Metrics for Assessing Coupling Density and Modularity in Complex Products and Systems

Abstract

The central role of modularity is becoming more and more apparent in design of complex products and systems. The question frequently arises how modularity can be measured. To better understand the degree of modularity, we developed two metrics based on a design structure matrix (DSM). The non-zero fraction (NZF) captures the coupling density of interconnections between components, while the singular value modularity index (SMI) measures the degree of modularity. Both metrics yield values between 0 and 1. These metrics are applied to 15 systems and products. We show that real products typically have NZF values between 0.05 and 0.4 and an SMI between 0.05 (very integral) and 0.95 (very modular). A randomly generated DSM population of equal size and density exhibits SMI values that are bounded in the range from 0.25 to 0.45. We conclude that neither a high degree of modularity nor strong integrality occurs accidentally; but are the result of deliberate design. In particular, we show a more integral design will emerge if a functionally-equivalent product is designed to be portable. The main advantage of SMI is that it enables analysis of the degree of modularity of any product or system independent of subjective module choices.