Modularity indices based on Design Structure Matrices (DSMs) have been utilised to help measure modularity and cluster a product’s architecture into independent or coordinated modules, but many metrics have difficulty (a) measuring the modularity of different types of architectures in real-world products such as bus-type architectures and (b) optimising module boundaries in architectures. After reviewing existing modularity indices and clustering algorithms, we introduce new modularity indices that can capture the degrees of (1) connection strengths within each independent module and between different modules, (2) density of connections within each module and between modules, (3) proximity of interactions to the diagonal of the DSM, and (4) density of connections between buses and other components. Moreover, the proposed metrics can serve as objective functions to obtain optimal DSMs to maximise modularity. A comparative analysis of the proposed modularity index shows that the proposed metric can measure the modularity for 28 different types of DSMs unlike other metrics. Also, the module definition results for an aircraft engine with complex connections between components indicate that clustering using the new modularity indices can help obtain optimal modular product architectures with higher modularity compared to existing clustering results in the literature.
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