Proceedings of IDETC/CIE 2005 ASME 2005 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference September 24-28, 2005. Long Beach, California, USA DETC2005/DTM-85422 A NETWORK APPROACH TO DEFINE MODULARITY OF PRODUCT COMPONENTS Manuel E. Sosa1 Anupam Agrawal Steven D. Eppinger Craig M. Rowles Assistant Professor of Technology and Operations Sloan School of Management Advanced Engine Program Technology and Operations Management Massachusetts Institute of Pratt & Whitney Aircraft Management INSEAD Technology East Hartford, Connecticut INSEAD Fontainebleau, FRANCE Cambridge, Massachusetts Fontainebleau, FRANCE ABSTRACT modularity, is particularly important for established firms We consider complex products as a network of which often fail to identify and manage novel ways in which components that share technical interfaces in order to function components share interfaces [6]. Furthermore, when designing as a whole. Building upon previous work in graph theory and complex products it is critical for managers to proactively social network analysis, we define three measures of identify the components that will require particular attention component modularity that consider how components may during the design process [7]. Defining modularity at the share direct interfaces with other adjacent components, how component level (as opposed to the product level) is important design interfaces may propagate to all other components in the because it can provide indication to managers about important product, and how components may act as “bridges” between component performance metrics such as design rework or other components. We calculate and interpret all three measures failure rate. Our proposed definitions of modularity at the of component modularity by studying the actual product component level can therefore be the starting point of a long- architecture of a large commercial aircraft engine. We illustrate needed discussion about architectural properties of product how to use these measures to test their impact on component components. redesign. Directions for future work are discussed. This paper is structured as follows. First, we review the relevant literature in the product architecture, social network, Keywords: Component Modularity, Product Architecture, and graph theory domains. Then, we define component Graph theory, Social Networks. modularity and propose specific measures. In the next section, we apply our definitions to determine the modularity of the INTRODUCTION components of a large commercial aircraft engine. Next, we Previous research on product architecture has defined define component redesign and test whether it could be modularity at the product and system level [1,2], however little predicted by component modularity. We conclude the paper effort has been dedicated to study modularity at the component with a discussion of the results and comments for future work. level [3]. Although complex products are typically considered as a network of components that share interfaces in order to LITERATURE REVIEW function as a whole [4,5], there are no quantitative measures that allow us to distinguish components based on how they This work builds upon three streams of research. The first share interfaces with other components in a product. Based on one is the body of work dedicated to product architecture the patterns of interfaces of each component, we define representations, and the second one is the established stream of measures to quantify the relative degree of modularity of work focused on social networks. We also build upon graph components in complex products. theory, which has provided the foundation to define properties This paper formally defines component modularity based of both products and social networks when considered as on the patterns of a component’s design interfaces. graphs of connected nodes. We blend these research streams Understanding architectural properties, such as component 1 Corresponding author: [email protected] Tel: ++33 (0)1 60 72 45 36. Fax: ++33 (0)1 60 74 61 79. 1 Copyright © 2005 by ASME together by defining and measuring three types of component modularity based on network structural properties. Social Networks and Graph Theory Social network analysis is the study of social relations Product Architecture and Graph Theory among a set of actors. Network analysts believe that how an The literature on product decomposition and product individual behaves depends in large part on how that individual architecture begins with Alexander [8] who describes the is tied into the larger web of social connections [27]. More design process as decomposition of designs into minimally importantly, they believe that the success or failure of societies coupled groups. Simon [4] elaborates further by suggesting that and organizations often depends on the patterning of their complex systems should be designed as hierarchical structures internal structure [28]. Beginning in the 1930s, a systematic consisting of "nearly decomposable systems" such that strong approach to theory and research, based on the above notions, interfaces occur within systems whereas weak interfaces occur began to emerge. In 1934 Jacob Moreno introduced the ideas across systems. Smith and Browne [9] describe decomposition and tools of sociometry [29]. At the end of World War II, as a fundamental approach to deal with complex engineering Bavelas [30] noted that the structural arrangement of ties efforts. linking members of a task oriented group may have Previous work has considered products as graphs of consequences for their productivity and morale. He proposed connected components. Kusiak and Wang [10] use binary that the relevant structural feature was centrality, and he digraphs representations to develop physical layouts. Moreover, defined this in formal terms. Since then, social network component connectivity is a central concept when studying analysis has extended into research areas that span from engineering changes and design propagation during the analysis of people in an organization to analysis of board development of complex products [11,12,13,14]. interlocks, joint ventures and inter-firm alliances and trade Ulrich and Eppinger [15, p. 165] define the architecture of blocks - drawing upon such fields as sociology, anthropology, a product as “the scheme by which the functional elements of and mathematics [27, 28, 31]. the product are arranged into physical chunks and by which the A social network is a set of actors who are connected by a chunks interact.”2 A key feature of product architecture is the set of ties. The actors or "nodes" can be people, groups, teams, degree to which it is modular or integral. In the engineering or organizations. Ties connect pairs of actors and can be design field, a large stream of research has focused on methods directed (for example, A gives advice to B) or undirected (for and rules to map functional models to physical components example, A and B are friends) and can be binary (for example, [3,16,17,18]. However, as Ulrich [1] suggested, establishing the whether A gives advice to B or not) or valued (for example, product architecture not only involves the arrangement of frequency of interactions between A and B). A set of ties of a functional elements and their mapping to physical components given type (such as friendship ties) constitutes a binary social but also the specification of the interfaces among interacting relation, and each relation defines a different network (for components. example, the friendship network is distinct from the advice In order to study the structure of product architectures network). in terms of component interactions we use the design structure We identify two streams of research in the field of social matrix (DSM) tool. The DSM is a graphical method introduced networks. First, and most relevant to our paper, is the work by Steward [19] and used by Eppinger et al [20] to study focused on developing network indices to capture structural interdependence between product development activities. properties of social networks at the individual level. Secondly, Gebala and Eppinger [21] compare DSM models with other is the stream of work that focuses on how social network graph based models such as program evaluation and review properties of individuals or teams impact the performance of technique (PERT) charts and structured analysis and design organizational processes such as product development [E.g. 28, technique (SADT), to study design procedures. DSM 32, 33]. representation has also been used to document product Graph theory has been widely used in social network decomposition [22] and team interdependence [23]. More analysis [34, 35, 27, 31]. One of the main notions that social recently, researchers have extended the use of DSM network analysis derives from graph theory is to identify the representations of complex products to analyze their most important actors in a network. Actors who are the most architectures at the product level [24, 25,26] and model design important (prominence and prestigious are also commonly change propagation [13]. referred terms) are usually located in “central” locations within Sosa et al [2] use a matrix representation not only to the network. Centrality measures aim to identify "the most capture the decomposition and interfaces between product important (or prominent)" actors in a social network. In our components but also to extend the concepts of product context,