Complexity and modularity are important inherent properties of the system. Complexity is the property of the system that has to do with individual system elements and their connective relationship, while modularity is the degree to which a system is made up of relatively independent but interacting elements, with each module typically carrying an isolated set of functionality. Modularization is not necessarily a means of reducing intrinsic complexity of the system but is a mechanism for complexity redistribution that can be better managed by enabling design encapsulation. In this paper, the notion of integrative complexity (IC) is proposed, and the corresponding metric is proposed as an alternative metric for modularity from a complexity management viewpoint. It is also demonstrated using several engineered systems from different application domains that there is a strong negative correlation between the IC and system modularity. This leads to the conclusion that the IC can be used as an alternative metric for modularity assessment of system architectures.

References

1.
Arena
,
M. V.
,
Younossi
,
O.
,
Brancato
,
K.
,
Blickstein
,
I.
, and
Grammich
,
C. A.
,
2008
, “Why Has the Cost of Fixed-Wing Aircraft Risen? A Macroscopic Examination of the Trends in Us Military Aircraft Costs Over the Past Several Decades,” RAND National Defense Research Institute, Santa Monica, CA,
Report
.
2.
Newman
,
M. E. J.
,
2010
,
Networks: An Introduction
,
Oxford University Press
,
Oxford, NY.
3.
Lindemann
,
U.
,
Maurer
,
M.
, and
Braun
,
T.
,
2008
,
Structural Complexity Management: An Approach for the Field of Product Design
,
Springer
,
New York
.
4.
Weber
,
C.
,
2005
, “
What Is ‘Complexity’?
,”
15th International Conference on Engineering Design
(
ICED 05
), Melbourne, VIC, Australia, Aug. 15–18, pp.
15
18
.
5.
Sinha
,
K.
, and
Suh
,
E. S.
,
2018
, “
Pareto-Optimization of Complex System Architecture for Structural Complexity and Modularity
,”
Res. Eng. Des.
,
29
(
1
), pp.
123
141
.
6.
Barton
,
J. A.
,
Love
,
D. M.
, and
Taylor
,
G. D.
,
2001
, “
Design Determines 70% of Cost? A Review of Implications for Design Evaluation
,”
J. Eng. Des.
,
12
(
1
), pp.
47
58
.
7.
Braha
,
D.
, and
Bar-Yam
,
Y.
,
2007
, “
The Statistical Mechanics of Complex Product Development: Empirical and Analytical Results
,”
Manage Sci.
,
53
(
7
), pp.
1127
1145
.
8.
Maier
,
M. W.
, and
Rechtin
,
E.
,
2009
,
The Art of Systems Architecting
,
CRC Press
,
Boca Raton, FL
.
9.
Crawley
,
E.
,
Cameron
,
B.
, and
Selva
,
D.
,
2016
,
System Architecture: Strategy and Product Development for Complex Systems
,
Pearson
,
Boston, MA
.
10.
Baldwin
,
C. Y.
, and
Clark
,
K. B.
,
2000
,
Design Rules
,
MIT Press
,
Cambridge, MA
.
11.
Yassine
,
A. A.
, and
Naoum-Sawaya
,
J.
,
2016
, “
Architecture, Performance, and Investment in Product Development Networks
,”
ASME J. Mech. Des.
,
139
(
1
), p.
011101
.
12.
Kafura
,
D.
, and
Henry
,
S.
,
1981
, “
Software Quality Metrics Based on Inter-Connectivity
,”
J. Syst. Software
,
2
(
2
), pp.
121
131
.
13.
McCabe
,
T. J.
,
1976
, “
A Complexity Measure
,”
IEEE Trans. Software Eng.
,
SE-2
(
4
), pp.
308
320
.
14.
Bralla
,
J. G.
,
1986
,
Handbook of Product Design for Manufacturing: A Practical Guide to Low-Cost Production
,
McGraw-Hill
,
New York
.
15.
Pahl
,
G.
, and
Beitz
,
W.
,
1996
,
Engineering Design: A Systematic Approach
,
Springer
,
London
.
16.
Whitney
,
D. E.
,
Dong
,
Q.
,
Judson
,
J.
, and
Mascoli
,
G.
,
1999
, “Introducing Knowledge-Based Engineering Into an Interconnected Product Development Process,” ASME International Design Engineering Technical Conferences, Las Vegas, NV, Sept. 12–15.
17.
Allaire
,
D.
,
He
,
Q. X.
,
Deyst
,
J.
, and
Willcox
,
K.
,
2012
, “
An Information-Theoretic Metric of System Complexity With Application to Engineering System Design
,”
ASME J. Mech. Des.
,
134
(
10
), p.
100906
.
18.
Kortler
,
S.
,
Kreimeyer
,
M.
, and
Lindemann
,
U.
,
2009
, “A Planarity-Based Complexity Metric,” 17th International Conference on Engineering Design (
ICED 09
), Stanford, CA, Aug. 24–27, pp. 31–42.
19.
Ameri
,
F.
,
Summers
,
J.
,
Mocko
,
G.
, and
Porter
,
M.
,
2008
, “
Engineering Design Complexity: An Investigation of Methods and Measures
,”
Res. Eng. Des.
,
19
(
2–3
), pp.
161
179
.
20.
Dehmer
,
M.
,
2011
,
Structural Analysis of Complex Networks
,
Birkha¨user
,
Dordrecht, The Netherlands
.
21.
Bearden
,
D. A.
,
2003
, “
A Complexity-Based Risk Assessment of Low-Cost Planetary Missions: When is a Mission Too Fast and Too Cheap?
,”
Acta Astronaut.
,
52
(
2–6
), pp.
371
379
.
22.
Summers
,
J. D.
, and
Shah
,
J. J.
,
2010
, “
Mechanical Engineering Design Complexity Metrics: Size, Coupling, and Solvability
,”
ASME J. Mech. Des.
,
132
(
2
), p.
021004
.
23.
Sinha
,
K.
, and
de Weck
,
O. L.
,
2013
, “
A Network-Based Structural Complexity Metric for Engineered Complex Systems
,”
IEEE International on Systems Conference
(
SysCon
), Orlando, FL, Apr. 15–18, pp.
426
430
.
24.
Tamaskar
,
S.
,
Neema
,
K.
, and
DeLaurentis
,
D.
,
2014
, “
Framework for Measuring Complexity of Aerospace Systems
,”
Res. Eng. Des.
,
25
(
2
), pp.
125
137
.
25.
Min
,
G.
,
Suh
,
E. S.
, and
Holtta-Otto
,
K.
,
2015
, “
System Architecture, Level of Decomposition, and Structural Complexity: Analysis and Observations
,”
ASME J. Mech. Des.
,
138
(
2
), p.
021102
.
26.
Sinha
,
K.
,
2014
, “Structural Complexity and Its Implications for Design of Cyber-Physical Systems,”
Ph.D. thesis
, Massachusetts Institute of Technology, Cambridge, MA.
27.
Sinha
,
K.
,
Shougarian
,
N. R.
, and
de Weck
,
O. L.
,
2017
, “
Complexity Management for Engineered Systems Using System Value Definition
,”
Complex Systems Design and Management
,
Springer
,
New York
, pp.
155
170
.
28.
Kim
,
G.
,
Kwon
,
Y.
,
Suh
,
E. S.
, and
Ahn
,
J.
,
2016
, “
Analysis of Architectural Complexity for Product Family and Platform
,”
ASME J. Mech. Des.
,
138
(
7
), p.
071401
.
29.
Kim
,
G.
,
Kwon
,
Y.
,
Suh
,
E. S.
, and
Ahn
,
J.
,
2017
, “
Correlation Between Architectural Complexity of Engineering Systems and Actual System Design Effort
,”
ASME J. Mech. Des.
,
139
(
3
), p.
034501
.
30.
Holtta-Otto
,
K.
,
Chiriac
,
N. A.
,
Lysy
,
D.
, and
Suh
,
E. S.
,
2012
, “
Comparative Analysis of Coupling Modularity Metrics
,”
J. Eng. Des.
,
23
(
10–11
), pp.
787
803
.
31.
Allen
,
K. R.
, and
Carlson-Skalak
,
S.
,
1998
, “Defining Product Architecture During Conceptual Design,” ASME International Design Engineering Technical Conferences, Atlanta, GA, Sept. 13–16, Paper No. DETC98/DTM-5650.
32.
Martin
,
M. V.
, and
Ishii
,
K.
,
2002
, “
Design for Variety: Developing Standardized and Modularized Product Platform Architectures
,”
Res. Eng. Des.
,
13
(
4
), pp.
213
235
.
33.
Sosa
,
M. E.
,
Eppinger
,
S. D.
, and
Rowles
,
C. M.
,
2007
, “
A Network Approach to Define Modularity of Components in Complex Products
,”
ASME J. Mech. Des.
,
129
(
11
), pp.
1118
1129
.
34.
Guo
,
F.
, and
Gershenson
,
J. K.
,
2004
, “A Comparison of Modular Product Design Methods Based on Improvement and Iteration,”
ASME
Paper No. DETC2004-57396.
35.
Holtta-Otto
,
K.
, and
de Weck
,
O.
,
2007
, “
Degree of Modularity in Engineering Systems and Products With Technical and Business Constraints
,”
Concurrent Eng. Res. A
,
15
(
2
), pp.
113
126
.
36.
Whitfield
,
R. I.
,
Smith
,
J. S.
, and
Duffy
,
A. B.
,
2002
, “
Identifying Component Modules
,”
Artificial Intelligence in Design'02
,
Springer
,
Dordrecht, The Netherlands
, pp.
571
592
.
37.
Jung
,
S.
, and
Simpson
,
T. W.
,
2017
, “
New Modularity Indices for Modularity Assessment and Clustering of Product Architecture
,”
J. Eng. Des.
,
28
(
1
), pp.
1
22
.
38.
Newcomb
,
P. J.
,
Bras
,
B.
, and
Rosen
,
D. W.
,
1998
, “
Implications of Modularity on Product Design for the Life Cycle
,”
ASME J. Mech. Des.
,
120
(
3
), pp.
483
490
.
39.
Gershenson
,
J. K.
,
Prasad
,
G. J.
, and
Allamneni
,
S.
,
1999
, “
Modular Product Design: A Life-Cycle View
,”
J. Integr. Des. Process Sci.
,
3
(
4
), pp.
13
26
.
40.
Siddique
,
Z.
,
Rosen
,
D. W.
, and
Wang
,
N.
,
1998
, “On the Applicability of Product Variety Design Concepts to Automotive Platform Commonality,” ASME International Design Engineering Technical Conferences (DETC), Atlanta, GA, Sept. 13–16, Paper No.
98-DETC/DTM5661
.
41.
Mikkola
,
J. H.
, and
Gassmann
,
O.
,
2003
, “
Managing Modularity of Product Architectures: Toward an Integrated Theory
,”
IEEE Trans. Eng. Manage.
,
50
(
2
), pp.
204
218
.
42.
Mattson
,
C. A.
, and
Magleby
,
S. P.
,
2001
, “The Influence of Product Modularity During Concept Selection Consumer Products,” ASME International Design Engineering Technical Conferences (
DETC
), Pittsburgh, PA, Sept. 9–12, Paper No. DETC2001/DTM-21712.
43.
Yu
,
T. L.
,
Yassine
,
A. A.
, and
Goldberg
,
D. E.
,
2007
, “
An Information Theoretic Method for Developing Modular Architectures Using Genetic Algorithms
,”
Res. Eng. Des.
,
18
(
2
), pp.
91
109
.
44.
Helmer
,
R.
,
Yassine
,
A.
, and
Meier
,
C.
,
2010
, “
Systematic Module and Interface Definition Using Component Design Structure Matrix
,”
J. Eng. Des.
,
21
(
6
), pp.
647
675
.
45.
Rissanen
,
J.
,
1999
, “
Hypothesis Selection and Testing by the MDL Principle
,”
Comput. J.
,
42
(
4
), pp.
260
269
.
46.
Van Beek
,
T. J.
,
Erden
,
M. S.
, and
Tomiyama
,
T.
,
2010
, “
Modular Design of Mechatronic Systems With Function Modeling
,”
Mechatronics
,
20
(
8
), pp.
850
863
.
47.
Li
,
S.
,
2010
, “
Methodical Extensions for Decomposition of Matrix-Based Design Problems
,”
ASME J. Mech. Des.
,
132
(
6
), p.
061003
.
48.
Borjesson
,
F.
, and
Holtta-Otto
,
K.
,
2014
, “
A Module Generation Algorithm for Product Architecture Based on Component Interactions and Strategic Drivers
,”
Res. Eng. Des.
,
25
(
1
), pp.
31
51
.
49.
Li
,
Y.
,
Wang
,
Z.
,
Zhang
,
L.
,
Chu
,
X.
, and
Xue
,
D.
,
2016
, “
Function Module Partition for Complex Products and Systems Based on Weighted and Directed Complex Networks
,”
ASME J. Mech. Des.
,
139
(
2
), p.
021101
.
50.
Sharman
,
D. M.
,
2002
, “Valuing Architecture for Strategic Purposes,”
M.Sc. thesis
, Massachusetts Institute of Technology, Cambridge, MA.
51.
Wynn
,
D. C.
,
2007
,
Model-Based Approaches to Support Process Improvement in Complex Product Development
,
University of Cambridge
,
Cambridge, UK
.
52.
Blondel
,
V. D.
,
Guillaume
,
J. L.
,
Lambiotte
,
R.
, and
Lefebvre
,
E.
,
2008
, “
Fast Unfolding of Communities in Large Networks
,”
J. Stat. Mech.
,
2008
, p. P10008.
53.
Sarkar
,
S.
,
Henderson
,
J. A.
, and
Robinson
,
P. A.
,
2013
, “
Spectral Characterization of Hierarchical Network Modularity and Limits of Modularity Detection
,”
PLoS One
,
8
(
1
), p.
e54383
.
54.
Nadakuditi
,
R. R.
, and
Newman
,
M. E. J.
,
2012
, “
Graph Spectra and the Detectability of Community Structure in Networks
,”
Phys. Rev. Lett.
,
108
(
18
), p. 188701.
55.
Fortunato
,
S.
, and
Barthelemy
,
M.
,
2007
, “
Resolution Limit in Community Detection
,”
Proc. Natl. Acad. Sci. USA
,
104
(
1
), pp.
36
41
.
56.
Lancichinetti
,
A.
, and
Fortunato
,
S.
,
2012
, “
Consensus Clustering in Complex Networks
,”
Sci. Rep.
,
2
(
1
), p. 336.
57.
Chen
,
L.
, and
Li
,
S.
,
2005
, “
Analysis of Decomposability and Complexity for Design Problems in the Context of Decomposition
,”
ASME J. Mech. Des.
,
127
(
4
), pp.
545
557
.
58.
Bernstein
,
D. S.
,
2005
,
Matrix Mathematics: Theory, Facts, and Formulas With Application to Linear Systems Theory
,
Princeton University Press
,
Princeton, NJ
.
59.
Horn
,
R. A.
, and
Johnson
,
C. R.
,
2012
,
Matrix Analysis
,
Cambridge University Press
,
Cambridge, UK
.
60.
Dobson
,
A. T.
,
2014
, “Cost Prediction Via Quantitative Analysis of Complexity in U.S. Navy Shipbuilding,” S.M. thesis, Massachusetts Institute of Technology, Cambridge, MA.
61.
Ulrich
,
K. T.
, and
Eppinger
,
S. D.
,
2012
,
Product Design and Development
,
McGraw-Hill/Irwin
,
New York
.
62.
Suh
,
E. S.
,
Furst
,
M. R.
,
Mihalyov
,
K. J.
, and
de Weck
,
O.
,
2010
, “
Technology Infusion for Complex Systems: A Framework and Case Study
,”
Syst. Eng.
,
13
(
2
), pp.
186
203
.
63.
Smaling
,
R.
, and
de Weck
,
O.
,
2007
, “
Assessing Risks and Opportunities of Technology Infusion in System Design
,”
Syst. Eng.
,
10
(
1
), pp.
1
25
.
64.
Eppinger
,
S. D.
, and
Browning
,
T. R.
,
2012
,
Design Structure Matrix Methods and Applications
,
MIT Press
,
Cambridge, MA
.
65.
Mosteller
,
F.
, and
Tukey
,
J. W.
,
1977
,
Data Analysis and Regression: A Second Course in Statistics
,
Addison-Wesley
,
Reading, MA
.
66.
Martinez
,
W. L.
, and
Martinez
,
A. R.
,
2016
,
Computational Statistics Handbook With MATLAB
,
CRC Press
,
Boca Raton, FL
.
You do not currently have access to this content.