Spectral Characterization of Hierarchical Modularity in Product Architectures.

Despite the importance of the architectural modularity of products and systems, existing modularity metrics or algorithms do not account for overlapping and hierarchically embedded modules. This paper presents a graph theoretic spectral approach to characterize the degree of modular hierarchical-overlapping organization in the architecture of products and complex engineered systems. It is shown that the eigenvalues of the adjacency matrix of a product architecture graph can reveal layers of hidden modular or hierarchical modular organization that are not immediately visible in the predefined architectural description. We use the approach to analyze and discuss several design, management, and system resilience implications for complex engineered systems.

[1]  Somwrita Sarkar,et al.  CHARACTERIZING MODULARITY, HIERARCHY AND MODULE INTERFACING IN COMPLEX DESIGN SYSTEMS , 2011 .

[2]  Kosuke Ishii,et al.  Design for variety: developing standardized and modularized product platform architectures , 2002 .

[3]  N. Biggs.  Algebraic Graph Theory , 1974 .

[4]  Steven D. Eppinger,et al.  The Misalignment of Product Architecture and Organizational Structure in Complex Product Development , 2004, Manag. Sci..

[5]  Mark W. Lange,et al.  Interfaces Per Module: Is There an Ideal Number? , 2009 .

[6]  Andrew Y. C. Nee,et al.  Optimal Design of Hierarchic Components Platform under Hybrid Modular Architecture , 2009, Concurr. Eng. Res. Appl..

[7]  Timothy W. Simpson,et al.  IMPROVING AN EXISTING PRODUCT FAMILY BASED ON COMMONALITY/DIVERSITY, MODULARITY, AND COST , 2007 .

[8]  Alex H. B. Duffy,et al.  Supporting `Design for Re-use' with Modular Design , 2007, Concurr. Eng. Res. Appl..

[9]  Dan Braha,et al.  The Topology of Large-Scale Engineering Problem-Solving Networks , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Katja Hölttä-Otto,et al.  Degree of Modularity in Engineering Systems and Products with Technical and Business Constraints , 2007, Concurr. Eng. Res. Appl..

[11]  Eun Suk Suh,et al.  Level of modularity and different levels of system granularity , 2011 .

[12]  Sidney Redner,et al.  Role of design complexity in technology improvement , 2009, Proceedings of the National Academy of Sciences.

[13]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[14]  John K. Gershenson,et al.  Product modularity: Definitions and benefits , 2003 .

[15]  Dan Braha,et al.  Information flow structure in large-scale product development organizational networks , 2004, J. Inf. Technol..

[16]  Panos Y. Papalambros,et al.  Optimal design of commercial vehicle systems using analytical target cascading , 2014, Structural and Multidisciplinary Optimization.

[17]  Piet Van Mieghem,et al.  Graph Spectra for Complex Networks , 2010 .

[18]  Fei Gao,et al.  Module-scale-based product platform planning , 2009 .

[19]  Carolyn Conner Seepersad,et al.  A high-definition design structure matrix (HDDSM) for the quantitative assessment of product architecture , 2012 .

[20]  Erik K. Antonsson,et al.  INFORMATION MEASURE FOR MODULARITY IN ENGINEERING DESIGN , 2004 .

[21]  Kristin L. Wood,et al.  A heuristic method for identifying modules for product architectures , 2000 .

[22]  Xin Guo Ming,et al.  On Modular Products Development , 2009, Concurr. Eng. Res. Appl..

[23]  David W. Rosen,et al.  Implications of Modularity on Product Design for the Life Cycle , 1998 .

[24]  John S. Gero,et al.  Design Optimization Problem Reformulation Using Singular Value Decomposition , 2009 .

[25]  Katja Hölttä,et al.  Comparing Three Different Modularity Methods , 2003 .

[26]  Kaushik Sinha,et al.  Technology Insertion in Turbofan Engine and assessment of Architectural Complexity , 2011 .

[27]  János Komlós,et al.  The eigenvalues of random symmetric matrices , 1981, Comb..

[28]  Qi D. Van Eikema Hommes.  Comparison and Application of Metrics That Define the Components Modularity in Complex Products , 2008 .

[29]  John K. Gershenson,et al.  DSM-Based Product Representation for Design Process Modularity , 2008 .

[30]  O. Sporns,et al.  Identification and Classification of Hubs in Brain Networks , 2007, PloS one.

[31]  A. Barabasi,et al.  Spectra of "real-world" graphs: beyond the semicircle law. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[33]  Somwrita Sarkar,et al.  Community detection in graphs using singular value decomposition. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Yaneer Bar-Yam,et al.  The Statistical Mechanics of Complex Product Development: Empirical and Analytical Results , 2007, Manag. Sci..

[35]  T. Vicsek,et al.  Uncovering the overlapping community structure of complex networks in nature and society , 2005, Nature.

[36]  Steven D. Eppinger,et al.  Identifying Modular and Integrative Systems and Their Impact on Design Team Interactions , 2003 .

[37]  Panos Y. Papalambros,et al.  Optimal Design of Commercial Vehicle Systems Using Analytical Target Cascading , 2012 .

[38]  Kaushik Sinha,et al.  Structural complexity metric for engineered complex systems and its application , 2012 .

[39]  Tyson R. Browning,et al.  Degree Distribution and Quality in Complex Engineered Systems , 2011 .

[40]  Somwrita Sarkar,et al.  Spectral Characterization of Hierarchical Network Modularity and Limits of Modularity Detection , 2013, PloS one.

[41]  Steven D. Eppinger,et al.  A Network Approach to Define Modularity of Components in Complex Products , 2007 .