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RESEARCH PAPERS

# A Network Approach to Define Modularity of Components in Complex Products

[+] Author and Article Information
Manuel E. Sosa1

Steven D. Eppinger

Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Craig M. Rowles

Pratt & Whitney Aircraft, East Hartford, Connecticut 06108

We refer to architectural properties of product components as those determined by the components’ patterns of interfaces with other components in the product.

We use the expression “design dependency” to refer to a specific type of connection between two components, such as the ones defined due to spatial or energy constraints, whereas we use the expression “design interfaces” to refer to component connections in a broader sense because they are typically formed by the aggregation of design dependencies of various types.

Note that we use the term connectivity as a property of the components of a product, whereas graph theory uses the term as an attribute of the entire graph. In graph theory, the connectivity of a graph is the minimum number of points whose removal results in a disconnected graph (41) (p. 43).

The coefficient of variation of a random variable is a unitless measure of variability equal to the standard deviation divided by the mean.

The ego network of component $i$ only shows the other components it directly shares dependencies with as well as the dependencies among them.

$R2=1−SSE∕SST=1−∑(yi−ŷi)2∕∑(yi−y¯i)2$, where $yi$ is the observed dependent variable, $y¯i$ is the mean of the dependent variable over the 54 observations, and $ŷi$ is the predicted value of the dependent variable obtained from our regression models. This index estimates the proportion of the total variation in the dependent variable that is explained by the regression model.

1

Corresponding author.

J. Mech. Des 129(11), 1118-1129 (Jan 12, 2007) (12 pages) doi:10.1115/1.2771182 History: Received February 20, 2006; Revised January 12, 2007

## Abstract

Modularity has been defined at the product and system levels. However, little effort has gone into defining and quantifying modularity at the component level. We consider complex products as a network of components that share technical interfaces (or connections) in order to function as a whole and define component modularity based on the lack of connectivity among them. Building upon previous work in graph theory and social network analysis, we define three measures of component modularity based on the notion of centrality. Our measures consider how components share direct interfaces with adjacent components, how design interfaces may propagate to nonadjacent components in the product, and how components may act as bridges among other components through their interfaces. We calculate and interpret all three measures of component modularity by studying the product architecture of a large commercial aircraft engine. We illustrate the use of these measures to test the impact of modularity on component redesign. Our results show that the relationship between component modularity and component redesign depends on the type of interfaces connecting product components. We also discuss directions for future work.

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Topics: Design , Networks

## Figures

Figure 5

Ego network for MC-oil pump component (spatial design dependencies)

Figure 6

Ego network for EC-air system (spatial design dependencies)

Figure 1

Hierarchical decomposition of a product

Figure 2

Network representation of a product

Figure 3

Hypothetical four-component product and modularity measures of components

Figure 4

PW4098 commercial aircraft engine studied

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