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Research Papers: Design Theory and Methodology

An Analysis of Modularity as a Design Rule Using Network Theory

[+] Author and Article Information
Hannah S. Walsh, Irem Y. Tumer

School of Mechanical, Industrial, and
Manufacturing Engineering,
Oregon State University,
Corvallis, OR 97331

Andy Dong

Faculty of Engineering and
Information Technologies,
University of Sydney,
Sydney, 2006, Australia
e-mail: andy.dong@sydney.edu.au

1Corresponding author.

Contributed by the Design Theory and Methodology Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 28, 2018; final manuscript received December 13, 2018; published online January 10, 2019. Assoc. Editor: Scott Ferguson.

J. Mech. Des 141(3), 031102 (Jan 10, 2019) (10 pages) Paper No: MD-18-1493; doi: 10.1115/1.4042341 History: Received June 28, 2018; Revised December 13, 2018

Increasing the modularity of system architectures is generally accepted as a good design principle in engineering. In this paper, we explore whether modularity comes at the expense of robustness. To that end, we model three engineering systems as networks and measure the relation between modularity and robustness to random failures. We produced four types of network models of systems—component-component, component-function, component-parameter, and function-parameter—to further test the relation of robustness to the type of system representation, architectural or behavioral. The results show that higher modularity is correlated with lower robustness (p <0.001) and that the estimated modularity of the system can depend on the type of system representation. The implication is that there is a tradeoff between modularity and robustness, meaning that increasing modularity might not be appropriate for systems for which robustness is critical and modularity estimates differ significantly between the types of system representation.

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Figures

Grahic Jump Location
Fig. 1

Left: conceptual model of a highly modular network. Right: conceptual model of a less modular network. If the flow between module 2 and module 4 were removed, those modules would no longer be connected. However, if the flow between module 6 and module 8 were removed, the modules would still be connected.

Grahic Jump Location
Fig. 2

Network models for simple jet engine example at high degree of abstraction

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Fig. 3

Adjacency matrix for component network. This matrix is square and symmetric since the network is unipartite.

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Fig. 4

Adjacency matrix for function-parameter network. This matrix is rectangular since the network is bipartite.

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Fig. 5

Degree distributions for each network model used in the case study. Each column shows different network representations of the same system. Each row shows different systems represented using the same kind of network.

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Fig. 6

All twelve models used in the study. Each column shows different network representations of the same system. Each row shows different systems represented using the same kind of network.

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Fig. 7

Plot of ASPL versus modularity showing a negative correlation. Higher modularity is associated with lower robustness (higher ASPL). Points are labeled by network kind: C (component), CF (component-function), CP (component-parameter), and FP (function-parameter).

Grahic Jump Location
Fig. 8

Plot of RC versus modularity showing a negative correlation. Points are labeled by network kind: C (component), CF (component-function), CP (component-parameter), and FP (function-parameter).

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