CHARACTERIZING MODULARITY, HIERARCHY AND MODULE INTERFACING IN COMPLEX DESIGN SYSTEMS

Modular engineering systems have multiple benefits over their more integral counterparts. Despite the importance of modularity, metrics and methods for a precise quantitative characterization of modularity, hierarchy and module interfacing remain relatively ambiguous. In this paper, using graph theory and linear algebra, we develop a spectral approach to establish: (1) a metric to characterize modularity, hierarchy and module interfacing in complex engineering systems; and, (2) a method for module identification and system decomposition that addresses hierarchical and overlapping organization of modularity in a complex system. The Singular Values (SV) signatures of random, regular, modular and hierarchically modular benchmark graph models are used to establish the metric. Then, the method is applied to a real design model and its modularity signature is assessed. The modularity signature of a real world system is shown to sit in the continuum established by the extremes of random, regular and modular and hierarchically modular graph models. The main contribution of the work is that it proposes that modularity is an aggregate concept that is measured in terms of multiple concepts expressed as graph properties. An ideal numeric modularity measurement index would have to incorporate these multiple criteria that affect modularity. The method can be used in the conceptual and detailed design stages for purposes of redesigning a product based on the degree of desired modularity.Copyright © 2011 by ASME

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