template of the program packaging the required parameters within the methods or
functions. It is an abstract definition of the object because in class it doesn’t have
“values” for the object’s parameters. It can be mapped into the conceptual design
stage because there are DPs but no values for the DPs.
With the capsulized functional sets, designer either can use the handbook to look
up the feasible modules or analogy or create the ideas from the existing design as a
module to match the design requirement of the grouped DP sets.
3.4.2 The Sequence in Component Diagram
Component Diagram in Unified Modeling Language (UML) is a diagram to
show system architecture with modules. It includes not only the module information
but also the sequence of data flow. If the provider and the receiver in the component
diagram are converted to higher precedence and lower precedence respectively, and
the big module which contains small modules is regarded as a capsule, then the
sequence and the two kinds of module are constructed.
57
3.4.3 Research Foundation II: Two Types of Functional Sets
Two types of functional sets are named the complete independent set U and the
unsolvable coupled set C. U stands for uncoupled and C stands for coupled. They
are not actual modules, but they could be used to match the existing modules or to
identify the functional couplings locally for applying the elimination method, so they
are named ‘sets’ rather than ‘modules’. The definition of the set U: the collection of
all the functionally dependent DPs in the system so that the set is independent to
other U sets. It is like the provider-receiver linked components in the component
diagram. The definition of the set C: the collection of coupled concepts that can’t be
decoupled by sequencing, so it prescribes the designer to consider the group of DPs
together to match the existing design modules.
These two types can be explained by Figure 3.6. In the matrix, DP
1
is a U-set,
and DP
2
and DP
3
are collected to be a U-set because DP1 is functionally independent
with DP
2
and DP
3
. DP
2
and DP
3
are also serving the role as a C-set due to the FR
2
and FR
3
coupling with both DPs.
Figure 3.6 An example for functional sets.
58
Chapter 4. The Approach: Design Coupling Sequence
1
With the foundations, the approach algorithm was developed. In this chapter,
the developed approach, Design Coupling Sequence, is elaborated in detail.
4.1 Introduction of DCS and DCS Representation
Wang et al. (2015) developed the Design Coupling Sequence (DCS) method to
manage DPs in sequences and by modules to reduce the complexity of the design. It
was further developed to improve the algorithm, to define the functional sets, and to
provide the strategies for concept improvement tasks in this research. The role of the
DCS method is to play as a prescription for concept improvement tasks after a design
matrix has been created during the concept generation or the reverse engineering.
The goal of DCS is to help the designer to determine the DPs with functional sets to
reduce both the real and the imaginary complexity as much as possible.
To achieve the goal, the DCS representation was defined first. The following
example explains the representation of DCS. For the design matrix as shown in
Figure 4.1, the representation was expected to be shown as Figure 4.2. It is the typical
outcome of DCS, which separates DPs into several U-sets, and in the U-set, some
arrows indicate the precedence and some C-sets capsuling by braces to indicate
unsolvable coupled DPs.
1
Some contents in this section have been previously published as a research paper [Wang and Lu, 2018 and Wang,
Lu, and Liu, 2015] that is co-authored with my advisor and committee chair Dr. Stephen Lu and research colleague
Dr. Ang Liu.
59
Figure 4.1 An example design matrix for explaining DCS representation.
Row
1 Set U1 𝐷𝑃
1
→𝐷𝑃
2
→ 𝐷𝑃
3
→𝐷𝑃
4
→𝐷𝑃
5
2 ↘ 𝐷𝑃
6
3 Set U2 {𝐷𝑃
7
, 𝐷𝑃
8
}
4 Set U3 𝐷𝑃
9
Figure 4.2 An example of the result of DCS.
In this example, “ ” is an arrow, {DP
7
,DP
8
} is a C-set, row 2 is a branch of row
1 from DP
2
, and row 1&2, row 3, and row 4 are the three U-sets. The following lists
the definition of each important item in the representation:
– U-set in DCS refers to a functionally independent set that is uncoupled
with other U-sets
– Arrow ( ) in the U-set shows the direction of the sequence
– C-sets represented by braces, { , }, in U-sets shows the unsolvable
coupling
– Branch in the U-set is uncoupled with other branches (equal precedence)
According to the representation, U-sets and C-sets function differently. U-set
decomposes the system into several functional independent subsystems, C-set
60
groups the strongly coupled DPs. The DCS algorithm orders the DPs by their
“precedence”. Arrow in the U-set indicates higher to lower precedence, and C-sets
and branches in the U-set indicates equal precedence. Therefore, the execution
sequence can be obtained according to the following rules regarding the precedence
and functional sets.
4.1.1 From DCS to The Acceptable Execution Sequences
The execution sequences can be formed from DCS sets by permutation and
combination. Arrow indicates the order; besides, branch can be any order with other
branches, and the order of the DPs in the branch follows above rules. The order in a
C-set is meaningless because all the DPs in the set should be determined together.
The number of all acceptable DCS sequences (that can minimize the complexity) is
calculated by multiplying the factorial of the number of the U-sets and that of the
branches for each node.
For the example in Figure 4.2, there should be 12 acceptable sequences in that
design (3!×2! = 12).
4.1.2 From DCS to The Design Matrix Rearrangement
DCS carries the functional coupling information, so the functional schematics
is also formed when the execution sequence obtained from DCS. This means that
DCS is capable of design matrix rearrangement by directing listing the DPs in the
design matrix without swapping the rows and columns in advance to seek the
functional schematics.
61
For example, the design matrix and the DCS result is shown in Figure 4.3.
According to DCS, the change of the branch of DP
31
and of DP
21
doesn’t matter. As
a result, Figure 4.4 shows the rearrangement is successfully implemented by the
execution sequence with DCS functional sets.
Figure 4.3 Design matrix rearrangement by DCS.
Figure 4.4 Design matrix rearrangement by DCS.
So far, it shows a new kind of design matrix could be developed to better shows
the functional coupling relationship between FR and DP. As stated earlier, two-
dimensional design matrix is limited, a three-dimensional DM could be built as
Figure 4.5 to show the actual functional schematics of the design.
Figure 4.5 Three-dimensional design matrix.
62
4.2 The Concept Improvement Strategies with DCS Sets
Conceptual design involves concept generation and concept improvement
phases. As stated in detail about the difficulties of creating ideal enough concept in
the concept generation phase, the concept improvement tasks should be strategically
deal with to reduce the complexity. There are three common types of the concept
improvement task and their strategies prescribed for design to use during the concept
improvement.
4.2.1 The Whole Design Concept Refinement
After the concept generation process or re-engineering, to refine the concept
with the execution sequence—either eliminate the coupling in the interior C-sets or
decide the DPs in the order of the sequence. When facing the interior C-set, one can
look up the handbook or searching the existing modules with same functions. If more
than one design are satisfied the FRs in design range, choosing the design with more
acceptable execution sequences would result in less imaginary complexity.
4.2.2 The Design Change without DM Change
Sometimes the improvement task is to change a part of the design but the design
matrix can remain the same. The scenario could be, for example, to adjust one of the
DPs such as out of stock (where the concept is from re-engineering) or difficult to
make it real (where the concept is from conceptual design).
For the task, one is suggested to find the changed DP in the U-set, and then
follow the sequence in the U to determine the rest DPs. If the corresponding FR of
63
the higher precedence DP in U can’t be satisfied due to the change, the complete U-
set is suggested to be redesigned. The strategy enables local improvement in the
design rather than redesign the whole system.
4.2.3 The Design Change with DM Change
In some cases, the improvement task is resulted in the design matrix change.
The scenario could be, for example, to modify the DPs when new FRs involved or
some FRs change (where the concept is from re-engineering).
For this task, one is suggested to rebuild the DM with new FRs and new DPs
(either expand the design matrix or re-identify the whole DM). Then, one is
suggested to follow the strategy of whole design refinement in Section 4.2.1 or the
partial design change in Section 4.2.2.
4.3 The DCS Algorithm
This section presents how to convert design matrix information into DCS
functional sets.
4.3.1 The Logic of the Algorithm
The logic of the algorithm firstly is following the precedence to order each DPs.
When assess the level of the precedence, the level of the functional coupling with
FRs is examined first then the level of the functional coupling of DPs. Meanwhile,
the equal precedence DPs are labeled as groups to further examine. Next, each
member in the group will be examined the functional coupling with its group
members. As stated in the research foundations, those equal precedence with
functional coupling DPs indicates the unsolvable coupling, which is represented by
64
braces of C-set. Finally, the functional coupling relationship of each DP ordered by
precedence is examined to build the connection forming the U-set.
For the numerical DM, means the designer has detailed information of the
design. If the purpose is to improve the design concept according to the current DPs,
then the different weights of the design should take into different weighted
considerations. If the purpose is to innovate the design concept basing one the
current DPs, then DM should be abstract into binary DM where O with no relations
and X with relations.
4.3.2 The Notions in the Algorithm
For handing both binary and numerical design matrix, binary design matrix (i.e.
ADT design matrix) is translated as zero and one design matrix where zero
represents O and one represents X. In addition, some notations are needed to better
explain the algorithm.
The element at row “m” and column “n” in the DM is denoted by DM
mn
. The
sets
S_DP
n
: {m | DM
mn
≠ 0} (3)
S_FR
m
: {n | DM
mn
≠ 0} (4)
express the position of those non-zero elements which indicate functional couplings
between FRs and DPs. In addition, the parameters
Sum_DP
n
= Σ|DM
mn
| (5)
Sum_FR
m
= Σ|DM
mn
| (6)
represent the degree of coupling of a specific DP and FR.
65
The algorithm of the DCS method is shown in Figure 4.6, and its steps are
explained in Section 4.3.3.
Figure 4.6 The flow chart of DCS algorithm.
4.3.3 The Procedure of the Algorithm
Each step of DCS algorithm is explained in detail as following.
Step 1: Reorder and Group.
Find the S_FR
i
that its Sum_FR
i
is the smallest, and obtain the n in S_FR
i
. Add
the DP
n
in Line 1, and then remove the column of the DP from the DM. Repeat this
step until all the DPs are in Line 1.
• If there are more than one different n, add these DP
n
in Line 1 by Sum_DP
n
from the most to the least, and mark the DPs with same values of Sum_DP
as a group by underlining.
66
Step 2: Manage Grouped DPs.
Manage the grouped DP
j
starting from the second DP in the first underlined
group. Check whether exists an x ∈ S_DP
j
of DP
j
such that x equals any y ∈ S_DP
k
of its preceding DP (DP
k
).
• If yes, put DP
j
in the set (i.e. { , }) with DP
k
.
• If no, move DP
j
to a new line under DP
k
, and then repeat the following
checking process with its current preceding DP (i.e. the preceding DP of
DP
k
) until it is put into a set or reach the first DP of the group.
• Note, the checking process can be expressed by
{
{𝐷𝑃
𝑗 ,𝐷𝑃
𝑘 }, ∃ 𝑥 ∈S_DP
𝑗 ∶𝑥 =𝑦
𝐷𝑃
𝑘 𝐷𝑃
𝑗 , ∀ 𝑥 ∈S_DP
𝑗 ∶𝑥 ≠𝑦 (7)
𝑤 ℎ𝑒𝑟𝑒 𝑦 ∈S_DP
𝑘 𝑎𝑛𝑑 DP
𝑘 is the preceding DP of DP
𝑗 .
Step 3: Arrange DPs into sequences.
Arrange all the DPs (DP
p
) into sequences starting from the second DP in Row
1. Check whether exists a u ∈ S_DP
p
of DP
p
such that u equals to v ∈ S_DP
q
of its
preceding DP (DP
q
) or one of the DPs in the preceding set (DP
q
).
• If yes, put a rightward arrow ( ) between DP
p
and its preceding DP or set.
• If no, put DP
p
to a new line under DP
q
, and then repeat the following
checking process until the DP
p
is linked by an arrow or reach the first DP in
the line.
67
• Note, the above checking process can be expressed by
{
𝐷𝑃
𝑞 𝑜𝑟 {…,𝐷𝑃
𝑞 ,…} → 𝐷𝑃
𝑝 , ∃ 𝑢 ∈S_DP
𝑝 ∶𝑢 =𝑣
𝐷𝑃
𝑞 𝑜𝑟 {…,𝐷𝑃
𝑞 ,…}
𝐷𝑃
𝑝 , ∀ 𝑢 ∈S_DP
𝑝 ∶𝑢 ≠𝑣 (8)
𝑤 ℎ𝑒𝑟𝑒 𝑦 ∈S_DP
𝑞 𝑎𝑛𝑑 DP
𝑞 is the preceding DP (or DP in the preceding set) of DP
𝑝 .
By following the algorithm described above, the designer can obtain a DCS
sequence showing the improvement order of DPs.
4.4 Summary of This Chapter
DCS uses arrow, branch, C-set to sequence and separate the functional
independent DPs by U-sets. The DCS algorithm includes three steps: 1) reorder and
group DPs, 2) manage grouped DP, and 3) arrange DP into sequence. C-set is used
to represent grouped coupled DPs which managed in step 2, and U-set are the
independent sequence arranged in step 3. DCS also provides strategies for three
concept improvement tasks and shows the capability of design matrix rearrangement.
A new kind of DM was also proposed for future study.
68
Chapter 5. The Software Implementation
A program was developed as a tool for designers to convert DM into DCS sets.
In this chapter, the program will be described in detail about its platform, system
architecture, user interface, and implementation.
5.1 Objectives and Software Introduction
5.1.1 Objectives
The objective of implementing software is to prove of the algorithm as well as
to expand the research approach for the use of large system design.
5.1.2 The DM-DCS Converter
The DM-DCS converter is a program exported as an EXE execution file for
Windows user based on the DCS algorithm. The programming language is C#.
Below describes them in detail.
The DM-DCS converter satisfies the following functional requirements (FRs):
1) To import DM data from Excel, 2) to display the imported DM, 3) to convert the
data according to the DCS three steps, and 4) to display the converted results. The
program is only interact with one user, who is the designer with the design matrix.
In the view of the user (designer), the functions are different from the FR for the
system. Figure 5.1 shows the use case diagram.
Basically, the user can load the data to the system by selecting the Excel file and
designate the sheet of the wanted DM, and then the user can view the data in the user
interface and have the system convert the DM into the DCS form. The user should
be able to view the converted DCS data to understand the converting progress and
69
results, and also the user should be able to capture/acquire the converted DCS data
for further use.
Figure 5.1 The use case diagram.
5.1.3 System Architecture
The system is implemented with C# program and an excel document (database).
Following are the basic components in this system:
a) Excel of DM database: This is an independent file storing design matrix
information. The binary design matrix should be stored as a numerical matrix
with only zero (0) and one (1), where 0 indicates O and 1 indicates X.
b) Graphical window of user interface: After double-clicking the execution file,
a window will pop up to show the interactive components in the panel. It is
like a normal window in Windows, so it can be expand to the full screen,
minimize to the task bar, or close.
Select DM
Excel file
Type Excel
sheet number
View the
imported data
Command the
system to convert
to DCS
View the DCS
converting progress
Obtain DCS data
designer
70
c) The button of “Import DM Excel File”: The button is a trigger of OleDb for
the user to command the system to import the file, and the file name and path
will show in a textbox.
d) The textbox of sheet name: An Excel file can have many sheets. This box
allows the user to change the sheet name to indicate the location of the target
DM interactively. The default sheet name is Sheet1 as it is the default name
of the first sheet in an Excel file.
e) The button of “Show Design Matrix”: It is an interactive button for the user
to request the system to show the imported design matrix. In the system view,
when the button event is triggered, the program calls the Data Grid View to
output the stored DM data.
f) The panel of Data Grid View: This is a reserved place to show the DM data.
By using Data Grid View and setting the scroll, the size of the design matrix
can be large as long as the Excel file can store it.
g) The button of “Show DCS”: If the button is pressed by the user, the program
will start to calculate and arrange the DPs by following the DCS algorithm.
h) The textbox of Rich Text Box: The program uses Rich Text Box to show the
design matrix basic information, the step-by-step converting progresses, and
the converted results. The Rich Text Box shows texts with font styles and
allows the user to copy the texts.
Following is the component diagram. As described in Section 5.1.3, the
connection of each component is shown in Figure 5.2.
71
Figure 5.2 The component diagram.
5.2 Graphical User Interface and the Program Manipulation
In this section, the three user interfaces and the application scenario are
presented.
5.2.1 The Database
The design matrix should be input in the Excel file as shown in Figure 5.3. Using
Microsoft Excel software as the data storage, the system can read the DM data from
an Excel file. The format in the Excel is like a normal matrix starting from B2. The
row 1 is for the DP names, and the column A is for the FR names.
Binary DM should be stored as a 0-1 matrix, and numerical DM is just stored as
it is. One Excel file can store several DMs in different sheets. For example, the user
stored nine DMs in the Excel file shown in Fig. 5.3, and the one in the figure is the
“Import”
button
“Sheet name”
textbox
“File name”
textbox
“DM Data”
Panel
“Show DM”
button
“Show DCS”
button
DCS results
Rich Text Box
DM
database
Stored
Data
72
seventh DM, which is a 4 ×5 binary DM. Designer should know the sheet name of
the target DM in order to import to the main system.
Figure 5.3 The DM in Excel.
5.2.2 The Main Interface
Executing the DM-DCS converter, the user can see the main window (Figure
5.4). The user can press the blue button to import the target DM data in the Excel
file to the program. The user interface of the file chosen will be described in the next
section. The user can revise the sheet name if the target DM is not in the first sheet
in the file or the name of the sheet has been changed. Then user can press the green
button to show the target DM as shown in Figure 5.5. If the DM is larger than the
DM data panel (the light blue one), scrolls will be shown in the window.
73
Figure 5.4 The main window.
Figure 5.5 The DM imported into the DM data panel.
Then the user can press the pink button to show the DCS. As shown in Figure
5.6, the results of each step in the DCS algorithm will be listed in the DCS results
textbox. The converted DCS can be obtained automatically.
74
Figure 5.6 The DCS showed in the DCS results textbox.
5.2.3 Design Matrix Importation
For the file import, a common file-chosen window will pop out when the
“import” button is pressed (Figure 5.7). The user can select any Excel file with the
formatted content described in Section 5.2.1.
Figure 5.7 The file import interface.
75
5.2.4 DCS Sequence Exportation
The results in the program are shown in a textbox, so it can be copied directly in
a text form as shown in Figure 5.8 below from the example in Figure 5.6:
Figure 5.8 The textbox copy
5.3 System Testing and DCS Algorithm Validation
The program system was tested and evaluated by different type of DM to
validate the generalization hypothesis. Besides, the user-friendly designs are also
discussed in this section.
5.3.1 The Test Results of the Three typical types of DM
This section validates the hypothesis H1-1: the consistency of the typical design
types.
The three typical types of DM
The results of the three typical types of DM, uncoupled, decoupled, and coupled
DMs, are shown in Figure 5.9, 5.10, 5.11 respectively. The result of the decoupled
design case is worthy to note that the original design matrix was a coupled design
before rearrangement but the DCS algorithm was capable to obtain the correct
execution sequence so that the decoupled design type was revealed.
DP1 →DP2 →DP4
DP3 ↗
76
Figure 5.9 The result of the uncoupled design.
Figure 5.10 The result of the decoupled design.
77
Figure 5.11 The result of the coupled design.
The results are consistent with the typical three types where the DPs of uncoupled
design can be in any order as independent sets of itself, the DPs of decoupled design
is the sequence of DPs within the triangular design matrix, the coupled design is
overall unsolvable as shown as an unsolvable C-set.
5.3.2 The Test Results of non-typical DM
The test is to validate hypothesis 1-2: the existence of the execution sequence.
The two sample DMs are partially-decoupled DM and partially-coupled DM.
Partially-Decoupled DM
The execution result of a 3 ×3 partially decoupled DM is shown in Figure 5.12.
The result matches the discussion for the example in Figure 2.27 in Section 2.5.3.
78
Figure 5.12 The result of the partially decoupled DM.
Partially Coupled DM
Using the sample DM in Figure 2.26 as an example. The execution result of the
partial coupled DM is shown in Figure 5.13. The result matches the discussion for
the example in Figure 2.26 in Section 2.5.2.
Figure 5.13 The result of the partial coupled DM.
79
5.3.3 The Test Results of the non-ADT’s DM
In this section, rectangular, zero-at-diagonal, numerical DMs are examined to
verify the hypothesis 1-3: no design type limitations.
Rectangular DM
The execution result of a 5 ×4 rectangular DM (Figure 5.14) is shown in Figure
5.15. Due to the functional independence between DP
2
and DP
3
, the branch precisely
indicated the feature.
Figure 5.14 A rectangular DM example.
Figure 5.15 The result of the example rectangular DM.
80
Another example is Figure 2.19 from the EA method. The execution result of a 4
×3 rectangular DM is shown in Figure 5.16. The result matches the result from EA
method; in addition, it tells two execution sequences (DP
3
DP
2
DP
1
DP
4
and
DP
3
DP
2
DP
4
DP
1
) that helps reduce imaginary complexity, which can not be
obtained by the EA method.
Figure 5.16 The DCS result of the rectangular DM from EA method.
The DM with zero(s) at diagonal
Using the sample DM in Figure 5.17 as an example because its functional
schematics is somehow clear to tell as some clusters appear at the diagonal. The
execution result of the sample DM with zero at diagonal is shown in Figure 5.18.
The result precisely displays the four U-sets and also provides the clear execution
sequence for the U-set of DP
2
and DP
3
and the U-set of DP
4
, DP
5
, and DP
6
.
81
Figure 5.17 The working DM with zero at diagonal.
Figure 5.18 The result of the 9×9 DM.
Numerical Design Matrix
The working sample (Figure 5.19) uses the numerical DM from the tire design
case study (Section 6.3). The demonstration by software implementation here in the
numerical DM case is only for the algorithm validation. The usability and feasibility
of the DCS approach on the numerical DM is further validated in the case study. The
executive result is shown in Figure 5.20.
82
Figure 5.19 The numerical DM sample from tire design case in section 6.3.
Figure 5.20 The result of the numerical DM.
Comparing with the result of binary DM (Figure 5.21), the result from the
numerical design matrix shows a more specific execution sequence. It matches that
the numerical information is more concrete than the binary information.
83
Figure 5.21 The result of the binary DM.
5.3.4 The Test Results of the Large DM with Mixed Design Types
In this section, some large DMs with mixed design types are examined to verify
the hypothesis 1-4: the ability of DM rearrangement.
The first example uses the sample DM in Figure 4.3. The execution result of a
9×9 DM is shown in Figure 5.22. The result of the software is the same as that in
Figure 4.3. Although 9×9 matrix is not very large, the multiple clusters as functional
sets were precisely indicated in the DCS result. Since the algorithm was
implemented by computer, the size of the design matrix doesn’t matter as long as it
can be put in an Excel file.
84
Figure 5.22 The result of the 9×9 DM.
From the DCS results, the DM can be rearranged accordingly. The original DM
and the DCS results are shown in Figure 5.23, and the two DM rearrangement results
are shown in Figure 5.24. The difference of the two rearrangements are from the
branches at the first U-set. If DP
21
goes first, the result is the left picture in Figure
5.24. The results not only validate the capability of DM rearrangement, but also
show an opportunity for a new kind of design matrix, a 3-D design matrix (such as
Figure 5.25), which could be built to show more precise functional coupling
information. In this thesis, the author only points out the research opportunity as a
future work for further definition and investigation.
Figure 5.23 The 9×9 DM and its DCS sets.
85
Figure 5.24 The DM rearrangement result from the DCS result.
Figure 5.25 A 3-D DM was built according to the above results.
5.4 Discussion
The discussion includes the software usability, the system scale and limitations,
and a summary.
5.4.1 The Usability of the Software
The program has some user-friendly designs. First, the system uses textbox for
the user to revise and/or extract the information easily. Second, using the Excel as
the database can make the database compatible with other tools as the Excel is still
most common datasheet software in current trends. Third, showing the results of all
the steps helps designers examine and trace the problem in the target design. Fourth,
the colorful graphical user interface could help users get familiar and comfortable
with the program.
86
There are still some improvable points in the program to make it more user-
friendly. First, it could be better if the format of the design matrix in Excel file can
be free. Second, to load a new DM, it requires the user to close the current program
and then to reopen the program.
5.4.2 System Scale and Limitations
The maximum size of the DM in the program depends on the maximum
accommodation of the Excel file, but the large size of DM may slow the loading
speed downward. In addition, the format of the design matrix is limited, and it
requires the binary design matrix to be represent as a numerical design matrix with
only zero and one in the values.
5.5 Summary and Future Extensions
The DM-DCS Converter program works with different types of design matrix.
The object-oriented GUI with DCS algorithm enables designers to use for converting
the design matrices into DCS automatically. In the future, the program could be
enhanced to be more user-friendly, and reduce the system limitation and the
restriction about the DM format in Excel. Also, one possible extension is to convert
to not only the DCS sets but also the execution sequences as well as rearranged DM.
The 3-D design matrix is also one of the future studies.
87
Chapter 6. Case Studies for DCS Validations
Four cases were studied to validate DCS hypothesis and foundations. The faucet
design case compares the design results between ADT approach with TRIZ method
and DCS approach with DCS strategy 1. The case of coffee maker design compares
the modular design results and the DCS modularity with strategy 2 and 3. The
vehicle tire design case aims to verify the usability and feasibility of DCS approach
in real-world product development within the Innovative Design Thinking (IDT
framework. Finally, a case of collision avoidance planning presents one of the
possible extensions of the DCS algorithm.
6.1 A Simple Design Case: The Kitchen Faucet Design
2
The first case is a normal concept improvement case using a kitchen faucet
design as an example. On one hand, a simple design case can clearly demonstrates
the application procedures; on the other hand, the design results can be easily
evaluated or compared.
6.1.1 The Objectives of the Case Study and the Case Introduction
Kitchen faucet is a common equipment in a household, and the first faucet with
a screw-down mechanism was invented in 1845. After about one hundred and
seventy years, the improvement of it is still ongoing. There are many different
designs on the market and are sold as modules. In this section, a case of the kitchen
faucet design is studied to demonstrate how DCS helps with the function sets to
improve the existing product, and the improvement using Suh’s method is also
studied as a comparison.
2
Some contents in this section have been previously published as a research paper [Wang and Lu, 2018] that is co-
authored with my advisor and committee chair Dr. Stephen Lu.
88
6.1.2 The Problem Statement
The focused design for the improvement is the kitchen faucet as shown in Figure
6.1a. The DM is a completely coupled design (Figure 6.1b). By reverse engineering,
the design has been transformed into two FRs and two DPs, which are FR
1
: to control
the flow rate, FR
2
: to control the temperature, DP
1
: a cold valve, and DP
2
: a hot valve.
In addition, there are two new FRs needed to be satisfied. They are FR
3
- to control
the flow-out direction and FR
4
- to control the reach-out position. In order to satisfy
the new FRs, the new DPs are given as an ideation result from the analogy of the
shower faucet design (Figure 6.2). DP
3
is an outlet head, and DP
4
is a hose. The
design ranges for those FRs are displayed in Table 6.1, and the overall DM of the
given problem is shown in Figure 6.3.
(a) (b)
Figure 6.1 (a) A common kitchen faucet (b) its DM.
(Kingston Kitchen Faucet, Model # FB2121NDL, $23.99 at Amazon)
Figure 6.2 A shower faucet example.
(Hiendure Handheld Shower Faucet, Model # HB001, $64.00 at Amazon)
89
Table 6.1 The design range of the kitchen faucet.
FR1 to control flow rate 1-1.5 ±0.1 gallons per minute (gpm)
FR2 to control temperature 70°F - 105°F ±1 °F
FR3 to control the flow-out direction the tilted angle from -80° to 80° ±5 °
FR4 to control the reach-out position
of the water head
in a partial cylinder with a height of 0.3(±0.01)m
and a 160°(±5°) sector with radius of 0.15(±0.01)m
Figure 6.3 The design that needs to be improved and its DM.
6.1.3 The Improvement by Suh’s method
Since the DM is neither triangular nor diagonal, the matrix rearrangement should
be done first. The result of the matrix rearrangement shows that it is a coupled design
(Figure 6.4). Because the less change from the original design causes less
complexity, rather than choosing the totally redesign or the elimination of the off-
diagonal non-zero elements, here is using the elimination of the off-triangular non-
zero elements in the study in order to achieve the minimum change of the design.
According to the rearrangement result as reported in Figure 6.4, the DM can be
triangular if the non-zero element at the new DM
31
(FR
1
-DP
2
) is eliminated. If so,
the improvement execution sequence will be DP
4
DP
3
DP
1
DP
2
.
90
Figure 6.4 The DM rearrangement result for the faucet design by Suh’s method.
To eliminate that non-zero element by using TRIZ, one would have the improving
FR
1
, which is in terms of number 9, speed, in TRIZ matrix and have the conflict of
DP
2
, which is in terms of number 17, temperature, in TRIZ. Therefore, the possible
principles are 28- Mechanics Substitution, 30- Flexible Shells and Thin Films, 36-
Phase Transitions, and 2- Taking Out. By using the principle 2A, a hot water on-off
button is generated as DP
2
*
(Figure 6.5).
Figure 6.5 The improved design from Suh’s method.
In order to match the design range, the design requires the further improvement
by following the execution sequence, DP
4
DP
3
DP
1
DP
2
*
. DP
4
should match
the design range for FR
4
first. In order to reach the farthest position, the hose should
be in the length of L, which is the diagonal length of the partial cylinder from the
middle of the arc to the vertex at the other side. Since the original PVC hose (Figure
4.2) does not match the design range, the design should be modified. Some options
91
as shown in Figure 6.6 are DP
4A
: a PVC hose (the original design), DP
4B
: a spring
hose, DP
4C
: a telescopic hose, DP
4D
: a foldable hose, DP
4E
: a bendable hose. There
are only DP
4D
and DP
4E
matching the design range of FR
4
, and DP
4E
is cheaper than
DP
4D
due to the joint-less. Hence, to completely satisfy FR
4
and considering the cost,
the hose would be designed as DP
4E
- a bendable hose.
Figure 6.6 Five possible options of DP4.
(DP4A: PartsmasterPro Faucet Hose, Model # 58583, $6.98 at Home Depot; DP4B: Husky Recoil Hose, Model # 4-50E-RET-HOM,
$12.98 at Home Depot; DP4C: Hansgrohe Pull-down Kitchen Faucet Hose, $35.00 at Home Depot; DP4D: KES Kitchen Faucet,
Model # K9250, $39.99 at Amazon; DP4E: YOSIL Bendable Kitchen Sink Faucets, $19.99 at Amazon)
Because the DP
4
is determined, DP
3
can be determined by matching the design
range of FR
3
. The options as shown in Figure 6.7 are DP
3A
- a simple outlet head (the
original design), DP
3B
- an outlet head with a universal joint, and DP
3C
- a PVC outlet
head. Since the original design with a bendable hose has matched the design range
of FR
3
and others are more expensive, DP
3A
is chosen.
Figure 6.7 Three possible options of DP3.
(DP3A: Sonline Faucet Aerator, Model # 017097, $2.18 at Amazon; DP3B: Topbeu 360 Swivel Tap Aerator, Model # LB52,
$3.29 at Amazon; DP3C: WillsCase Faucet Extender, $8.99 at Amazon)
DP4A DP4B DP4C DP4D DP4E
DP3A DP3B DP3C
92
A normal temperature of a tap water is roughly 55 degrees Fahrenheit (13 degrees
Celsius.) So, while improving the cold valve (DP
1
) to match the design range of FR
1
(to control flow rate between 1-1.5 gpm), the temperature of the cold water can
remain the same, and the valve should be adjustable in the range of 1-1.5 gpm. In
short, the DP1 is determined as a cold valve (~55°F) in an adjustable flow rate
between 1 - 1.5 gpm.
Taking the determined DP
1
in consideration, the flow rate of DP
2
has to be no
more than 0.5 gpm when DP
2
is on, so the system range can match the design range
of the FR
1
. Also, DP
2
*
has to vary its temperature in order to satisfy the design range
of FR
2
(to control temperature between 70°F - 105°F) so a heater in an adjustable
temperature between a and b °F is added in DP
2
*
. a is the solution of the equation 3,
and b is the solution of the equation 4.
0.5×55 + 0.5×a = 70 (9)
1.5×55 + 0.5×b = 105 (10)
The DP
2
*
is determined as a hot water on-off button (when on, the flow rate is
0.5gpm) plus a heater in an adjustable temperature between a and b °F.
Consequently, the final improved design is DP
1
: a cold valve (~55°F) in an
adjustable flow rate between 1 - 1.5 gpm, DP
2
*
: a hot water on-off button (when on,
the flow rate is 0.5gpm) and a heater in an adjustable temperature between a and b
°F, DP
3
: an outlet head, and DP
4
: a telescopic hose with the extendible length L. The
overall design concept is as exhibited in Figure 6.8.
93
Figure 6.8 The final improved design from Suh’s method.
(A.B Crew Electric Hot Water Heater Kitchen Faucet, Model # COMIN18JU011922, $49.98 at Amazon)
6.1.4 The Improvement by DCS method
By applying DCS to the DM, the sequence is obtained as shown in Figure 6.9.
According to DCS, there are two independent sets in the design, which are a set of
DP
1
and DP
2
, and that of DP
3
and DP
4
.
Figure 6.9 The DCS’s sequence.
The execution sequence of the second U-set: DP
4
DP
3
is the same as the
beginning part of the execution sequence in the last case, so the improvement results
of the DP
3
and DP
4
in DCS would be the same as what in Suh’s method. As a result,
DP
3
would be a simple outlet head and DP
4
would be a bendable hose with the length
of L. L is the diagonal length of the partial cylinder from the middle of the arc to the
vertex at the other side.
To improve the first U-set as well as a C-set, {DP
1
, DP
2
}, one should consider
those DPs as an indivisible set to function both “to control the flow rate” and “to
control water temperature”. One way to improve it is to redesign this whole set
94
because FRs and DPs in this set form a full DM (i.e. infinity real complexity.) The
other way is to analyze the two DPs—they both are a valve that controls the flow
rate, and the difference between the two is the temperature feature, which determines
the satisfaction of “to control water temperature” by different ratios of the hot water
to cold water. Therefore, as a set to eliminate the interior coupling, the two valve can
be combined into a single valve (DP
1
*
) to control the flow rate between 1-1.5 gpm.
As to the temperature control, a mechanism such as a valve to mix the water with
different temperatures in different ratios (DP
2
*
) can be developed because it is a
similar mechanism in the original design. As a result, the fully coupled DP
1
and DP
2
turn into the uncoupled DP
1
*
and DP
2
*
(Figure 6.10).
Figure 6.10 The process of the DCS’s improvement.
Another way is simply to find or to create the modules that function both FR
1
and
FR
2
. For example, in this case, the options might be {DP
1
, DP
2
}
A
- a hot valve and a
cold valve, {DP
1
, DP
2
}
B
- a temperature adjustable valve, {DP
1
, DP
2
}
C
- a integrated
design with a flow-rate adjustable valve and a hot-cold water mixing valve, and
{DP
1
, DP
2
}
D
- a flow-rate adjustable valve and a hot-cold water mixing valve (Figure
6.11). Option C and D can match the design range, and the option C is selected
because of the physical integration. Therefore, the new DP
1
and DP
2
are DP
1
*
- a
flow-rate adjustable valve and DP
2
*
- a hot-cold water mixing valve.
95
Figure 6.11 Four possible options of the module of DP1 and DP2.
({DP1, DP2}A: DANCO Replacement Lavatory Faucet Handles, Model # 10422, $10.12 at Home Depot; {DP1, DP2}B: DANCO
Lavatory Handle, Model # 80967, $9.97 at Home Depot ;{DP1, DP2}C: American Standard Colony Soft Lavatory Faucet Handle,
Model # M961627-0020A, $14.06 at Home Depot; {DP1, DP2}D: CHINAURBANLAB Temperature Control Shower Faucet,
Model # T21CP32B00-33, no price info.)
To summarize the final improved design from DCS, DP
1
is a valve with an
adjustable flow rate between 1-1.5 gpm, DP
2
is a cold-hot mixing valve, DP
3
is a
simple outlet head, and DP
4
is a bendable hose with the length of L. The overall
design concept is as exhibited in Figure 6.12. The design matrix of the design is also
changed to be a decoupled design as shown in Figure 6.10.
Figure 6.12 The final improved design from DCS method.
(Churun Kitchen Sink Faucet, Model # ZT100, $32.99 at Amazon)
6.1.5 Discussions
Both the design results enable the system range to match the design range, and
the coupled design has been improved into a decoupled design.
{DP1, DP2}A {DP1, DP2}B {DP1, DP2}C {DP1, DP2}D
96
In the case of using Suh’s approach, the original design that using different
proportions of the hot and cold water to achieve the function of “to control water
temperature” was changed by using a heater because the hot water valve turned into
an on-off button due to the elimination of the coupling non-zero element. That is an
example that shows that the elimination changes the fundamental design.
In the case of using DCS approach, the fundamental design wasn’t changed but
improved. The function of “to control water temperature” is still satisfied by mixing
the hot and cold water in different ratios. That is because the design was decomposed
into several independent sets from the DCS’s sequence so that it is easier to analyze
each subsystem due to the complexity of each subsystem is reduced. Taking the C-
set in DCS to improve the design not thinking the elimination makes the concept
improvement of a coupled design in a simpler way with lower cost than the way of
rearranging the DM and eliminating the coupling elements.
6.1.6 Summary
The faucet design case reveals the benefit of U- and C- sets in DCS that enable
the designer either improve the design partially according to the U-set or improve
the design as a physical module according to the C-set. Although the design result
by following Axiomatic Design Theory and TRIZ is good, the result from DCS
method shows the modularity and the additional value of the execution sequence
from design theory to practice.
97
6.2 A Re-Engineering Product Design Case: The Coffee Maker Design
The coffee maker design case aims to further examine the modularity ability of
DCS method. It was reengineered to obtain the design matrix with FR and DP
hierarchies. Then, the application of ADT and TRIZ in this case is to show how the
traditional concept improvement way within design theory as a reference. The DCS
application is presented to demonstrate how the DCS incorporate with its concept
improvement strategies to approach the design target.
6.2.1 The Case Introduction
Coffee maker is a popular device and has been on market for a long time. It has
many varieties. The design selected in this case is the most common electric coffee
maker, which presented as a modular product in Gershenson’s paper (Gershenson
and Prasad, 1997) (Figure 6.13).
Figure 6.13 The DP hierarchy of a coffee maker design from layer 0 to 2.
98
The design task in this case was “to use coffee mug to replace the glass carafe”
with the following design problem scenario:
“A company wants to save the manufacturing cost of a glass carafe, so the design
task for their product development department in the company is to improve the
current coffee maker design with using a common coffee mug to replace the glass
carafe. All the functions in the original design are required in the new design.”
6.2.2 The Re-Engineering Results
To resolve the problem, the design should be analyzed into design matrix. Since
the paper provides the clear structure of the DP hierarchy, the FR hierarchy can be
directly generated according to the DP hierarchy. First, it is reengineered according
to the DP hierarchy referenced from Gershenson’s paper. It is a bottom-up process.
The FRs were generated from the fourth layer (Figure 6.14-6.16) and then reverse-
engineered up till the first layer.
Figure 6.14 The DP hierarchy of DP1 and the FRs at layer 4.
99
Figure 6.15 The DP hierarchy of DP2 and the FRs at layer 4.
Figure 6.16 The DP hierarchy of DP3 and the FRs at layer 4.
100
At layer 4, the FR-DP relationship at layer four was further identified as a
23FRs- 26DPs design matrix as shown in Figure 6.17. Then the corresponding FRs
and the design matrices from layer 3 to 1 are shown in Figure 6.18 to Figure 6.20.
Therefore, the overall design concept was examined.
Figure 6.17 The design matrix of the coffee maker at layer 4.
101
Figure 6.18 The design matrix of the coffee maker at layer 3.
Figure 6.19 The design matrix of the coffee maker at layer 2.
102
Figure 6.20 The design matrix of the coffee maker at layer 1.
From the above results, the design concept overall is functionally coupled
although it is already production modular.
6.2.3 The Conceptual Design with ADT and TRIZ
To achieve the target task, the designer needs to obtain the execution sequence
from design matrix. To improve the design concept by using ADT with TRIZ, the
design matrix can only be square. Since only the first layer DM is square, the
improvement started from the first layer. As shown in Figure 6.20, the design is a
coupled design before design matrix arrangement. After the arrangement by Suh’s
method, the design is still a coupled design with the extra coupling at FR
2
-DP
1
. The
elimination of the extra coupling couldn’t apply directly since the concept is too
abstract at layer 1 to understand the coupling.
103
Figure 6.21 The design matrix of the coffee maker at layer 1.
The FR-DP relationship across layers was traced till layer four to obtain the
specific enough functional coupling, FR
2116
-DP
1211
(Figure 6.22). To set 17-
Temperature as undesired conflict and 8- V olume of stationary object as improved
target, the design was improved as a carafe with a metal bottom and contact to be
heated by the electricity from the heating unit. The design is as shown in Figure 6.23,
and the design was improved with a new design matrix as shown in 6.24.
Figure 6.22 The extra coupled FR-DP in the coffee maker design at layer 4.
104
Figure 6.23 The improved coffee maker by extra coupling elimination.
Figure 6.24 The design matrix at layer 1 of the original and improved coffee maker.
The execution sequence can be obtained as DP
3
DP
2
DP
1
. Since glass
carafe is at the end of the sequence, there is no way to improve the design from
previous method only if the designer applies the DCS strategies. However, the
concept at layer 1 is too abstract to improve on one hand, and one can not apply ADT
on rectangular design matrix to work on detailed design concepts on the other hand,
the designer can not use ADT with TRIZ to improve the design for achieving the
design task.
105
6.2.4 The Conceptual Design with DCS
The DCS method can directly work on rectangular DM at layer 4. The applied
results are shown in Figure 6.25. There are six U-sets (i.e., U
I
to U
VI
) and two C-sets
(i.e., C
I
and C
II
) according to the DCS method. The sets are proved by design matrix
rearrangement (Figure 6.26). Then designer can obtain the execution sequence such
as the sequence shown in Figure 6.27. The U sets are functionally independent from
each other, therefore any order between them is an acceptable sequence Similarly,
the independent branches in a U-set can also be randomly ordered within each other.
Figure 6.25 The DCS sets in the coffee maker design.
106
Figure 6.26 The DM rearrangement with modular clusters by DCS in the coffee maker
case.
Figure 6.27 One of the execution sequence for the coffee maker case.
By following the execution sequence, the design strategy was the strategy 3 to
examine the design change for the replacement of DP
1211
: DP
1211
- Carafe changes to
DP
1211
*
- Coffee mug. Some of the DPs including DP
1411
- Plastic Handle, DP
1511
-
Metal Band, DP
1111
- Plastic Insert, and DP
1311
- Screw were eliminated according the
change. Since the design relationship remained the same, one can directly use the
107
execution sequence in Figure 6.27. By following the sequence, DP
2222
was first
changed with two options as shown in Figure 6.28. The DP
2222A
was selected because
of the cost and the coffee taste. Also, DP
2116
was changed correspondingly, and the
options are shown in Figure 6.29. The DP
2116A
was selected because it is easy to
manufacture. Other DPs in the sequence are remain the same. The final design result
in Figure 6.30 was designed to achieve the design task.
Figure 6.28 The options for DP2222 swivel filter cup design.
Figure 6.29 The options for DP2116 heating plate design.
Figure 6.30 The design result by DCS approach.
108
6.2.5 Discussions
The major design changes via DCS method are the heating plate and the filter
cup to achieve the concept improvement task. If observing the design concept that
uses two mugs, the design result is also similar to have the major changes of the
heating plate and the filter cup (Figure 6.31). This can be explained that the
execution sequence is useful in the set U
I
, an independent set identified by DCS.
While other DPs in other sets change to satisfy more FRs, the basic design for using
a coffee mug is remain the same changes (i.e. the change of the heating plate and the
filter cup). In Figure 6.32, the coffee maker design is added a grinder module, and
the heating plate and the filter cup are having the same choices as the presented
design. Similarly, compare to the presented design, the espresso coffee maker is also
with the change of the heating plate and the filter cup for the set U
I
. Therefore, DCS
sets increase the modularity of the design.
Figure 6.31 The design of the coffee maker with two mugs.
Figure 6.32 Different coffee makers with similar design improvement for using mug.
109
6.2.6 Summary
The coffee maker design concept can be created by reengineering, but the design
is a coupled design. The design task can be done through DCS strategies, and the
DCS sets increased the modularity in this case.
6.3 A Complex Design Case: The Product Development of PCR Tire
The empirical case study of a PCR tire improvement for the MAXXIS company
is investigated as the third case study. This case employed Innovative Design
Thinking as its design framework and the DCS method with strategies to show the
application onto a complex and dynamic design case.
6.3.1 The Objectives of the Case Study and the Case Introduction
The tire is a complex high-tech product which plays a very important role in the
modern transportation industry. As global market demands for mobility expand, the
functional requirements of tires, such as safety, comfort, sustainability, and
affordability are also increasing. For example, a tire must be able to transmit
longitudinal and lateral forces under various manoeuvre and weather conditions to
assure reliable and safe road handling. These wide-ranging functional requirements
often force tire engineers to settle for compromises among competing performance
goals. Fig. 6.33 shows performance compromises under wet breaking conditions for
tires – e.g., an improvement in the tread compound can affect tire life, rolling
resistance, and ride comfort.
110
Figure 6.33 Tire Performance Compromises Under Wet Breaking Conditions.
To compete on diverse market segments that have different functional
requirements, using benchmark results with competitions to trade-off performance
targets has been a common practice in the tire industry today. Engineers often must
rely on their experiences to carry out these trade-offs by the trial-and-error approach,
which is ineffective, expensive and time-consuming. Even if an acceptable trade-off
for the current market is found, it will quickly change due to dynamic market
conditions. Short of an ideal “one-for-all” tire design, companies need to have better
ways to develop and improve such an important product to sustain market
competitions. This is the main motivation for us to apply the IDT framework to
improve Passenger Car Radial (PCR) tires in this case study.
To begin with, it is important to note that performance compromises of a product
are often the direct result of the functional couplings exist in its design concept. In
other words, functional couplings in the upstream functional (FR) domain are the
root cause of performance compromises in the downstream physical (DP) domain.
111
Finding resolutions at the source (or cause) from upstream is always a better strategy
that can yield more improvements than just simply seeking compromises of the
result (or consequence) at downstream. Therefore, rather than manipulating PVs or
DPs of the products to trade-off their performance targets, our approach focuses on
the existing functional couplings (i.e., FRs, and how they relate to DPs) of current
design concepts to reduce their system complexities. To do so, we must first find the
functional schematics of the product’s design concept to determine a proper
improvement strategy. Since existing PCR tires are not previously designed by the
IDT framework, their functional schematics are not directly available and must be
carefully reengineered to begin the improvement process. As well, because a
complete redesign of current PRC tires (by eliminating some existing functional
couplings, for example) is deemed to be impractical because it requires major
changes of production facilities, our solution focuses on finding better execution
sequences of DPs based on how they relate to FRs to minimize the functional
couplings of current PCR tires for their improvements.
6.3.2 The Problem Statement
Our application follows the IDT framework (explained in Section 2.1.2) to
formulate the concept improvement problem for current PCR tires, and uses the DCS
method to find the best execution sequences of functional couplings in existing
design concepts. The first step is to carefully reengineer the functional schematics
of the existing design concept from current PCR tires.
112
Per “Regulation (EC) No 1222/2009 on the labelling of tyres” (the European tyre
labelling regulations of the European Commission) (European Commission, 2012),
the rolling resistance (RR) coefficient must reach the Grade A fuel efficiency label.
However, meeting this performance target to satisfy the fuel efficiency requirement
will inevitably influence other performance targets, such as wet braking (WET,
which must maintain the level of wet grip class B of Euro Labelling) and wear
mileage (WEAR, which must be more than 40000 km), which will negatively impact
on other important functional requirements, such as safety, etc. In other words, the
performance targets of RR, WET, and WEAR are intrinsically tangled in current
PCR tires, making simultaneous satisfaction of multiple functional requirements
very difficult in practice. As well, other practical considerations, such the production
mold can’t be changed (i.e. tires must maintain the same profile and pattern) for
obvious economic reasons, further constraint the possibility for improving PCR tires.
Our goal is to use IDT and DCS to improve PCR tires’ RR to satisfy the main
functional requirement of fuel efficiency with minimal negative impacts on WET
and WEAR, so that other important main or sub-functional requirements will not be
violated. In this study, we assume that changing RR will only influence WET and
WEAR, and no other performance targets (and their corresponding FRs) will be
effected.
6.3.3 The Traditional Tire Improvement Method
PCR tires are the most important product category in the tire industry because of
their large market shares and stable profitability. Our study is based on the current
113
PCR tires produced by MAXXIS, the 9
th
largest tire producer in the world with active
presence in multiple global markets. The typical performance targets of PCR tires
include:
1. Rolling Resistance (RR), defined as the energy consumed by a tire per unit of
distance covered. It influences the vehicle’s fuel consumption directly.
2. Wet Braking (WET), representing the tire’s ability to brake on the wet ground.
It ensures the safety of the vehicle running in wet weather conditions.
3. Dry Braking (DRY), representing the tire’s ability to brake on the dry ground.
It ensures the safety of the vehicle running in dry weather conditions.
4. Comfortability, typically evaluated by measuring the tire’s noise, vibration,
and harshness characters during operating.
5. Wear Mileage (WEAR), denoting the maximum mileage of a tire before it is
totally wearing out. It corresponds to the mileage that a vehicle can travel, and
influences the economics of tires.
6. Durability, referring to the structural integrity of the tire in actual service.
Since PCR tires have existed in the global market with high demands for a long
time, they constantly face severe competitions, such as shorter life cycles, more
functional requirements, higher performance targets, and lower usage costs. In our
study, we denote these competitive factors of PCR tires, respectively, as: CNs for
market demands, FRs for functional requirements, PDs for performance targets
(because performances can only be known after DPs are known), and PVs the
product costs (because costs can only be determined after PVs are fixed). To develop
a complete new tire, the task typically starts from upstream to downstream (i.e., from
CNs, FRs, DPs, to PVs); however, to improve an existing tire, this task must follow
114
a reversed order from downstream to upstream (i.e., from costs, performances,
functions, to demands). Since PCR tires are been commoditized quickly, costs
(determined by PVs) have always been an overarching factor constrained by market
competitions. Given this principal constraint, engineers are asked to improve some
performance targets (determined by DPs) while maintaining others to make products
more competitive on the market. Thus, their main focuses are often limited to DPs
and PVs in the physical domain, without paying much attentions to FRs in the
functional domain and how FRs and DPs are related to each other (i.e., the design
concept), which play the most critical role in the competitiveness of products. The
case study described below explores this missing opportunity to better improve PCR
tires.
As noted before, current PCR tires are based on highly coupled and/or decoupled
design concepts with strong, but unknown, functional dependencies between FRs
and DPs. In other words, the design concept and corresponding functional
schematics of current PCR tires is a complex “black-box” which makes their
developments and improvements very difficult. To improve these products, we need
to open this “black-box” so that the complexity of their design concepts can be
strategically reduced and managed.
6.3.4 The Application Results by DCS
The problem was resolved by using the IDT framework and the DCS approach
with DCS strategies. The results were collected through the DCS concept refinement
115
strategy, DCS design change with DM change, and the DCS design change without
DM change.
First of all, the reengineering through IDT framework was implemented. To
reengineer the functional schematics of existing design concepts from current PCR
tires, we first identify a set of 11 PVs that are deemed by tire engineers to be most
relevant to our goal of improving fuel efficiency. Then, based on extensive
discussions among tire engineers, these PVs are carefully mapped backward to their
corresponding sub-sub-DPs at the same abstraction layer. Next, the 11 sub-sub-DPs
are carefully grouped upward into 4 main sub-DPs, each of which is then mapped
horizontally in the reverse direction to a corresponding sub-FR in the functional
domain. Note that all sub-sub-DPs and sub-DPs are in the same hierarchy in the
physical domain with different abstraction layer, whereas sub-FRs are in a different
hierarchy in the functional domain. This reengineering process is illustrated in
Figure 6.34 and the details of all PVs, DPs and FRs parameters are listed in Table
6.2.
Figure 6.34 The reengineering process of PCR tires.
116
Table 6.2 The list of PVs, DPs, and FRs.
PVs Sub-Sub-DPs Sub-DPs Sub-FRs
PV
1
: F723
DP
11
: New Cap-
ply
DP1: New Cap-ply
FR1: to be small
shape change
FR2: to be light
weight
PV
2
: TV23
DP
21
: Belt
diameter DP2: Line diameter
(decrease)
FR2: to be light
weight
PV
3
: P830
DP
22
: Ply
diameter
PV
4
: Body-ply
thickness A mm
DP
31
: Body-ply
rubber thickness
DP3: Rubber
thickness
(decrease)
FR2: to be light
weight
FR3: to cool
quickly
PV
5
: Belt
thickness B mm
DP
32
: Belt
rubber thickness
PV
6
: Cap-ply
thickness C mm
DP
33
: Cap-ply
rubber thickness
PV
7
: NSB
thickness D mm
DP
34
: NSB
thickness
PV
8
: #304T1
DP
41
: Tread
formula
DP4: Low thermal
formula
FR4: to be hot
hardly
PV
9
: #345
DP
42
: Wing
formula
PV
10
: #229
DP
43
: Cap-ply
formula
PV
11
: #217
DP
44
: Belt
wedge formula
The numeric design matrix of the design as shown in Figure 6.35 was provided
by the engineers in MAXXIS company. The execution sequences for this design
concept is: {DP
1
, DP
4
} → DP
3
→ DP2 for the numerical DM, and {DP
1
,
DP
4
}→{DP
3
, DP
2
} if it’s converted to be binary. No matter the execution sequences
117
from numerical DM or binary DM, it indicated {DP
1
, DP
4
} is a C-set that needs to
be improved first together.
Figure 6.35 The numerical DM for RR design.
Taking {DP
1
, DP
4
} as a set with the strong coupling (Figure 6.36) to design the
low rolling resistance tire matches the design result from the Car Advice report
(2009) for the Hankook low RR tire (Figure 6.37).
Figure 6.36 Tire construction.
118
Figure 6.37 A Low Rolling Resistance Tire Design Result from Hankook (2009).
The strategy for design change with DM change was implemented due to the
WET performance was reduced due to the reduction of RR. The new FRs-DPs are
shown in Table 6.3 expanded DM as shown in Figure 6.38 was used for this task.
Table 6.3 The new FRs and new and changed DPs.
FRs DPs
FR5: to drain
DP5: Pattern void ratio
DP6: Tread profile
FR6: to break water
membrane
DP7: Sipe density
FR7: to grip wet road DP8: Wet grip formula of tread
Re-identified DPs: DP4: Low thermal formula of carcass
Figure 6.38 The design matrix for RR + WET design.
119
Then the improvement strategy 2 was applied in the manner of partial design.
The DP
5
, DP
6
, and DP
7
were eliminated due to the task. The result of the execution
sequence is DP
8
→ {DP
1
, DP
4
} →DP
3
→DP
2
. The result illustrates the reason that
the fail of WET constraint in the past improvement due to the selection of DP
8
. The
DP
8
: Tread wet grip formula should be improved first to better satisfy the sub-
functions of WET before improving the DPs for the RR.
6.3.5 The Application Results by the Traditional Method
The other engineer team in the factory was also solving the same case by the
traditional method. After many trial and error process and several iterations of the
design improvement cycle, the final design passed the test. The spider diagram
(Figure 6.39) displays six test items, and the red and green line are the test results
for the old and new design. Although the performance of dry braking which was not
considered in this case was slightly decreased, it was still acceptable within the
tolerance of 3%. The adjustment of the final design via the traditional method was
also on the DP
8
and DP
4
, which matches the DCS result.
Figure 6.39 Test result.
120
6.3.6 Discussions
The results showed that it could be feasible to use the DCS in the case of the tire
improvement because it matched the final design of the traditional method, and it
can save the cost and time from trial and error. However, in practice, the arrival time
of the raw materials are different such that some DP may not be able to follow the
improvement order from DCS; otherwise, the improvement may need to stop
temporarily until the arrival of the needed material of the improving DP.
To assess the waiting time and the trial-and-error time, the time line of the product
development should be considered. If the change of the DP is imperative, the final
design from the traditional method must come out after the arrival of the material of
the DP. Designers may do another design project during the waiting time or may
have a rest to keep their brains clearly. Therefore, using DCS is still better than using
the traditional method in the perspective of saving time and cost.
However, in industry, the project manager or the company executer
psychologically doesn’t allow the progress stop temporarily. Also, the arrival time is
usually predictable. To be better to apply to the industrial product improvement, it
would be better to have a strategy for dealing with the problem of the material arrival
time in the method of IDT-DCS.
6.3.7 Summary
The PCR tire design demonstrates the application of IDT-DCS on an existing
product. IDT helped designers identify the system elements and their relationships
121
gradually and clearly from downstream to upstream, and DCS provided strategies
and the DP improvement order for designers to follow. The application results show
that the IDT-DCS enabled designers improve the partial system for the targeted FR,
and the numerical DCS sequences in the case provided more detailed information
than the binary ones did. In addition, the suggestion of the improvement order from
IDT-DCS matches the final design after many trial-and-errors from the traditional
method. This shows the DCS approach would be feasible in the use of industrial
product development.
In summary, the benefits of our approach are 1) providing a logic and systemic
way for designers to follow, 2) avoiding the waste of time and cost, 3) helping
designers construct system schematics as a common language for current and future
improvement.
6.4 An Extended Application: Collision Avoidance Planning Strategy
The case of the object interaction planning problem among multiple objects was
investigated in this section. The study exhibits one of the possible extensions of the
DCS method.
6.4.1 The Objectives of the Case Study and the Case Introduction
The multi-object problem is common in many engineering domains. For
example, the proper planning of such a problem is becoming increasingly important
as more autonomous vehicles and drones are creating many severe safety-related
challenges. Although the California government allowed some autonomous car on
the road, it stipulated that a licensed driver is required in the vehicle (California
122
Department of Motor Vehicles, 2016). In fact, such a planning problem is too
complex to comprehensively resolve, even though it is just a 2-dimensional problem
(Hopcroft, et al., 1984). Many researchers have developed different methods and
algorithms to solve these complex problems (Katrakazas, 20115; Cáp, 2015; Vieira,
2016). Instead of attempting to solve the entire problem directly, our research has
focused on reducing the complexity of strategic planning tasks for these problems
during the conceptual design stage. This is because that, as early as during the
conceptual design stage, more than 70% of the total costs and performance of a
typical engineering system is determined (Zimmer and Zablit, 2001).
This section presents the special application of DCS, which is an application to a
multiple object problem in the conceptual design stage via IDT framework to reduce
the complexity of the problem so that a real-time reaction of a controllable object
can be properly planned among multiple objects.
6.4.2 The Problem Statement
A controllable object X is surrounded by multiple uncontrollable objects O in a
system. The goal is to plan the behavior of X, called B
x
, in advance so that it can
properly react to the behaviors of O, called B
o
, such as to avoid collision with O, or
to catch O. The behavior of X, i.e., B
x
, is defined by a combination of a series of
actions (a
i
), i.e., B
x
=f (a
1
, a
2
, …, a
n
) selected from a group of action sets A
1
, A
2, …,
A
n
, where a
i
∈ A
i
, and each action sets are independent of other action sets so that X
is able to perform many actions at the same time.
123
It is further assumed that, at every sampling time t, a batch of surrounded objects
O = {O
1
,O
2
, …, O
m
} can be uniquely detected, and the behaviors of each object O
i
at the next sampling time t+1, B
i
, can be predicted at time t. In other words, a
predictive behavior set B = {B
1
,B
2
, …, B
m
} is also known at time t. For the object
X, to properly react at time t+1 with each O
i
whose next behavior is B
i
, some specific
actions with the constraint c
i
should be chosen from some action sets A. Since the
each possible behaviors B
x
corresponding to the different objects are different and
complex, to determine a proper reaction plan with multiple objects O for the object
X during each sampling time interval t to t+1 is a challenging problem.
This problem can be regarded as a multi-object problem for an autonomous
vehicle X. First of all, the possible actions A of X can be categorized to A
1
= to turn
{left, right, straight}, A
2
= to change lever {forward, backward, neutral, park}, A
3
=
to change speed {increase, decrease, hold}, A
4
= to light up {left turn, right turn, side,
head, tail, eyeline, backup, brake, fog}, A
5
= to horn {on, off}. To form the behavior
of the controlled autonomous vehicle by picking up one action in each category, the
behavior B
x
could be f(straight, forward, decrease, brake, null) to behave as a speed-
decreasing vehicle, and this may avoid the collision with the front car which is
decreasing its speed. In the practical case, the autonomous vehicle X is required to
promptly react to many objects in different manners. At each sampling time, it
perceives many surrounded objects, and these are O. To react with different objects,
the behavior may vary. According to their current behaviors, it is not difficult to
predict at what position in what speed that those objects would be in the next
moment, hence B is formed. For example, it may perceive an approaching vehicle
from behind, a leaving vehicle at front, a walking person approaching from right,
124
and a green traffic light, so the proper reaction to the vehicles and the person is to
avoid collision and to the green light is to move forward; however, the autonomous
vehicle X can only behave one behavior at a time, so to properly react to every
detected object in real-time is the problem.
6.4.3 The Problem Formulation
This section explains how we can use our Innovative Design Thinking (IDT)
framework to formulate the above strategic planning problem as a conceptual design
problem. To do so, the first step is to clearly identify a set of functional requirements
(FRS) and their associated design parameters (DPs) and then defined the possible
interdependencies between FRs and FRs with DPs. Recall that the main task is to
plan the behavior B
x
of an object X in advance at each sampling time t, so that it can
properly react with O={O
1
,O
2
, …, O
m
} at every moment. Therefore, the main
functional requirement (FR) of the planning for the object X is to properly react with
O in the system. To further decompose the FR, one can identify m FRs, such as FR
1
:
to react with object O
1
whose behavior is B
1
, FR
2
: to react with object O
2
whose
behavior is B
2
, …, FR
m
: to react with object O
m
whose behavior is B
m
(Figure 6.40).
Figure 6.40 The FR hierarchy.
FR: To properly react
with every object O
in the system
FR
1
: To properly react
with object O
1
whose
behavior is B
1
FR
2
: To properly react
with object O
2
whose
behavior is B
2
FR
m
: To properly
react with object O
m
whose behavior is B
m
…
125
Then following the steps of IDT which use design steps from the Axiomatic
Design Theory, to satisfy the main FR, the proper behavior of X is the main design
parameter (DP). By decomposing the main DP, the DPs are the independent action
sets A
1
, A
2, …,
A
n
(Figure 6.41). However, on the most occasions, this is not a simple
1-on-1 mapping between FRs and DPs (m FRs and n DPs) so that each FR may be
satisfied by more than one DP.
Figure 6.41 The DP hierarchy.
6.4.4 The Application Approach
The known information is the X’s actions, and O and B will be obtained at each
sampling time t, and the m-by-n design matrix can be formed accordingly. The steps
of the planning strategy are as following:
(1) Set X’s actions to be independent action sets A
1
, A
2, …,
A
n
(2) Obtain O and B at each sampling time t
(3) Construct the design matrix, and list the constraint c
i
={c
i1
, c
i2
, …, c
in
}
corresponding to the elements of i row for each action.
(4) Obtain DCSs.
DP: A proper
behavior of X
DP
1
: A
1
DP
2
: A
2
DP
n
: A
n
…
126
(5) Follow the order of DCS to determine a proper action a
i
in each A
j
by
examining the intersection between the constraint c
1j
∩c
2j
∩c
3j
∩…∩c
mj
for A
j
.
(6) Combine the actions to determine B
x
(7) At time t+1, behave B
x
and return to step (2)
The flow of the planning steps is shown in the Figure 6.42.
Figure 6.42 The flow chart of the planning strategy.
6.4.5 The Application Example and the Results
To clearly explain the strategy, an example of the autonomous vehicle safety
problem mentioned in the section 6.4.2 is used here.
(1) The action sets A of the controlled autonomous vehicle X has set as A
1
= to turn
{left, right, straight}, A
2
= to change lever {forward, backward, neutral, park},
A
3
= to change speed {increase, decrease, hold}, A
4
= to light up {left turn, right
turn, side, head, tail, eyeline, backup, brake, fog}, A
5
= to horn {on, off}.
The multi-object problem
Set A
Obtain O & B
Construct DM with c
Obtain DCS
Follow DCS to decide a
Form Bx and act
t = t+1
at time t
127
(2) It is assumed that the sampling time is 1 second, and at time t, the X is at a speed
of 25 mph moving forward, and four objects are detected O={O
1
, O
2
, O
3
, O
4
}.
These are two vehicles O
1
and O
2
, a walking person O
3
, and a traffic light O
4
.
The predictive behaviors are listed in Table 6.1.
(3) To construct DM with c, the functional requirements are listed first in Table 6.4,
and the design parameters DP
1
, DP
2
, DP
3
, DP
4
, DP
5
are the action sets A
1
, A
2
, A
3
,
A
4
, A
5
. So, the design matrix is constructed in Table 6.5. The constraints c is also
listed in Table 6.4.
Table 6.4 Predictive behaviors of O.
O B
O
1
B
1
: It is approaching in a relative speed -5 mph from the back, and the
relative distance will be -5 ft next second.
O
2
B
2
: It is leaving in a relative speed 10 mph at the front, and the relative
distance will be 50 ft next second.
O
3
B
3
: It is approaching in a relative speed 2.5 mph from right, and the
relative distance will be -1 ft next second.
O
4
B
4
: It is still green next second.
Table 6.5 Functional requirements of X.
FR
1
To avoid collision with O
1
FR
2
To avoid collision with O
2
FR
3
To avoid collision with O
3
FR
4
To follow the traffic rule from the signal of O
4
DP 1 DP 2 DP 3 DP 4 DP 5
FR 1 X X X X O
FR 2 O X X O O
FR 3 X X X O X
FR 4 O X O O O
Figure 6.43 The design matrix of the avoidance situation.
128
Table 6.6 The constraints corresponding to the design matrix elements.
DM c
DM
11
Choose to left or right turn in an angle larger than 45 degrees if going
straight is not possible.
DM
12
To go forward. The backward, neutral, and park are not allowed.
DM
13
To increase speed more than 3.5mph. The decrease and hold are not
allowed.
DM
14
To light up the turn signal if turn left or right.
DM
22
To go forward when the acceleration won’t exceed 16m/s
2
. The
backward, neutral, and park are okay.
DM
23
To increase speed no more than 34mph. The decrease and hold are
okay.
DM
31
The right turn is not allowed. Choose to left turn in an angle larger
than 10 degrees if going straight is not possible.
DM
32
To go forward when the acceleration exceeds 4 m/s
2
or the
deceleration exceeds 1m/s
2
. The backward, neutral, and park are okay.
DM
33
To increase speed more than 3mph or to decrease more than 0.7mph.
Hold is not allowed.
DM
35
To horn.
DM
42
To go forward. The backward, neutral, and park are not allowed.
(4) The DCS in this case is
Row Sequence
1
𝐷𝑃
2
→𝐷𝑃
3
→𝐷𝑃
1
→𝐷𝑃
4
2
↘ 𝐷𝑃
5
(5) Following the DCS, each DP can be determined as in Table 6.6.
(6) The combination of the actions, the B
x
is f(straight, forward, increase 4 mph,
NULL, horn on), which means the autonomous vehicle X plans to go straight
forward at a speed of 29 mph and honking.
(7) At next second, the X go straight forward at a speed of 29mph and honking, and
new O and B obtained.
129
Table 6.7 The decisions for the DP.
Order Decisions
DP
2
a
2
: forward.
(Only the forward is allowed)
DP
3
a
3
: to increase speed 4 mph.
(The increased speed should be between 3.5mph to 34mph)
DP
1
a
1
: straight.
(Go left won’t choose because go straight is okay.)
DP
4
*
a
4
: NULL.
(No left or right turn is chosen, so there is no action acting in this action
set.)
DP
5
*
a
5
: horn on.
* DP5 can be determined before DP4.
Obviously, this strategy made the coupling problem decoupled, and easily to
determine the next behavior of the controlled autonomous vehicle. That is because
the IDT framework set the problem in the conceptual design to formulate the
problem from upstream to downstream, and the DCS enables the system range to
match the design range in a decoupled execution sequence.
6.4.6 Summary
The case shows the possible extension of the DCS algorithm applied to different
subject. The planning result seems acceptable in this multi-object planning problem.
Further assessment is required.
6.5 Conclusions, Limitations, and Future Extensions
A mechanical design such as the faucet design in the study can be improved well
by using DCS approach. But also, with the IDT framework and the DCS strategies,
130
the DCS sets enable to be applied onto the complex industrial mechanical design
case as the PCR tire design case providing the systematic simple guidance.
In short, it is possible to apply DCS to any kind of designs because the limitations
of the existing methods such as design coupling types, matrix size, and the numbers
of FRs and DPs are not problems at all when applying DCS approach.
131
Chapter 7. Summary, Contributions, and Future Works
7.1 Summary
The research prescribes a functional coupling managing algorithm with
functional sets for suggesting acceptable execution sequences in conceptual design.
The complete research includes DCS sets, DCS algorithm, and DCS strategies. DCS
sets define the functional sets to increase modularity. DCS algorithm extract
precedence information from the design matrix for generating the execution
sequence, which can lead to the minimal relative complexity. DCS strategies provide
strategic guidance for designers to use the execution sequence when facing different
concept improvement tasks. It not only helps designers with complexity reduction
but also bridges the ideal design theory to practical modules. The designer can create
better designs that are most creative and yet practical by using the DCS strategies.
7.2 Contributions
There are theoretical and practical contribution in this research.
For the theoretical contribution, it is a more general method, and DCS can apply
to any design type. The design matrix type includes square, rectangular, zero-at-
diagonal, large, and/or numerical matrices. It also shows the ability of design matrix
rearrangement. In addition, the research approach uses functional sets to find the
execution sequence for minimizing both real and imaginary complexity. The DCS
approach guides designers to improve concepts not only organizing design matrix
but also extract additional coupling information to increase modularity.
For the practical contribution, DCS functional sets helps concept improvement
132
by using “independent U-set” and “coupled C-set”. Because of the sets, the concept
can be improved partially rather than redesign the whole design so that the method
can be applied to practical cases. Also, the research demonstrates the usability of the
DCS algorithm within an executive program to generate the DCS functional sets
automatically for large design system. Moreover, the concept improvement
strategies are useful for practical design cases. The research demonstrates the
feasibility and usability of the DCS strategies in practical design cases.
It is a fundamental contribution that demonstrates how the ideal principles (or
axioms) of design theories can be used together strategically with practical design
methods (or considerations) in industry practices to generate real-world design
results that are both most practical and creative.
7.3 Future Works
There are three possible extensions of this research as our future works in the
following aspects: DCS algorithm, DCS sets, DCS strategies
For DCS Algorithm, it would be further revised to extend to software design or
machine learning with functional sets in terms of a component diagram. For the new
Form of DM with DCS sets, the 3D design matrix would be further investigated and
assessed for showing the functional schematics. For DCS strategies, it would be able
to use in the detailed design case because it can also work with numerical design
matrix.
133
Works cited
Allison, J. T., 2004, “Complex System Optimization: A Review of Analytical Target
Cascading, Collaborative Optimization, and Other Formulations.” Master
Thesis, University of Michigan.
Bartolomei, J., Cokus, M., Dahlgren, J., de Neufville, R., Maldonado, D., & Wilds,
J., 2007, “Analysis and applications of design structure matrix, domain
mapping matrix, and engineering system matrix frameworks.” Massachusetts
Institute of Technology.
Benavides, E. M. and Rodriguez, L. G., 2011, “Extended Algorithm for Design-
Matrix Reorganization.” Proceedings of 6th International Conference on
Axiomatic Design, Daejeon, 30-31 March 2011, pp. 20-26.
Blanchard, B.S. and Fabrycky, W.J., 1990. “Systems engineering and analysis.” (V ol.
4). New Jersey, Prentice Hall.
California Department of Motor Vehicles, “Autonomous Vehicles in California-
Autonomous Vehicles Regulations Summary,”
http://dmv.ca.gov/portal/dmv/detail/vr/autonomous/auto.
Cáp, M., Novák, P., Kleiner, A. and Selecky, M., 2015. “Prioritized planning
algorithms for trajectory coordination of multiple mobile robots.” Automation
Science and Engineering, IEEE Transactions on, 12(3), pp.835-849.
Car Advice, “Hankook Enfren Low Rolling Resistance Tyre Launch”,
https://www.caradvice.com.au/32036/hankook-enfren-low-rolling-resistance-
tyre-launch/.
Chikofsky, E.J. and Cross, J.H., 1990. Reverse engineering and design recovery: A
taxonomy. Software, IEEE, 7(1), pp.13-17.
Danilovic, M. and Brown, T., 2007, “Managing complex product development
projects with design structure matrices and domain mapping matrices.” Int. J.
Project Manage, vol. 25, pp. 300–314.
Demaine, E.D., Demaine, M.L., Eisenstat, S., Lubiw, A. and Winslow, A., 2011,
134
“Algorithms for solving Rubik’s cubes.” In Algorithms–ESA 2011 (pp. 689-
700). Springer Berlin Heidelberg.
Finger, S. and Dixon, J.R., 1989. “A review of research in mechanical engineering
design. Part I: Descriptive, prescriptive, and computer-based models of design
processes.” Research in engineering design, 1(1), pp.51-67.
Gershenson, J.K. and Prasad, G.J., 1997. Modularity in product design for
manufacturability. International Journal of Agile Manufacturing, 1(1), pp.99-
110.
Gershenson, J.K., Prasad, G.J. and Zhang, Y ., 2003. Product modularity: definitions
and benefits. Journal of Engineering design, 14(3), pp.295-313.
Gershenson, J.K., Prasad, G.J. and Zhang, Y ., 2004. Product modularity: measures
and design methods. Journal of engineering Design, 15(1), pp.33-51.
Guo, D. “Simple Solution for Rubik’s cube.” http://www.davidguo.idv.tw/
cube/beginner2.html.
Hopcroft, J.E., Schwartz, J.T. and Sharir, M., 1984. “On the Complexity of Motion
Planning for Multiple Independent Objects; PSPACE-Hardness of the
Warehouseman's Problem.” The International Journal of Robotics Research,
3(4), pp.76-88.
Hsu, W. and Woon, I.M., 1998. “Current research in the conceptual design of
mechanical products.” Computer-Aided Design, 30(5), pp.377-389.
Jagdev, H., Bradley, P. and Molloy, O., 1997. A QFD based performance
measurement tool. Computers in industry, 33(2), pp.357-366.
Katrakazas, C., Quddus, M., Chen, W.H. and Deka, L., 2015. “Real-time motion
planning methods for autonomous on-road driving: State-of-the-art and future
research directions.” Transportation Research Part C: Emerging Technologies,
60, pp.416-442.
Kim, H.M., 2001, “Target cascading in optimal system design.” Ph.D. thesis, The
University of Michigan, Ann Arbor.
135
Kim, H. M., Michelena, N. F., Papalambros, P. Y . and Jiang, T., 2003, “Target
cascading in optimal system design.” ASME Journal of Mechanical Design,
vol. 125, pp. 474–480.
Lee, T., 2003, “Complexity theory in axiomatic design.” Doctoral dissertation,
Massachusetts Institute of Technology.
Lee, T., 2006, “Optimal Strategy for Eliminating Coupling Terms from a Design
Matrix.” Integrated Design & Process Science, V ol. 10, No. 2, pp. 45-55.
Lee, T. and Jeziorek, P. N., 2006, “Understanding the Value of Eliminating an Off-
Diagonal Term in a Design Matrix.” Proceedings of 4th International
Conference on Axiomatic Design, Florence, 13-16 June 2006.
Liu, A. and Lu, S. Y ., 2014, “Comparison of Questioning-based and Reasoning-
based Design Approaches.” Paper presented at 2014 ASEE Annual Conference,
Indianapolis, Indiana. https://peer.asee.org/20190.
Lu, S. C.-Y . and Suh, N. P., 2009, “Complexity in Design of Technical Systems.”
CIRP Annals- Manufacturing Technology, V ol. 58, No. 1, pp. 157-160.
Lu, S. C. Y . and Liu, A., 2012, “Abductive reasoning for design synthesis.” CIRP
Annals-Manufacturing Technology, 61(1), 143-146.
Liu, A. and Lu, S. C-Y ., 2013, “Impacts of Synthesis Reasoning on Ideation
Effectiveness.” ASME - Journal of Mechanical Design, 135(4):061009-11.
Liu, H., Chen, W., Kokkolaras, M., Papalambros, P. Y . and Kim, H. M., 2006,
“Probabilistic Analytical Target Cascading: A Moment Matching Formulation
for Multilevel Optimization Under Uncertainty.” ASME Journal of Mechanical
Design, vol. 128, pp. 991-1000.
Lu, S. Y ., ElMaraghy, W., Schuh, G. and Wilhelm, R., 2007, “A scientific foundation
of collaborative engineering.” CIRP Annals-Manufacturing Technology, 56(2),
605-634.
McNeill, T., Gero, J.S. and Warren, J., 1998. “Understanding conceptual electronic
design using protocol analysis.” Research in Engineering Design, 10(3),
136
pp.129-140.
Moen, R., and Norman, C., 2006. “Evolution of the PDSA cycle.” Retrieved
04.04.16 from http://deming.ces.clemson.edu/pub/den/deming_pdsa.htm.
Pahl, G. and Beitz, W., 1996, “Engineering design: a systematic approach.” 2
nd
ed.
Springer, London.
Pahl, G., Beitz, W., Feldhusen J. and Grote, K. H., 2007, “Engineering Design: A
Systematic Approach.” 3
rd
Edition, Springer, London.
Pimapunsri, K. and Tichkiewitch, S., 2013, “Integrated design approach for solving
complexity of design problem.” American Journal of Operations Research, 3
(1), pp. 138–146.
Rokicki, T., 2008, “Twenty-five moves suffice for Rubik's cube.” arXiv preprint
arXiv:0803.3435.
Saaty, T.L., 1986. “Axiomatic foundation of the analytic hierarchy process.”
Management science, 32(7), pp.841-855.
Saaty, T.L., 1990. “How to make a decision: the analytic hierarchy process.”
European journal of operational research, 48(1), pp.9-26.
Suh, N. P., 1990, “The Principles of Design.” Oxford University Press, New York.
Suh, N.P., 1999, “A theory of complexity, periodicity and the design axioms.”
Research in Engineering Design, 11(2), pp.116-132.
Suh, N. P., 2001, “Axiomatic Design.” Oxford University Press, New York.
Suh, N. P., 2005, “Complexity: Theory and Applications.” Oxford University Press,
Oxford.
Ulrich, K. and Seering, W., 1988. “Computation and conceptual design.” Robotics
and Computer-Integrated Manufacturing, 4(3), pp.309-315.
Vieira, M., Faria, D.R. and Nunes, U., 2016. “Real-time Application for Monitoring
Human Daily Activity and Risk Situations in Robot-Assisted Living.” In Robot
2015: Second Iberian Robotics Conference (pp. 449-461). Springer
International Publishing.
137
Wang, C.-Y. and Lu, S. C.-Y., 2014, “The Comparison of Three Different Reasoning
Approaches of Dual-Hierarchical Representation in Conceptual Design with
Computer-Aided Product and Process Development.” In: CIE Graduate
Research Poster Session, 34
th
ASME-CIE Conference, Buffalo, NY .
Wang, C.-Y ., Lu, S. C.-Y . and Liu, A., 2015, August. “Managing Functional
Coupling Sequences to Reduce Design Complexity during Concept
Improvements.” In ASME 2015 International Design Engineering Technical
Conferences and Computers and Information in Engineering Conference (pp.
V004T05A034-V004T05A034). American Society of Mechanical Engineers.
Wang, C.-Y . and S.C.-Y . Lu, “Managing Functional Coupling Sequence to
Modularize Design Concept.” In ICAD 2018- the 12th International
Conference on Axiomatic Design. (Submitted; Octobor, 2018).
Wang, L., Shen, W., Xie, H., Neelamkavil, J. and Pardasani, A., 2002. “Collaborative
conceptual design—state of the art and future trends.” Computer-Aided Design,
34(13), pp.981-996.
Zimmer, L. and Zablit, P., (2001), “Global Aircraft Predesign based on Constraint
Propagation and Interval Analysis.” Proceedings of CEAS Conference on
Multidisciplinary Aircraft Design and Optimization, Köln, Germany.
Abstract (if available)
Abstract
According to the Axiomatic Design Theory (ADT), a design concept that can satisfy the upstream objectives under downstream constraints with the minimal relative complexity can lead to the most ideal design. As stated by Suh’s Complexity Theory, the relative complexity of a design concept is caused by couplings between functional requirements (FRs) and design parameters (DPs), and can be reduced by strategically ordering the execution (i.e., implementation) sequence of DPs. However, it is generally very difficult in the current design practice to obtain this “execution sequence” with existing methods due to their inherent limitations and/or many real-world restrictions. Meanwhile, many practical methods, such as the modular design approach, have been widely used in industries to produce real-world design results that don’t necessarily conform with the principles required by those ideal design theories. As a result, from the perspectives of design theories, most real-world designs are “not ideal” (i.e., having some relative complexities due to FR-DP couplings) and therefore can (and should) be improved by better sequencing their DPs. This is the motivation under which the Design Coupling Sequence (DCS) method was developed in this thesis research. The DCS method can assist designers to automatically obtain the “execution sequences,” in the forms of functional sets, that can yield the minimal relative complexity, hence making a practical design concept most ideal (i.e., as close to the ideal concept with the minimal relative complexity as possible) while taking into practical considerations (such as increasing the modularity to lower the production costs) in real-world conceptual designs. ❧ The DCS method defines the ‘precedence’ between ‘functional sets’ to manage coupled design concepts to support the modular approach during conceptual design. It identifies the ‘precedence’ by the level of functional coupling to determine the proper sequencing order to minimize the overall complexity. Two types of functional sets are defined in DCS as 1) the complete independently set U: the collection of all the functionally dependent DPs in the system so that the set is independent to other U sets, and 2) the indivisible coupled set C: the collection of coupled concepts that can’t be decoupled by sequencing, so it prescribes the designer to consider the group of DPs together as a set to match existing modules in the database. To handle the real complexity of design concepts which require redesign, the DCS algorithm helps to determine the proper execution sequence. To minimize the imaginary complexity, which occurs when design concepts “appear” to be functionally coupled due to a lack of understanding of the system structure, the DCS method provides a formula to reveal the number of acceptable execution sequences that can lead to the simplest design implementation. Compared with existing methods, the DCS method is applicable for any design cases with known design matrices, including the square, rectangular, zero-at-diagonal, large, and/or numerical matrices. In short, for all practical design cases, DCS can organize functional-coupled design concepts as “functional sets” with execution sequences of DPs that lead to the minimal complexity of this design concept. ❧ The foundation, hypothesis, algorithm and its usability of the DCS method are validated by four case studies in this research. The faucet design case demonstrates how to apply the DCS method and shows the differences between ADT and DCS results. The case of coffee maker design shows how the DCS method manages the functional sets based on the design matrices reengineered from existing design concepts. The vehicle tire design case demonstrates how different DCS strategies within the Innovative Design Thinking (IDT framework during the conceptual design stage can work in a real-world product development situation. The IDT framework prescribes four consecutive steps: (1) following the top-down process to ideate new design concepts that satisfy the principles/axioms suggested by the design theory to reach a certain layer of details, (2) following the bottom-up process to identify some existing design modules from available engineering database (or catalogs) that can satisfy the functional requirements at this detail layer, (3) constructing the design matrix that shows the couplings between FRs and DPs at this detail layer, and (4) apply the DCS algorithm to determine the execution sequence of DPs based on the above design matrix. This will yield a new design concept with an execution sequence that is most creative (because it satisfies the design principles at the top layers) and most practical (because it utilizes the existing modules at the bottom layers). Finally, a case of collision avoidance planning presents one of the possible extensions of the DCS algorithm. ❧ The results of this research have significant impacts on both design theory and design practice. Theoretically, the approach in this research 1) guides designers to improve concepts not only organizing design matrix but also extract additional coupling information to increase modularity and 2) is a more generalized approach than the previous methods that can be applied to any design cases with design matrix. Practically, the research 1) demonstrates the usability of the DCS algorithm within an executive program to generate the DCS functional sets automatically for large design system and 2) allows the principle of functional dependency and the practice of modular design to be considered simultaneously as much as possible during the conceptual design stage. It is a fundamental contribution that demonstrates how the ideal principles (or axioms) of design theories can be used together strategically with practical design methods (or considerations) in industry practices to generate real-world design results that are both most practical and creative. For future research, there would be three aspects- DCS algorithm, DCS sets, and DCS strategies. Number one, DCS algorithm would be further revised to extend to software design or machine learning with functional sets in terms of a component diagram. Number two, with DCS sets, the three-dimensional design matrix could be studied further. Number three, DCS strategies would be investigated further for applying on detailed design cases. ❧ As a recap, the research prescribes a functional coupling managing algorithm with functional sets for suggesting acceptable execution sequences in conceptual design. It not only helps designers with complexity reduction but also bridges the ideal design theory to practical modules. The designer can create better designs that are most creative and yet practical by using the DCS strategies.
Linked assets
University of Southern California Dissertations and Theses
Conceptually similar
PDF
Building cellular self-organizing system (CSO): a behavior regulation based approach
PDF
A synthesis approach to manage complexity in software systems design
PDF
Design, modeling and analysis of piezoelectric forceps actuator
PDF
Large-scale path planning and maneuvering with local information for autonomous systems
PDF
Dynamic social structuring in cellular self-organizing systems
PDF
Radio localization techniques using ranked sequences
PDF
An approach to dynamic modeling of percussive mechanisms
PDF
Calibrating COCOMO® II for functional size metrics
PDF
Security-driven design of logic locking schemes: metrics, attacks, and defenses
PDF
Performant, scalable, and efficient deployment of network function virtualization
PDF
Transient modeling, dynamic analysis, and feedback control of the Inductrack Maglev system
PDF
Speeding up trajectory planning for autonomous robots operating in complex environments
PDF
Two-step study designs in genetic epidemiology
PDF
AI-driven experimental design for learning of process parameter models for robotic processing applications
PDF
Striking the balance: optimizing privacy, utility, and complexity in private machine learning
PDF
Metasurfaces in 3D applications: multiscale stereolithography and inverse design of diffractive optical elements for structured light
PDF
Electronic structure analysis of challenging open-shell systems: from excited states of copper oxide anions to exchange-coupling in binuclear copper complexes
PDF
Understanding diffusion process: inference and theory
PDF
Modeling and simulation of complex recovery processes
PDF
Toward understanding speech planning by observing its execution—representations, modeling and analysis
Asset Metadata
Creator
Wang, Chu-Yi
(author)
Core Title
Managing functional coupling sequences to reduce complexity and increase modularity in conceptual design
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Mechanical Engineering
Publication Date
08/10/2018
Defense Date
04/25/2018
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
complexity,concept improvement,conceptual design,functional coupling,modularity,OAI-PMH Harvest,sequencing
Format
application/pdf
(imt)
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Lu, Stephen (
committee chair
), Chen, Yong (
committee member
), Khoshnevis, Behrokh (
committee member
), Shiflett, Geoffrey R. (
committee member
), Yan, Jin (
committee member
)
Creator Email
chuyiwan@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c89-67231
Unique identifier
UC11670513
Identifier
etd-WangChuYi-6721.pdf (filename),usctheses-c89-67231 (legacy record id)
Legacy Identifier
etd-WangChuYi-6721.pdf
Dmrecord
67231
Document Type
Dissertation
Format
application/pdf (imt)
Rights
Wang, Chu-Yi
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Tags
complexity
concept improvement
conceptual design
functional coupling
modularity
sequencing