Product Modularity Measures and Design Methods

J. ENG. DESIGN, VOL.

15,

NO.

1, FEBRUARY 2004, 33–51

Product modularity: measures and design methods J. K . GERSHENSON { *, G. J. PRASAD { and Y. ZHANG § This paper presents an overview of existing research on measures of product modularity and methods to achieve modularity in product design. Discussions of the development of modular products have increased in recent years. The research activity into the development of modularity measures and methods has also increased. These measures and methods vary considerably in purpose and process. Some are highly quantitative and some are completely qualitative. Some are information intensive and some are more easily applied. The relationship to product platform planning is also shown. This overview shows no clear consensus beyond those found in the definition of modularity. There are, however, several themes that are prevalent. Most measures center on measuring dependencies with components external to modules. Some measures include a measure of component similarity. However, what is measured as dependencies and similarities varies by measure and by context. Additionally, there is always some subjectivity in the measures. The design methods vary greatly. Many are based on measures. Most are information intensive. Noticeably, the measures and methods lack rigorous verification and validation. There is also a lack of quantitative comparison among the various measures and methods. It is hoped that this research will highlight the present inconsistencies in the field of modular product design and put forward some critical questions, which will shape future research into this field. Key words: modularity, design, design theory, design methods, optimization

1. Motivation This paper is the second of a trio of articles describing the current state of research into product modularity. The first two are qualitative discussions of key issues in product modularity; the third is a quantitative comparison of existing measures and methods. All three share a similar motivation. While all of the content and discussion are different, much of the motivation section of this paper, some of the abstract, and the conclusion are identical to the accompanying paper entitled ‘Product Modularity: Definitions and Benefits’ (Gershenson et al., 2002). Modularity arises from the decomposition of a product into subassemblies and components. This division facilitates the standardization of components and increased product variety (Gershenson and Prasad 1997a, 1997b). As firms strive to rationalize their product lines and to provide an increasing diversity of products at a lower cost, the concept of Revision received June 12, 2002. { Life-cycle Engineering Laboratory, Department of Mechanical—Engineering Mechanics, Michigan Technological University, 936 R.L. Smith, 1400 Townsend Drive, Houghton, Michigan 49931-1295. { Ford Motor Company, Dearborn, MI. § Department of Mechanical and Aerospace Engineering, Utah State University, Logan, UT. * To whom correspondence should be addressed. e-mail: [email protected] Journal of Engineering Design ISSN 0954-4828 print/ISSN 1466-1387 online # 2004 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080/0954482032000101731

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modularity has gained attention. Although product modularity has been increasingly applied to industrial products over the past two decades, the science of modular design has not been studied in detail until recently. There is neither a widely adopted measure of a product’s modularity nor a widely adopted systematic methodology that helps designers increase the modularity of a product. After commencing their own research into modular product design, the authors began a validation study to show that their modular design method did in fact lead to more modular products. The idea was to have ten consumer products that would be rated for modularity by third parties and then to rate these by our own modularity measure and validate the correlation. They began with a group of graduate students as the third party. The results were surprising. There was no statistical significance to the students’ ranking of product modularities. There was not agreement on the placement of a single product. Note that, by their measure, there was a very wide spectrum of modularity represented by the ten products. Assuming that the fault of the study laid in the choice of subject pool, the study was redone with small, separate third-party pools of: undergraduate students, design engineers with more than ten years experience, product development managers, and a group of design engineers/researchers who had indicated an interest in and familiarity with modular product design. The results were the same for each subject pool—a complete lack of agreement as to which products were more modular. A small study using pairwise comparison was of no help either. After sifting through additional industrial and academic literature on modularity, it became clear that, while the term ‘modular’ is used often, there has been little effort made to come to a consensus on the definition of this term and its appropriate use. The authors therefore began the task of collating much of the available literature and looking for common threads. This paper is meant as a review of the current thoughts on two topics integral to modular design: measures of modularity and modular product design methods. In discussing these topics, a third issue, methods of product representation for modular design, becomes pervasive. This issue will therefore be discussed first. The framework for these discussions is set in the accompanying paper where the definition of modularity is discussed as encompassing an element of independence between modules and an element of similarity within modules and where modularity is applied across the entire product life-cycle. Every effort was made to review all English-language literature from the past thirty years in a variety of fields. The authors understand that they may have missed some excellent works, especially those that have not been translated into English. The authors looked for modularity discussions in every area of Engineering, in Computer Science, in Biology, in Architecture, and in Art. They also had difficulty fitting all of this great work into a single paper. Therefore, only a cursory discussion of each work’s elements is included and some works that reiterate stated concepts are omitted. The reader is encouraged to seek out referenced work for more detail. The references section of this paper has also been expanded and is more bibliographical in nature. What follows is a review of the state of the art of product modularity with the conclusions of the authors.

2. Method of product representation for modular design Representation of products in modularity research is not a critical issue. However, since most modularity research has gone through considerable effort to represent

Measures and design methods for product modularity

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product information, the authors are including this topic in this paper. The representations of information in product modularity are shaped by the definitions of modularity—most involving relationships among components in a product. The necessary information naturally lends itself to a matrix representation in which components in the products make up both the rows and the columns and the constitutive matrix elements show the relationships between the components. One matrix might suffice showing a single dependence relationship or showing some relationship measurement as in Sosale et al. (1997) or Newcomb et al. (1996). Alternatively, there might be a need for two matrices to show both dependence and similarity as in Huang and Kusiak (1998) and Gershenson et al. (1999). Some choose to show process relationships too, but most later distill these into component–component relationships. There is no record of significantly different methods to represent the modular product information that is also later used in the design of modular products or the calculation of a measure of product modularity. The matrix-based methods follow in this section and many are detailed in the measurement and design methods sections. Pimmler and Eppinger (1994) use system decomposition (design structure matrix) to drive their matrix representation. The initial step involves specification of the overall product concept in terms of functional and/or physical elements. The authors suggest decomposition to one level of detail further than desired for the product architecture. They rely on the use of functional or physical elements for decomposition or even both depending on the type of design (incremental or novel design). Later works by that group, including Sosa et al. (2000), expand to use a design structure matrix to represent component interfaces. Sosale et al. (1997) fill their relationship matrices with physical interactions in the product, spatial and geometric relationships, which include:

attachment: physical contacts, joints, fasteners, welds, couplings, etc.; positioning: relative distance or angle between components, alignment, etc.; motion: cam-controlled objects, trajectory of joints, end effectors, etc.; containment: e.g. components contained in the same housing; as well as life-cycle issues.

Sosale et al. then use a qualitative 0–10 scale, based on these physical interactions and the weight of these interactions as objectives, to fill in a single relationship matrix. This is one of only a few representations to account for similarity in life-cycle objectives. These constraints are later considered during the grouping of components into modules. Huang and Kusiak (1998) base their mature method of modular product representation on interaction and suitability matrices. The two types of relationships involved in the modularity concept are similarity of functional interactions (on a 0–10 scale for frequency of interaction), and suitability of inclusion of components in a module (on an a, e, o, u basis for strongly desired to strongly undesired). Components not belonging to any module are independent components. The modularity matrix allows representation of different types of modularity—component swapping, component sharing, or bus modularity—based on the interpretation using the axioms. Gershenson et al. (1999) also use two matrices, one each for dependencies and similarities, to represent component interactions. The rows of the matrices represent each component and the columns represent each component and each life-cycle task the product undergoes (manufacturing, assembly, service, retirement, etc.). This allows for component–component and component–process relationships. The elements of

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the matrix are filled with a subjective, 1-5 rating of the strength of the dependency or similarity. The subjective rating, although it includes guidelines, are the primary source of error in this representation. An important consideration when defining the relative modularity of a product is the level of detail chosen when looking at the product structure. A product may seem modular but, at some levels of detail, the structure may not be modular. Similar to Pimmler and Eppinger (1994), Gershenson et al. (1999) use component trees as a tool to describe the levels of detail of a product. Component trees show all of the components and subassemblies that make up a product. The tree-like structure is helpful in discerning levels of detail and showing subassembly interactions. Another important consideration when defining life-cycle modularity is the chosen level of abstraction of the life-cycle process itself. Process graphs are similarly used to describe the levels of detail of each life-cycle processes. Process graphs delineate each task and subtask of a process. Ishii et al. (1995) and Allen and Carlson-Skalak (1998) make use of product decomposition graphs or reverse fishbone diagrams to represent relationships between modules. This method lacks the information content of the previous methods and, while promising for product recycling description (the authors’ intent), may not have other life-cycle applications. Prior to Huang and Kusiak’s (1998) matrix representation, Kusiak and Szczerbicki (1993) used requirements and functions that determine the type of material, energy, or information flow to develop a digraph that can be used for the retrieval of strongly connected components. The digraph represents strongly connected components as a vertex and edges represent cluster to cluster connections. The adjacency matrix of the digraph is constructed with elements representing the number of paths of length 1 leading from vertex i to vertex j in the digraph. The reachability matrix R is then constructed. If all the entries of the product of R and its transpose are equal to 1, then the object consists of one cluster and cannot be decomposed. If the product results in all entries equal to 0, then the designed object is disconnected. The sequence in which the vertices representing components of the designed object are numbered is not relevant. The precedence matrix is then defined for the clusters by performing logical operations on the matrices. This work was expanded upon by He and Kusiak (1996) for the case of a product structure represented by an acyclic digraph, the nodes represent operations and the arcs represent precedence relations between the operations. Each product in the family shares the same basic features and differs only by the variant structure. These works give a strong understanding of the product but their complexity does not lend itself to product design nor is there a built in measurement. A few works have taken very different approaches to modular product representation. These works have borrowed from the representation of complex products and systems used elsewhere in design theory and design automation research. The goal of Newcomb et al. (1996) is to develop an evaluation methodology/tool that the designer can use in configuration design to determine the degree to which a design simultaneously meets its function, service, and post life-cycle goals. The authors use a product decomposition and module comparison approach to achieve product modularity. This work has evolved into a tradeoff analysis (Ortega et al. 1999), and a similar approach has used graph-grammars (Siddique and Rosen 1999) to represent products and families of product. The use of graph-grammars to ‘design in’ or extract commonality and dependence information allows for the automation of some very tedious tasks.


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This approach is more likely to allow for optimization as well. Other research (Schmidt and Cagan 1998) has looked at the representation of component combinations, a similar, but not directly related problem. Constantine et al. (1998), in work that only happens to touch on modularity but is important to the topic of product representation, use shape grammars to allow for the rapid generation of a variety of designs by applying different rules in a rule set. A designer can receive immediate feedback on the effects of a design change and its effect on manufacturing cost. This may have significant implications on the future of modular product representation. Other researchers such as Du et al. (2000) and Line and Steiner (2000) have worked at extracting and representing modular architecture elements in CAD systems. Additionally, Finch (1999) has begun to look at the possibility of set-based causal representation for higher-level product family decisions. As part of set-based design, this method will probably have long-range implications. In several works (Erens and Hegge 1994, Erens and Breuls 1995, McKay et al. 1996, Erens and Verhulst 1996, 1997), Erens et al. have laid out a detailed product modeling language geared towards describing product families. In summary, product representation is a very important issue in design theory and methodology. While matrices have dominated product representation in modularity literature, it is because the representation has been shaped by the problem definition. Matrix representation fits the need for component manipulation and comparison, as discussed later in the paper.

3. Measure of modularity The question of just how modular a product is, while interesting and challenging to answer, is not necessarily an important question. If a modular design method is followed, and it can be shown to guarantee improved modularity (and if the benefits of improved modularity have been proven), then the measure of modularity as an abstract number is unimportant. However, when incremental changes in design are made and their effect on modularity are questioned or when there are decisions to be made and modularity will serve as the basis of that decision, a measure of product modularity is important. There are few of these measures in the literature. Gershenson et al. (1999), like most researchers, state that modularity is a relative property. Products possess a higher or lower degree of modularity. A product with a higher degree of modularity either contains a larger percentage of components or subassemblies that are modular or contains components and subassemblies, which are, on average, more modular. The measure of relative modularity that they developed is the ratio of intra-module similarities to all similarities, both intra- and inter-module, added to the ratio of intra-module dependencies to all dependencies, both intra- and inter-module. The similarities considered are component–process similarities while the dependencies are both component–component and component–process dependencies. Each element is calculated using subjective ratings of the above parameters for relationships between each component in the product and all other components as well as each component and each life-cycle process the product goes through. The measure shows, on a 0 to 2 scale with two being more modular, what fraction of these relationships occurs inside a module as opposed to between modules. Calculations of each quantity in this measure are detailed in their work (Gershenson et al. 1999), as space

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does not permit here. This work is applicable to all life-cycle elements. However, this work still relies upon subjective measurements of component–component and component–process similarity and dependency. While measurement guidelines are offered, they are sparse. Newcomb et al. (1998) use a measure of modularity based upon the multiplication of inter-module connections and the average correspondence between modules. They use the material compatibility between components to calculate the compatibility within a module relative to the compatibility of within and between modules (correspondence ratio). They do likewise with the physical connections between components (cluster independence). Multiplying the correspondence ratio and the cluster independence gives a measure of modularity. Newcomb et al.’s measure is similar to those of Zhang et al. (2001) and Gershenson et al. (1999) in that it incorporates an element of similarity (compatibility) and dependency ( physical connections). However, their similarity and dependency are far more constrained. The intended application of this measure is product retirement. The use of material compatibility as the sole issue of similarity and the use of connections as the sole issue of dependence strengthens the product retirement tie but precludes other life-cycle issues. This limits the applicability of the measure but increases the precision. It would be interesting to compare Newcomb et al.’s multiplicative measure with Gershenson et al.’s additive measure. The multiplicative measure intuitively captures the idea of both similarity and independence being necessary where one cannot make up for the other. In later works by a similar group, Siddique and Rosen (1998, 1999) expand into the measurement of interface modularity—the standardization of the module interfaces. Their candidate measurement is the number of common interface components divided by the total number of interfaces both common and unique. Sosale et al. (1997) base their modularity measurement on interaction analysis that uses a set of design objectives to be considered. To evaluate the interactions for the overall objective, values are assigned to each objective. The interaction matrix, having the interaction values between components, is then constructed. These values are scaled to lie between 0 and 10. A weighted average is then calculated for the interactions for any two components. This method is quite open-ended leaving room for life-cycle processes. However, the method lacks specific guidelines to assist in implementing the elements of modularity in the measure. The measure also relies on two instances of subjective ratings, which are then multiplied, calling its accuracy and range into question. Erixson et al. (1994) offer that the optimal number of modules in a product is dependent upon the number of parts in the product and their assembly time. Although no explicit measure is given, this offers a considerably different direction in which to research. DiMarco et al. (1994) created a tool, which groups components by the type of recycling done and assesses a qualitative recycling cost. In an extension to this work, Ishii et al.’s (1995) design for variety model helps capture the indirect costs involved through the measurement of three indices, namely commonality, differentiation point, and set-up cost. The authors use tools like quality function deployment, conjoint analysis, and utility theory for estimating the importance of variety and build upon the concept of product structure graphs, to represent the basic information (Martin and Ishii 1997). Other works, including Kota and Sethuraman (1998) have used similar, although less encompassing commonality indices. Maupin and Stauffer (2000) discuss a measure of


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modularity geared towards understanding design for assembly decisions at small companies. They use simplicity, a measure of assembly operation time, and then multiply the sales effect of each model in a family to develop a total measure. They then look at the reuse of components relative to simplicity—a measure they call standardization. Standardization, with a direct cost model, is incorporated into a delayed differentiation index. This index, along with cost is tracked to measure the ‘goodness’ of product architecture decisions. This method is similar to and simpler than Ishii et al.’s method is, but Maupin and Stauffer’s does include a cost model. Hillstrom (1994) uses information from functional and physical hierarchies to clarify interface or function interactions, while design for manufacture and assembly tools are used to obtain a measure of complexity of each interface. He and Kusiak (1996) discuss the performance of form/function modules in terms of manufacturing cost. None of these tools uses a modularity measure per se but other life-cycle measures within a modular design framework. The closest is the clumping index used by DiMarco et al. (1994). However, these will never lead to optimal modularity, if that is a goal. In summary, while the measure used by Gershenson et al. (1999) is the only one that is meant explicitly for any life-cycle stage, it is important to note that the more specific measures such as Newcomb et al. (1996) could be generalized beyond function or whatever elements they do discuss. Alternatively, the more generalized methods could be adapted to encompass multiple sets of specific definitions of dependence and similarity like those of Newcomb et al. (1996). A problem with the measures, as with the design methods to follow, is that they are extremely information intensive and are therefore quite cumbersome. It is for this reason that few, if any, complex examples have been used in research. However, most measures can be automated using the previously described representation. Therefore, if you have gotten to the point of representing the product in terms of its modularity, measuring is a short step away. There seems to be a move towards interaction ratings (dependence and/or similarity) between components. These ratings are then somehow multiplied or added to give an overall measure. A quantitative comparison of the few different methods should be undertaken to better understand the benefits of each. There is also a need for less accurate, less information intensive measures that are useful during concept development and layout design, when many modularity-impacting decisions are made.

4. Modular product design methods The heart of research into product modularity is the development of modular products. Therefore, methods for developing more modular products are essential. Baldwin and Clark (1997, 2000) discuss the difficulties in designing modular systems and say that the design of modular systems is far more difficult than comparable interconnected systems. Modular design methods fall into four main categories—checklist methods, design rules, matrix manipulations, and step-by-step measure and re-design methods. Checklist methods are usually simplistic and inefficient. Design rules are usually proactive and easily applied but lack an ability for specific or complete design. Matrix representation and manipulation allows for guided component/module manipulation. These manipulations are information intensive but perhaps more detailed. The step-by-step measure and redesign methods are nearly always included as part of the matrix methods. These methods require that the component/module manipula-

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tions be done one at a time based upon a modularity measure. The checklist methods are far more ‘high level’ and include product family and organizational decisions. The Holonic Product Design (HPD) method developed by Marshall et al. (1998) embodies the framework, methodology, and process of modularity. Attention is given to cellular manufacturing and the relationship of cells to manufacturing and the implications for life-cycle stages beyond manufacturing. The method is a checklist to ensure corporate goals and product requirements are accounted for along with modularity decisions. The HPD self-assessment provides evaluations to help companies: clarify reasons to change to a modular product architecture; clarify business strategies and corporate objectives; define the organization of the company; provide a platform for the HPD methodology; examine existing and future products and their features for suitability to modularity; and provide guidance on the level of modularity suited to the product and the company.

The HPD method is detailed in its coverage. It is precise and easy to follow. However, unlike forthcoming methods, this is only a design guideline, a checklist. There is no real method, but a set of rules that can sometimes conflict with no guide in trading off conflicts. Although lacking the structure and depth of HPD, other guideline methods for modular design exist. Spencer (1998) puts forth a set of design guidelines to address issues like module size, complexity, and minimization of interactions between modules. Pimmler and Eppinger (1994) focus on finding alternative architectures and evaluating product decompositions. The steps involved in the methodology adopted for this purpose include decomposition of the system into elements, documenting interactions between elements, and clustering the elements into chunks. After decomposing the system, four types of interactions are considered for documentation: spatial: the need for adjacency or orientation between elements; energy: the need for energy transfer between two elements; information: the need for information or signal transfer between two elements;

and material: the need for material exchange between two elements.

The documentation of interaction involves identification of interaction type and assigning scores to interactions. Interactions are quantified on a þ2 to 2 scale, based on their level of requirement or how detrimental their presence is. Based on the relative importance of interaction types, the methodology allows clustering of either single interaction types or composite weightings. The clustering algorithm reorders rows and columns in a matrix such that the positive elements are clustered close to the diagonal. The goal of clustering is to reduce design interfaces that occur across system boundaries. This method, which relies heavily on concepts from Pahl and Beitz’s (1984) function structure diagram, uses a subjective interaction rating method to describe the product. This is a fault common to all of the methods described here. Pimmler and Eppinger’s description of each rating, from þ2 to 2, is more obvious than most. The clustering algorithm works well to reduce inter-module interaction but ignores similarity. In addition, the method does not insure that the design remains feasible


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in its final form as it treats the components as interaction numbers only and not as design elements. The clustering algorithm also ‘lacks a systematic technique for clustering elements’ (Stone et al. 1998). In an extension to this work (Sosa et al. 2000), the authors have gone on to use similar methods to describe a product development organization and compare the organizational structure to the product structure. They then look at the effect of organizational boundaries, specifically those that do not align with the products modular and integrative boundaries. The authors find that matching organizational structure to the product structure is not necessary. Kusiak and Chow (1987) look at the similar problem of group technology—how to efficiently group manufacturing machines and processes into sub-systems. Their result, a cluster identification algorithm, is a graphical, step-wise method to cluster a machine-part incidence matrix. The method uses the act of crossing out rows and columns of a machine incidence matrix to cluster all machines with even indirect connections. This method does not yield optimal results (which is not its goal) but does lead to significantly improved groupings faster. They then expand the use of this algorithm with subcontracting cost information. The algorithm’s key is its simplicity—in application and computation. However, there is no guarantee that it would continue to move a design towards a more modular product. A measure of modularity could be added to insure that each move was an improvement. Several other researchers have built upon this work. Newcomb et al.’s (1996) work is based on their hypotheses that product architecture is the governing force in life-cycle design and that a more modular architecture is better for all life-cycle viewpoints. They partition a product’s architecture into block diagonal modules (in a component–component matrix) using the graphical algorithm developed by Kusiak and Chow (1987). The method then measures modularity and leaves the designer to maximize this measure. Their modularity measure was detailed earlier. The authors emphasize product modularity and how it influences life-cycle issues, not just product functionality. In a continuation of this work, Coulter et al. (1998) develop a method for suggesting changes to the product to improve the correspondence between modules from different life-cycle viewpoints. However, only recyclability is really discussed. They show how the identification of limiting factors can be used to improve product recyclability during configuration design. Again, only material compatibility (a key element in product recyclability) and physical connectedness are considered, but expansion to other life-cycle issues would not be difficult. Limiting factors are those non-maximized recycling characteristics. Products are partitioned into clusters, the cluster independence is calculated, and module-external physical connections are identified. Each of these module-external physical connections is considered for elimination and a corresponding cluster independence is calculated for each possible redesign. The changes are then performed in order from best to worst cluster independence until a goal cluster independence is reached or design resources are expended. However, it should be noted that this method’s goal is not to increase modularity but to increase recyclability. Modularity may be an offshoot, but correspondence between material recycling and architecture is the goal. Coulter et al.’s (1998) continuation of Newcomb et al.’s work is closer to a design method with its suggestion of which changes to try first based upon limiting factors, therefore allowing feasibility checks at each stage. One major problem is that, after the first change is made, the following changes on the list could no longer be the limiting factors. Therefore, the limiting factors should be continually recalculated.

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Newcomb et al.’s method is an application of Kusiak and Chow’s (1987) with a more comprehensive measure. However, Kusiak and Chow’s graphical method is still divorced from feasibility issues of particular product structures. The method leads to a final configuration that may or may not be feasible with no intermediate steps to allow a designer to move towards a better design. Tate et al. (1998), like the works by Newcomb et al. (1996) and Coulter et al. (1998), have used extensive matrix manipulations as the basis of their modular design method. Once a set of functional requirements is formulated and sets of design parameters have been synthesized, Suh’s (1990) independence and information axioms are applied to evaluate proposed designs. Axiomatic design provides a structure for evaluating different designs in terms of how well they are able to satisfy their functional requirements. The independence axiom is utilized for checking the functional independence. The resulting design matrix shows functional and design parameter relationships as strong or weak depending upon the derivative of the functional requirement with respect to the design parameter. A dependency is an off-diagonal element in a design matrix. Discussed dependencies are of three types: operational dependency, design decision dependency, and manufacturing dependency. Other types of dependencies might include recycling, maintenance, etc., but are not discussed. The design is a decoupled design if the matrix is triangular, uncoupled if it is a diagonal matrix, and coupled in any other form. Again, Tate et al.’s (1998) method is more of a method of measurement coupled with a design goal (a diagonal matrix) than a design method. Their measurements are similar to others’ and have a strong foundation in independence. These measurements lack the element of similarity. As described earlier, Huang and Kusiak (1998 and others) have a modular design method in which modularity refers to the decomposition of the product family into modules that are used to meet various functions of the products. Although they use it for product families, the work is applicable to singular products as well. Product architecture is the ‘scheme by which its functional elements are arranged and interact’. The component– component interaction matrix is decomposed into mutually separable sub-matrices with a minimum number of non-empty high value entries outside the block diagonal matrix and a maximum number of strongly desired entries. Additionally, a minimum number of strongly undesired entries should be included in the sub-matrices of the block diagonal suitability matrix. These two matrices describe interactions between components and the suitability of combining components into a single module. As with other methods, suitability could be extended to represent similarity or any life-cycle constraint. Matrix entries are typically 0 or 1 for interaction (although they could be scaled) and a, e, o, and u (representing strongly desired to strongly undesired) for suitability. These actions are subject to three constraints—empty modules are not allowed, the number of components in a module cannot exceed the upper bound, and the total cost of the components cannot exceed a total budget. The decomposition approach adopted in this method involves the transformation of the interaction and suitability matrices based on triangularizing the interaction matrices, analysis of the corresponding suitability matrix for ‘goodness’, and combination of components into a new product. This iterative process allows for the removal of a component from a module if it is incompatible, the formation of new modules from this process, or the duplication of components if it is ‘strongly desired’ in two modules simultaneously. Huang and Kusiak’s method for grouping components is different from others in some significant ways. While they use two matrices, one is a constraint matrix.


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Although this means that the interaction matrix contains less information, it is a simpler way to include constraints in the process. They have opted for a manual process with a very simple set of procedures. This allows for an easy implementation, even with more complex products. However, they do not clearly spell out when to make deletions or duplication. Therefore, users could easily get many different answers. Lastly, the inclusion of cost as a driver in the process, even if it is not done systematically, is surprisingly rare in modularity research. Allen and Carlson-Skalak (1998) developed a design methodology for evolutionary and feature-change development effort. The method is based on Ishii et al.’s (1995) fishbone diagram for disassembly but it allows for sub-modules based on functionality. Allen and Carlson-Skalak’s method leads to a measure of disassembly modularity in only a few simple steps. However, it is not a redesign method since it offers no input to or mechanism for redesign. It can be used as an information source (although the metric used is quite simple) for other design methods. The steps involved are identification of modules of previous product generations, identification of the function structure with respect to the company’s structure, the development of a product’s system function structure, and calculation of metrics to indicate the modularity of the product. Their measure of modularity, number of modules/number of parts, is similar to Ishii et al.’s (1995) commonality measure. These steps are iterated to verify and update information from previous steps. After the development of architecture and sub-teams for the previous generation product, the architecture will have to be applied to new products to yield the ‘design’. Gu et al. (1997) state that product modularization may be applied in different forms. Different modularization scenarios have different impacts on the life-cycle characteristics of a product. A product could be modularized to enhance assembly, reusability, etc. The effect of modularization on functions can be represented by functional interactions among components in terms of exchanges of materials, energy, and signals, or spatial and geometric relationships. The geometric relationships include attachment, positioning, motion, and containment. In work by similar researchers, the goal of Sosale et al. (1997) is to develop a modular design method to assist in grouping components into easily detachable modules such that they can be easily reused or remanufactured. Material compatibility has to be considered for recycling in addition to ease of disassembly. Modular design can be approached in two ways: 1) form modules based on each objective separately and then make trade-off decisions between different modular configurations or 2) modularize a product based on a weighted average objective. Their design method has three phases. Problem definition: this includes identification of type and characteristics of design problems, decomposing the problem into sub-problems, and determining the objectives of modularization. Interaction analysis: as described earlier, each modular design requires a set of factors to be considered. To evaluate the interactions for the objective, values are assigned to each objective. An interaction matrix, having the interaction values between components, is constructed. These values are then scaled to lie between 0 and 10. A weighted average is then calculated for the interactions for any two components. Module formulation: an algorithm is then implemented to cluster the components into modules such that the component–component interactions within a module are maximized. If two components are not separable at all, they are considered

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J. K. Gershenson et al. as a single component. The algorithm generates random configurations in search of the best configuration. Specifying the duration controls the period of search. Objective function values are calculated for each new configuration so that new configuration replaces older configurations based on the probability of change.

The outstanding facet of this work is that it is specifically designed to accommodate multiple life-cycle elements simultaneously. The use of a weighted objective function at once adds definition and increased subjectivity to the method. This is on top of the already subjective nature of the interaction ratings. The goal of the design method is to maximize the interactions within a module. However, it should be questioned whether maximizing intra-module interactions is a more relevant goal than minimizing inter-module interactions. In addition, the notion of similarity is missing. The algorithm appropriately accounts for design constraints by treating component–component inseparability. However, component–component incompatibility is not considered. For Gershenson et al. (1999), creating modular products involves comparing the component tree and process graphs of a product and making sure that, at each level of detail, the product’s components are as independent from one another as possible for each level of detail of the life-cycle processes. If a dependency does occur, it should occur within a module. In addition, within a module and at each level of detail, every process should be similar for every component (Gershenson and Prasad 1997a). The goal of Gershenson et al.’s design methodology is to redesign a product by eliminating components or modules, rearranging components or modules, or changing component attributes. Elimination is the simplest process. Reconfiguration is the shifting of components to other modules to increase the total relative modularity. Redesign is the changing of component attributes to reduce outside similarities and dependencies or increase inside similarities and dependencies. Each step of the method is controlled by their previously discussed total relative modularity measure. A designer moves from elimination to redesign and from least modular components to most modular until a feasible design change is identified that improves the modularity measure. The method then begins anew with updated matrices and measurements. Gershenson et al.’s concept of elimination of external similarities and dependencies is not unique; nor is their idea of using a measure of modularity to guide that elimination. What is unique in their work is their combination of these with a step-wise iterative design approach. This approach allows for few or many design changes, all of which are moving towards a more modular product. However, this strength is also a significant weakness. The method is slow and calculation intensive, especially for complex products. Their move towards semi-automation (Zhang et al. 2001) may ease this burden. Perhaps, too, they should seek to include some form of optimization that includes feasibility to reduce the design time. Another unique element is the inclusion of elimination—of modules and components—to increase modularity. This signals that the design method would fit in well with other design for X methods that stress allowing elimination. Hillstrom (1994) sets the design task of optimizing modularity. The task of determining the optimum number of modules is a complex task, which is influenced by factors like:

function variants must be created from simple assembly modules; modules may be broken only to the extent that functions and costs allow; quality must be met and error propagation must be taken into account; and common modules must be designed for equal wear and easy replacement.


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This method of identifying modules consists of using quality function deployment analysis to make sure the right product specifications are attained, then module creation, analysis of interfaces, and module selection to organize the product, and finally design for assembly analysis of each module to minimize cost. While there are no rules for module creation, the next step is to design the module interfaces according to the principles of independence in axiomatic design. Based on functional analysis, a decision as to whether a proposed solution is functionally acceptable is made. The remaining solutions are filtered to obtain the best possible solutions. The number of surfaces contained in the interface, form, and tolerances associated with each surface provide a measure of the information content. This can be used to choose a better or simpler design. Relative cost can be related to interface complexity, and is used as a measure for comparing different solutions in the framework of axiomatic design. This heuristic application of traditional axiomatic (independence) design combined with a qualitative measure of ‘goodness’ based on axiomatic design (information content) is novel but lacks the functionality of most of the previously described methods and never realizes the stated goal of optimization. Stone et al. (1998), based on Little et al. (1997) and McAdams et al. (1999), put forward a heuristic method to identify modules from a functional description of a product’s architecture. Using a function structure diagram based upon the work of Pahl and Beitz (1984), they define the material, energy, and signal flows. Stone et al. use the function structure diagram to identify: 1) dominant flows—a set of sub-functions a flow passes through from system entry/flow initiation to system exit/flow conversion; 2) branching flows—a set of sub-functions making a parallel function chain associated with a branched flow; and 3) conversion-transmission flows—a set of sub-functions responsible for the transition between flows. Each of these flows is a potential module or module type. The material, energy, and signal flows are then used to identify dependencies between modules. These lead to a quantified device-function matrix using weighted customer requirements. This work is unique for its structure in module identification. This work stops at function-based modules but similar function structure diagrams can be developed for other life-cycle processes. However, we would still be left with a heuristic approach to modular design that is not easily quantified. Expansions to this work (Zamirowski and Otto 1999, Dahmus et al. 2000) have centered on portfolio architecting—the design of a product family by using modular and integrative assemblies. Although beyond the scope of this paper, their method utilizes a qualitative modularity matrix to examine commonalities across a platform and look for modular opportunities. Their improved method integrates customer needs analysis as a basis for tradeoffs on the goodness of portfolio decisions. A limited move towards portfolio optimization that incorporates the uncertainty of a project being funded was made by this group (Gonzalez-Zugasti et al. 1998, 1999, Gonzalez-Zugasti and Otto 2000, Yu et al. 1999) with respect to spacecraft platforms but the work is not as complete as their design work. Other methods that concentrate on product platform or family design (Conner et al. 1999, Coulter et al. 1998, Erens and Verhuist 1996, Fujita et al. 1998, 1999, GonzalezZugasti et al. 1998, Ishii et al. 1995, Martin and Ishii 1996, 1997, 2000, Ortega et al. 1999, Siddique and Rosen 1998, Simpson et al. 1999), although relevant because elements of the works depend upon modularity and may be applicable to single product modularity, have been omitted. In summary, despite the apparent differences in the aforementioned modular design methods there is quite a bit of commonality. All modular design methods have a

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similar goal of clustering components into modules. Most methods include a represent, measure, manipulate, and measure iteration. Some do this as a guided iteration, others just iterate through all possibilities. Some methods try to limit the number of possibilities. Clearly, checking all feasible designs is important, as is a method open to multiple life-cycle modularity criteria. One problem with nearly all of the described modular design methods is that they require a considerable amount of information that is not always readily available, especially at the point where modular design considerations are most effective. Therefore, all of these methods work best in well structured and information intensive product development environments. All of these methods also require significant amounts of information input, calculation, and manipulation. Therefore, they are only reasonable as computer implementations. One other issue is that methods that give a single, final result do not take into account the minor design changes that are necessary to accommodate each reconfiguration and their impact on dependencies. That is, often the design changes are more complex than simply moving components into new modules. In addition, the feasibility of these individual changes is often not accounted for in methods that seek a singular, optimal configuration. Lastly and most importantly, none of the design methods has shown an improved design by any independent measurement, and most cannot guarantee improved modularity. However, a solid foundation exists upon which to build modular design methods.

5. Discussion This paper is meant to give an overview of the measures and design methods in current product modularity research. Given the depth that this format permits, it is difficult to fully understand each work. Despite the brief descriptions, one can find near consensus on some points and disagreement on others. Overall, there is a significant lack of consensus in modularity measures and modular product design methods. Whatever consensus there is exists due to a common understanding of what modularity is. The agreement is at the more abstract levels. When the measures and methods get down to details, there is significant disagreement. However, the disagreement is not as much conflicting ideas as it is a set of greatly different ways of accomplishing similar tasks. Areas of consensus, or at least significant similarity, are based in representation, the overall structure of the modularity measure, and the normalization of the measure. Matrix-based methods represent the relationships between components as a first step towards measuring modularity and grouping components into modules. Typically, the matrices have rows and columns that represent components. Occasionally, additional columns that represent life-cycle processes are added. The contents of these matrices—the cells that represent the relationships—vary in nature and meaning. Some representations merely record the existence of relationships, a 0/1 or O/X content. Other representations quantify the strength of the relationship. The description of the relationships differs from one representation to another as well. Most use a single matrix to represent dependencies. Some use two matrices to represent dependencies and similarities. However, the definition of dependencies and similarities are often contextual, whether for retirement-based representations or group technology-based representations. There is some agreement as well on the measures of independence and similarity. For independence, the measure of relationships among components inside the module


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versus those relationships with components outside the module is common. However, the types of dependencies (design dependencies, functional connections, assembly connections, disassembly connections, etc.) vary among researchers. Similarity, when it is considered, is not so easily corralled. Similarity is usually used to denote a like processing or the ability to be processed in a like manner. This can be for specific life-cycle processes (material compatibility for recycling) or any life-cycle process. Typically, independence and similarity are measured separately but correspondingly. Usually, a measure is the number of dependencies (or similarities) that occur between components in the same module as a percentage of the total number of dependencies (or similarities) in the whole product or system. Occasionally, the strength of those relationships is accounted for in the measure as well. While there are several areas of consensus, there are also several aspects of the modularity measures and modular design methods that are parallel, if not conflicting. These aspects include how the design method is implemented, the role of the measure in the design method, and representation’s impact on the inclusion of multiple lifecycle stages. As mentioned in the discussion of modular design methods, the goal of some design methods is to optimize the modularity while for others the goal is to improve the modularity. The difference between the two is critical in implementation. While all designers would like to optimize the modularity, the methods for optimization presented in this paper do not guarantee that the optimized design is also a feasible design. The step by step methods either include a feasibility check at each proposed design change or their stepped nature would allow for it. Can feasibility be included into the optimization methods? Perhaps that is possible if the optimization is semi-automatic. This disagreement between optimization and improvement brings to light another question on the specifics of the implementation of modular design methods. What is the role of the modular design measure? Nearly every research group tackling modularity has proposed some sort of measure of modularity. Most have discussed what makes a product more modular. Some have proposed systematic modular design methods to improve product modularity. Some of these methods include the modular design method as a guide for improving modularity and some use guidelines to improve the modularity. The big reason for the disagreement is the amount of information and work that goes into calculating the modularity measures. Again, there is a way to achieve consensus if the measures can be automated, especially if they are automated from standard product descriptions. The last major area of disagreement is over the inclusion of life-cycle issues in the measure and design of modular products. The question here is one of representation as well as measure. Can the same representation and measurements be used to include any life-cycle issue of interest? Some have measured each life-cycle issue separately and then weighted and combined them. Some have used very different definitions of dependencies and other variables of interest depending upon the life-cycle issue of interest. In the end, it comes down to finding a single way to define and accommodate all the information needed. No method has a definition of variables that cleanly and easily spans the life-cycle. Considerably more time should be placed on the definitions of at least dependence and similarity to achieve this. As described previously, each measure or method may have varying benefits and efficiencies. Clearly, the overriding problem is that most methods are worked on in isolation. There is a strong need to compare and/or connect the various methods.

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The lack of a true consensus in any of these foundation areas points to the central matter of this paper—there is an obvious need for further research in product modularity. Some aspects lacking consensus or utilization in the current works include: 1. 2. 3. 4.

a widespread definition for modularity that takes into account aspects of a product other than its function and perhaps one life-cycle aspect; a concentration on methods for designing modular products; modularity measure that takes into account the above two points as well as being useful to a designer; and a more object method of measuring dependence and similarity relationships. Due to the immature nature of modularity and the need for rigor in its definition, considerable research effort has been put into conveying the definitions.

The above research requirements point to the need for more quantitative research that compares and contrasts existing modularity research. It is this need that serves as the motivation for the third article in this series—Product Modularity: A Quantitative Study of Measures and Methods. That article compares the modularity measures and modular design methods using a singular basis, multiple life-cycle concerns, and over a dozen products of varying complexity. The goal is a combination of attributes that result in a verifiably better measure and method.

6. Conclusions While much has changed in modularity research in the 17 years since the independence axiom, some questions remain unanswered. Ulrich and Tung (1991) ask several research questions that are even more relevant a decade later: ‘How much modularity is optimal?’ ‘What is the impact of product modularity on customer utility?’ ‘What is the impact of product modularity on product quality?’ ‘What is the impact of product modularity on product development management?’ ‘Are there principles to guide the choice of where to place product interfaces?’ ‘What is the connection between the organizational structure of the firm and the types of modularity that can be successfully implemented within the firm?’ The authors believe the next phase is a rigorous and application-laden investigation of the utility, incorporation, and information content of modular design. Experimentation in the design process will be a common theme among successful works.

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Product Modularity Measures and Design Methods

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