0
Research Papers: Design Theory and Methodology

Integrative Complexity: An Alternative Measure for System Modularity

[+] Author and Article Information
Kaushik Sinha

Sociotechnical Systems Research Center (SSRC),
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139
e-mail: sinhak@mit.edu

Eun Suk Suh

Graduate School of Engineering Practice,
Institute of Engineering Research,
Seoul National University,
1 Gwanak-ro, Gwanak-gu,
Seoul 08826, South Korea
e-mail: essuh@snu.ac.kr

Olivier de Weck

Department of Aeronautics and Astronautics,
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139
e-mail: deweck@mit.edu

1Corresponding author.

Contributed by the Design Theory and Methodology Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 23, 2017; final manuscript received January 4, 2018; published online March 1, 2018. Assoc. Editor: Katja Holtta-Otto.

J. Mech. Des 140(5), 051101 (Mar 01, 2018) (11 pages) Paper No: MD-17-1649; doi: 10.1115/1.4039119 History: Received September 23, 2017; Revised January 04, 2018

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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

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.
Newman, M. E. J. , 2010, Networks: An Introduction, Oxford University Press, Oxford, NY. [CrossRef]
Lindemann, U. , Maurer, M. , and Braun, T. , 2008, Structural Complexity Management: An Approach for the Field of Product Design, Springer, New York.
Weber, C. , 2005, “ What Is ‘Complexity’?,” 15th International Conference on Engineering Design (ICED 05), Melbourne, VIC, Australia, Aug. 15–18, pp. 15–18.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Maier, M. W. , and Rechtin, E. , 2009, The Art of Systems Architecting, CRC Press, Boca Raton, FL.
Crawley, E. , Cameron, B. , and Selva, D. , 2016, System Architecture: Strategy and Product Development for Complex Systems, Pearson, Boston, MA.
Baldwin, C. Y. , and Clark, K. B. , 2000, Design Rules, MIT Press, Cambridge, MA.
Yassine, A. A. , and Naoum-Sawaya, J. , 2016, “ Architecture, Performance, and Investment in Product Development Networks,” ASME J. Mech. Des., 139(1), p. 011101. [CrossRef]
Kafura, D. , and Henry, S. , 1981, “ Software Quality Metrics Based on Inter-Connectivity,” J. Syst. Software, 2(2), pp. 121–131. [CrossRef]
McCabe, T. J. , 1976, “ A Complexity Measure,” IEEE Trans. Software Eng., SE-2(4), pp. 308–320. [CrossRef]
Bralla, J. G. , 1986, Handbook of Product Design for Manufacturing: A Practical Guide to Low-Cost Production, McGraw-Hill, New York.
Pahl, G. , and Beitz, W. , 1996, Engineering Design: A Systematic Approach, Springer, London.
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.
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. [CrossRef]
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.
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. [CrossRef]
Dehmer, M. , 2011, Structural Analysis of Complex Networks, Birkha¨user, Dordrecht, The Netherlands. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
Tamaskar, S. , Neema, K. , and DeLaurentis, D. , 2014, “ Framework for Measuring Complexity of Aerospace Systems,” Res. Eng. Des., 25(2), pp. 125–137. [CrossRef]
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. [CrossRef]
Sinha, K. , 2014, “Structural Complexity and Its Implications for Design of Cyber-Physical Systems,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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.
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. [CrossRef]
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. [CrossRef]
Guo, F. , and Gershenson, J. K. , 2004, “A Comparison of Modular Product Design Methods Based on Improvement and Iteration,” ASME Paper No. DETC2004-57396.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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.
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
Rissanen, J. , 1999, “ Hypothesis Selection and Testing by the MDL Principle,” Comput. J., 42(4), pp. 260–269. [CrossRef]
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. [CrossRef]
Li, S. , 2010, “ Methodical Extensions for Decomposition of Matrix-Based Design Problems,” ASME J. Mech. Des., 132(6), p. 061003. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Sharman, D. M. , 2002, “Valuing Architecture for Strategic Purposes,” M.Sc. thesis, Massachusetts Institute of Technology, Cambridge, MA.
Wynn, D. C. , 2007, Model-Based Approaches to Support Process Improvement in Complex Product Development, University of Cambridge, Cambridge, UK.
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.
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. [CrossRef] [PubMed]
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.
Fortunato, S. , and Barthelemy, M. , 2007, “ Resolution Limit in Community Detection,” Proc. Natl. Acad. Sci. USA, 104(1), pp. 36–41. [CrossRef]
Lancichinetti, A. , and Fortunato, S. , 2012, “ Consensus Clustering in Complex Networks,” Sci. Rep., 2(1), p. 336.
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. [CrossRef]
Bernstein, D. S. , 2005, Matrix Mathematics: Theory, Facts, and Formulas With Application to Linear Systems Theory, Princeton University Press, Princeton, NJ.
Horn, R. A. , and Johnson, C. R. , 2012, Matrix Analysis, Cambridge University Press, Cambridge, UK. [CrossRef]
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.
Ulrich, K. T. , and Eppinger, S. D. , 2012, Product Design and Development, McGraw-Hill/Irwin, New York.
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.
Smaling, R. , and de Weck, O. , 2007, “ Assessing Risks and Opportunities of Technology Infusion in System Design,” Syst. Eng., 10(1), pp. 1–25. [CrossRef]
Eppinger, S. D. , and Browning, T. R. , 2012, Design Structure Matrix Methods and Applications, MIT Press, Cambridge, MA.
Mosteller, F. , and Tukey, J. W. , 1977, Data Analysis and Regression: A Second Course in Statistics, Addison-Wesley, Reading, MA.
Martinez, W. L. , and Martinez, A. R. , 2016, Computational Statistics Handbook With MATLAB, CRC Press, Boca Raton, FL.

Figures

Grahic Jump Location
Fig. 1

Complexity typology for engineering systems (Reprinted with permission from Sinha and Suh [5]. Copyright 2018 by Springer.)

Grahic Jump Location
Fig. 2

Explanation of individual terms of the structural complexity metric (Reprinted with permission from Sinha and Suh [5]. Copyright 2018 by Springer.)

Grahic Jump Location
Fig. 3

A hypothetical system composed of two modules, ten elements, and ten bidirectional interfaces in network and binary adjacency matrix form

Grahic Jump Location
Fig. 4

Original train undercarriage decomposition and the modularity (Q) maximized decomposition in DSM format (Q-maximized decomposition from Ref. [5])

Grahic Jump Location
Fig. 5

Regression plots for ICn and Q of train undercarriage system with decompositions

Grahic Jump Location
Fig. 6

Regression plots for ICn and Q of industrial printing system with decompositions

Grahic Jump Location
Fig. 7

Regression plots for ICn and Q of office printing system with decompositions

Grahic Jump Location
Fig. 8

Regression plots for ICn and Q of geared turbofan aircraft engine with decompositions

Grahic Jump Location
Fig. 9

Regression plots for ICn and Q of two-spool turbofan aircraft engine with decomposition

Grahic Jump Location
Fig. 10

Regression plots for ICn and Q of HECE with decomposition

Grahic Jump Location
Fig. 11

Plot of integrative complexity and modularity for systems shown in Table 2

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In