product modularity measures and design methods

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 productmodularity and methods to achieve modularity in product design. Discussions ofthe development of modular products have increased in recent years. The researchactivity into the development of modularity measures and methods has alsoincreased. These measures and methods vary considerably in purpose and process.Some are highly quantitative and some are completely qualitative. Some areinformation intensive and some are more easily applied. The relationship toproduct platform planning is also shown. This overview shows no clear consensusbeyond those found in the definition of modularity. There are, however, severalthemes that are prevalent. Most measures center on measuring dependencies withcomponents external to modules. Some measures include a measure of componentsimilarity. However, what is measured as dependencies and similarities varies bymeasure and by context. Additionally, there is always some subjectivity in themeasures. The design methods vary greatly. Many are based on measures. Most areinformation intensive. Noticeably, the measures and methods lack rigorousverification and validation. There is also a lack of quantitative comparison amongthe various measures and methods. It is hoped that this research will highlight thepresent inconsistencies in the field of modular product design and put forwardsome critical questions, which will shape future research into this field.

Key words: modularity, design, design theory, design methods, optimization

1. MotivationThis 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 accom-

panying paper entitled ‘Product Modularity: Definitions and Benefits’

(Gershenson et al., 2002).

Modularity arises from the decomposition of a product into subassemblies and com-ponents. This division facilitates the standardization of components and increased productvariety (Gershenson and Prasad 1997a, 1997b). As firms strive to rationalize their productlines 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 DesignISSN 0954-4828 print/ISSN 1466-1387 online # 2004 Taylor & Francis Ltd

http://www.tandf.co.uk/journalsDOI: 10.1080/0954482032000101731

J. ENG. DESIGN, VOL. 15, NO. 1, FEBRUARY 2004, 33–51

modularity has gained attention. Although product modularity has been increasinglyapplied to industrial products over the past two decades, the science of modular designhas not been studied in detail until recently. There is neither a widely adopted measureof a product’s modularity nor a widely adopted systematic methodology that helpsdesigners increase the modularity of a product.

After commencing their own research into modular product design, the authorsbegan a validation study to show that their modular design method did in fact leadto more modular products. The idea was to have ten consumer products that wouldbe rated for modularity by third parties and then to rate these by our own modularitymeasure and validate the correlation. They began with a group of graduate students asthe third party. The results were surprising. There was no statistical significance to thestudents’ ranking of product modularities. There was not agreement on the placementof a single product. Note that, by their measure, there was a very wide spectrum ofmodularity represented by the ten products.

Assuming that the fault of the study laid in the choice of subject pool, the studywas redone with small, separate third-party pools of: undergraduate students, designengineers with more than ten years experience, product development managers, anda group of design engineers/researchers who had indicated an interest in and familia-rity with modular product design. The results were the same for each subject pool—acomplete lack of agreement as to which products were more modular. A small studyusing pairwise comparison was of no help either.

After sifting through additional industrial and academic literature on modularity, itbecame clear that, while the term ‘modular’ is used often, there has been little effortmade to come to a consensus on the definition of this term and its appropriate use. Theauthors therefore began the task of collating much of the available literature and look-ing for common threads.

This paper is meant as a review of the current thoughts on two topics integral to modu-lar design: measures of modularity and modular product design methods. In discussingthese topics, a third issue, methods of product representation for modular design, becomespervasive. This issue will therefore be discussed first. The framework for these discus-sions is set in the accompanying paper where the definition of modularity is discussedas encompassing an element of independence between modules and an element of simi-larity 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 thirtyyears in a variety of fields. The authors understand that they may have missed someexcellent works, especially those that have not been translated into English. The authorslooked for modularity discussions in every area of Engineering, in Computer Science, inBiology, in Architecture, and in Art. They also had difficulty fitting all of this great workinto a single paper. Therefore, only a cursory discussion of each work’s elements isincluded and some works that reiterate stated concepts are omitted. The reader is encou-raged to seek out referenced work for more detail. The references section of this paperhas also been expanded and is more bibliographical in nature. What follows is a reviewof the state of the art of product modularity with the conclusions of the authors.

2. Method of product representation for modular designRepresentation of products in modularity research is not a critical issue. However,

since most modularity research has gone through considerable effort to represent

34 J. K. Gershenson et al.

product information, the authors are including this topic in this paper. The representationsof information in product modularity are shaped by the definitions of modularity—mostinvolving relationships among components in a product. The necessary informationnaturally lends itself to a matrix representation in which components in the productsmake up both the rows and the columns and the constitutive matrix elements show therelationships between the components. One matrix might suffice showing a singledependence 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 matricesto show both dependence and similarity as in Huang and Kusiak (1998) and Gershensonet al. (1999). Some choose to show process relationships too, but most later distill theseinto component–component relationships. There is no record of significantly differentmethods to represent the modular product information that is also later used in thedesign 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 measure-ment 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 overallproduct concept in terms of functional and/or physical elements. The authors suggestdecomposition 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 bothdepending on the type of design (incremental or novel design). Later works by thatgroup, including Sosa et al. (2000), expand to use a design structure matrix to repre-sent component interfaces.

Sosale et al. (1997) fill their relationship matrices with physical interactions in theproduct, 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 theweight of these interactions as objectives, to fill in a single relationship matrix. This is oneof only a few representations to account for similarity in life-cycle objectives. These con-straints are later considered during the grouping of components into modules.

Huang and Kusiak (1998) base their mature method of modular product represen-tation on interaction and suitability matrices. The two types of relationships involvedin the modularity concept are similarity of functional interactions (on a 0–10 scale forfrequency of interaction), and suitability of inclusion of components in a module (onan a, e, o, u basis for strongly desired to strongly undesired). Components not belong-ing to any module are independent components. The modularity matrix allows repre-sentation 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 andsimilarities, to represent component interactions. The rows of the matrices representeach component and the columns represent each component and each life-cycle taskthe product undergoes (manufacturing, assembly, service, retirement, etc.). This allowsfor component–component and component–process relationships. The elements of

Measures and design methods for product modularity 35

the matrix are filled with a subjective, 1-5 rating of the strength of the dependency orsimilarity. The subjective rating, although it includes guidelines, are the primarysource of error in this representation. An important consideration when defining therelative modularity of a product is the level of detail chosen when looking at the pro-duct structure. A product may seem modular but, at some levels of detail, the structuremay 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 pro-duct. The tree-like structure is helpful in discerning levels of detail and showing sub-assembly interactions. Another important consideration when defining life-cyclemodularity is the chosen level of abstraction of the life-cycle process itself. Processgraphs 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 productdecomposition graphs or reverse fishbone diagrams to represent relationships betweenmodules. This method lacks the information content of the previous methods and,while promising for product recycling description (the authors’ intent), may not haveother 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, orinformation flow to develop a digraph that can be used for the retrieval of strongly con-nected components. The digraph represents strongly connected components as a vertexand edges represent cluster to cluster connections. The adjacency matrix of the digraphis constructed with elements representing the number of paths of length 1 leading fromvertex i to vertex j in the digraph. The reachability matrix R is then constructed. If allthe entries of the product of R and its transpose are equal to 1, then the object consistsof one cluster and cannot be decomposed. If the product results in all entries equal to0, then the designed object is disconnected. The sequence in which the vertices repre-senting components of the designed object are numbered is not relevant. The prece-dence matrix is then defined for the clusters by performing logical operations onthe matrices.

This work was expanded upon by He and Kusiak (1996) for the case of a productstructure represented by an acyclic digraph, the nodes represent operations and the arcsrepresent precedence relations between the operations. Each product in the familyshares the same basic features and differs only by the variant structure. These worksgive a strong understanding of the product but their complexity does not lend itselfto product design nor is there a built in measurement.

A few works have taken very different approaches to modular product representa-tion. These works have borrowed from the representation of complex products andsystems used elsewhere in design theory and design automation research. The goalof Newcomb et al. (1996) is to develop an evaluation methodology/tool that thedesigner can use in configuration design to determine the degree to which a designsimultaneously meets its function, service, and post life-cycle goals. The authors usea product decomposition and module comparison approach to achieve product modu-larity. This work has evolved into a tradeoff analysis (Ortega et al. 1999), and a similarapproach has used graph-grammars (Siddique and Rosen 1999) to represent productsand families of product. The use of graph-grammars to ‘design in’ or extract commona-lity and dependence information allows for the automation of some very tedious tasks.


This approach is more likely to allow for optimization as well. Other research(Schmidt and Cagan 1998) has looked at the representation of component combina-tions, a similar, but not directly related problem.

Constantine et al. (1998), in work that only happens to touch on modularity but isimportant to the topic of product representation, use shape grammars to allow for therapid generation of a variety of designs by applying different rules in a rule set. Adesigner can receive immediate feedback on the effects of a design change and itseffect on manufacturing cost. This may have significant implications on the futureof modular product representation.

Other researchers such as Du et al. (2000) and Line and Steiner (2000) haveworked at extracting and representing modular architecture elements in CAD systems.Additionally, Finch (1999) has begun to look at the possibility of set-based causalrepresentation for higher-level product family decisions. As part of set-based design,this method will probably have long-range implications. In several works (Erens andHegge 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 towardsdescribing product families.

In summary, product representation is a very important issue in design theory andmethodology. While matrices have dominated product representation in modularityliterature, it is because the representation has been shaped by the problem definition.Matrix representation fits the need for component manipulation and comparison, asdiscussed later in the paper.

3. Measure of modularityThe 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 fol-lowed, and it can be shown to guarantee improved modularity (and if the benefits ofimproved modularity have been proven), then the measure of modularity as an abstractnumber is unimportant. However, when incremental changes in design are made andtheir effect on modularity are questioned or when there are decisions to be made andmodularity will serve as the basis of that decision, a measure of product modularity isimportant. There are few of these measures in the literature.

Gershenson et al. (1999), like most researchers, state that modularity is a relativeproperty. Products possess a higher or lower degree of modularity. A product with ahigher degree of modularity either contains a larger percentage of components or sub-assemblies that are modular or contains components and subassemblies, which are, onaverage, more modular. The measure of relative modularity that they developed is theratio of intra-module similarities to all similarities, both intra- and inter-module, addedto the ratio of intra-module dependencies to all dependencies, both intra- and inter-mod-ule. The similarities considered are component–process similarities while the dependen-cies are both component–component and component–process dependencies.

Each element is calculated using subjective ratings of the above parameters forrelationships between each component in the product and all other components as wellas each component and each life-cycle process the product goes through. The measureshows, on a 0 to 2 scale with two being more modular, what fraction of these relation-ships occurs inside a module as opposed to between modules. Calculations of eachquantity in this measure are detailed in their work (Gershenson et al. 1999), as space


does not permit here. This work is applicable to all life-cycle elements. However, thiswork still relies upon subjective measurements of component–component and compo-nent–process similarity and dependency. While measurement guidelines are offered,they are sparse.

Newcomb et al. (1998) use a measure of modularity based upon the multiplicationof inter-module connections and the average correspondence between modules. Theyuse the material compatibility between components to calculate the compatibilitywithin a module relative to the compatibility of within and between modules (corres-pondence ratio). They do likewise with the physical connections between components(cluster independence). Multiplying the correspondence ratio and the cluster indepen-dence gives a measure of modularity.

Newcomb et al.’s measure is similar to those of Zhang et al. (2001) andGershenson et al. (1999) in that it incorporates an element of similarity (compatibility)and dependency ( physical connections). However, their similarity and dependency arefar 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 connec-tions as the sole issue of dependence strengthens the product retirement tie but pre-cludes other life-cycle issues. This limits the applicability of the measure butincreases the precision. It would be interesting to compare Newcomb et al.’s multipli-cative measure with Gershenson et al.’s additive measure. The multiplicative measureintuitively captures the idea of both similarity and independence being necessarywhere one cannot make up for the other.

In later works by a similar group, Siddique and Rosen (1998, 1999) expand intothe measurement of interface modularity—the standardization of the module inter-faces. Their candidate measurement is the number of common interface componentsdivided by the total number of interfaces both common and unique.

Sosale et al. (1997) base their modularity measurement on interaction analysis thatuses a set of design objectives to be considered. To evaluate the interactions for theoverall objective, values are assigned to each objective. The interaction matrix, havingthe interaction values between components, is then constructed. These values arescaled to lie between 0 and 10. A weighted average is then calculated for the inter-actions for any two components. This method is quite open-ended leaving room forlife-cycle processes. However, the method lacks specific guidelines to assist in imple-menting the elements of modularity in the measure. The measure also relies on twoinstances of subjective ratings, which are then multiplied, calling its accuracy andrange into question.

Erixson et al. (1994) offer that the optimal number of modules in a product is depen-dent upon the number of parts in the product and their assembly time. Although no expli-cit 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 recyclingdone 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 themeasurement of three indices, namely commonality, differentiation point, and set-upcost. The authors use tools like quality function deployment, conjoint analysis, and uti-lity theory for estimating the importance of variety and build upon the concept of pro-duct structure graphs, to represent the basic information (Martin and Ishii 1997). Otherworks, including Kota and Sethuraman (1998) have used similar, although less encom-passing commonality indices. Maupin and Stauffer (2000) discuss a measure of


modularity geared towards understanding design for assembly decisions at small com-panies. They use simplicity, a measure of assembly operation time, and then multiply thesales effect of each model in a family to develop a total measure. They then look at thereuse of components relative to simplicity—a measure they call standardization.Standardization, with a direct cost model, is incorporated into a delayed differentiationindex. This index, along with cost is tracked to measure the ‘goodness’ of product archi-tecture decisions. This method is similar to and simpler than Ishii et al.’s method is, butMaupin and Stauffer’s does include a cost model. Hillstrom (1994) uses informationfrom functional and physical hierarchies to clarify interface or function interactions,while design for manufacture and assembly tools are used to obtain a measure of com-plexity of each interface. He and Kusiak (1996) discuss the performance of form/func-tion modules in terms of manufacturing cost. None of these tools uses a modularitymeasure per se but other life-cycle measures within a modular design framework. Theclosest is the clumping index used by DiMarco et al. (1994). However, these will neverlead to optimal modularity, if that is a goal.

In summary, while the measure used by Gershenson et al. (1999) is the only onethat is meant explicitly for any life-cycle stage, it is important to note that the morespecific measures such as Newcomb et al. (1996) could be generalized beyond func-tion or whatever elements they do discuss. Alternatively, the more generalized methodscould be adapted to encompass multiple sets of specific definitions of dependence andsimilarity like those of Newcomb et al. (1996). A problem with the measures, as withthe design methods to follow, is that they are extremely information intensive and aretherefore quite cumbersome. It is for this reason that few, if any, complex exampleshave been used in research. However, most measures can be automated using the pre-viously described representation. Therefore, if you have gotten to the point of repre-senting 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 givean overall measure. A quantitative comparison of the few different methods shouldbe undertaken to better understand the benefits of each. There is also a need for lessaccurate, less information intensive measures that are useful during concept develop-ment and layout design, when many modularity-impacting decisions are made.

4. Modular product design methodsThe heart of research into product modularity is the development of modular pro-

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


tions be done one at a time based upon a modularity measure. The checklist methodsare 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 givento cellular manufacturing and the relationship of cells to manufacturing and theimplications for life-cycle stages beyond manufacturing. The method is a checklistto ensure corporate goals and product requirements are accounted for along with mod-ularity 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 noreal method, but a set of rules that can sometimes conflict with no guide in trading offconflicts. Although lacking the structure and depth of HPD, other guideline methodsfor modular design exist. Spencer (1998) puts forth a set of design guidelines toaddress issues like module size, complexity, and minimization of interactions betweenmodules.

Pimmler and Eppinger (1994) focus on finding alternative architectures and eval-uating product decompositions. The steps involved in the methodology adopted forthis purpose include decomposition of the system into elements, documenting interac-tions between elements, and clustering the elements into chunks. After decomposingthe 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 andassigning scores to interactions. Interactions are quantified on a þ2 to �2 scale, basedon their level of requirement or how detrimental their presence is. Based on the relativeimportance of interaction types, the methodology allows clustering of either singleinteraction types or composite weightings. The clustering algorithm reorders rows andcolumns 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 bound-aries. This method, which relies heavily on concepts from Pahl and Beitz’s (1984)function structure diagram, uses a subjective interaction rating method to describe theproduct. This is a fault common to all of the methods described here. Pimmler andEppinger’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 ignoressimilarity. In addition, the method does not insure that the design remains feasible


in its final form as it treats the components as interaction numbers only and notas design elements. The clustering algorithm also ‘lacks a systematic technique forclustering 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 productdevelopment organization and compare the organizational structure to the productstructure. They then look at the effect of organizational boundaries, specifically thosethat do not align with the products modular and integrative boundaries. The authorsfind that matching organizational structure to the product structure is not necessary.

Kusiak and Chow (1987) look at the similar problem of group technology—how toefficiently group manufacturing machines and processes into sub-systems. Theirresult, a cluster identification algorithm, is a graphical, step-wise method to clustera machine-part incidence matrix. The method uses the act of crossing out rows andcolumns of a machine incidence matrix to cluster all machines with even indirect con-nections. This method does not yield optimal results (which is not its goal) but doeslead to significantly improved groupings faster. They then expand the use of this algo-rithm with subcontracting cost information. The algorithm’s key is its simplicity—inapplication and computation. However, there is no guarantee that it would continueto move a design towards a more modular product. A measure of modularity couldbe added to insure that each move was an improvement. Several other researchers havebuilt upon this work.

Newcomb et al.’s (1996) work is based on their hypotheses that product architec-ture is the governing force in life-cycle design and that a more modular architecture isbetter for all life-cycle viewpoints. They partition a product’s architecture into blockdiagonal modules (in a component–component matrix) using the graphical algorithmdeveloped by Kusiak and Chow (1987). The method then measures modularity andleaves the designer to maximize this measure. Their modularity measure was detailedearlier. The authors emphasize product modularity and how it influences life-cycleissues, 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 corres-pondence between modules from different life-cycle viewpoints. However, onlyrecyclability is really discussed. They show how the identification of limiting factorscan be used to improve product recyclability during configuration design. Again, onlymaterial compatibility (a key element in product recyclability) and physical connec-tedness are considered, but expansion to other life-cycle issues would not be difficult.Limiting factors are those non-maximized recycling characteristics. Products are parti-tioned into clusters, the cluster independence is calculated, and module-external phy-sical connections are identified. Each of these module-external physical connections isconsidered for elimination and a corresponding cluster independence is calculated foreach possible redesign. The changes are then performed in order from best to worstcluster independence until a goal cluster independence is reached or design resourcesare expended. However, it should be noted that this method’s goal is not to increasemodularity but to increase recyclability. Modularity may be an offshoot, but corres-pondence 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 itssuggestion of which changes to try first based upon limiting factors, therefore allowingfeasibility checks at each stage. One major problem is that, after the first change ismade, the following changes on the list could no longer be the limiting factors.Therefore, the limiting factors should be continually recalculated.


Newcomb et al.’s method is an application of Kusiak and Chow’s (1987) with amore comprehensive measure. However, Kusiak and Chow’s graphical method is stilldivorced from feasibility issues of particular product structures. The method leads to afinal configuration that may or may not be feasible with no intermediate steps to allowa 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 designmethod. Once a set of functional requirements is formulated and sets of design para-meters have been synthesized, Suh’s (1990) independence and information axioms areapplied to evaluate proposed designs. Axiomatic design provides a structure for eval-uating different designs in terms of how well they are able to satisfy their functionalrequirements. The independence axiom is utilized for checking the functional indepen-dence. The resulting design matrix shows functional and design parameterrelationships as strong or weak depending upon the derivative of the functionalrequirement with respect to the design parameter. A dependency is an off-diagonal ele-ment in a design matrix. Discussed dependencies are of three types: operationaldependency, design decision dependency, and manufacturing dependency. Other typesof dependencies might include recycling, maintenance, etc., but are not discussed. Thedesign is a decoupled design if the matrix is triangular, uncoupled if it is a diagonalmatrix, and coupled in any other form. Again, Tate et al.’s (1998) method is moreof a method of measurement coupled with a design goal (a diagonal matrix) than adesign method. Their measurements are similar to others’ and have a strong founda-tion in independence. These measurements lack the element of similarity.

As described earlier, Huang and Kusiak (1998 and others) have a modular designmethod in which modularity refers to the decomposition of the product family into mod-ules that are used to meet various functions of the products. Although they use it for pro-duct families, the work is applicable to singular products as well. Product architecture isthe ‘scheme by which its functional elements are arranged and interact’. The component–component interaction matrix is decomposed into mutually separable sub-matrices witha minimum number of non-empty high value entries outside the block diagonal matrixand a maximum number of strongly desired entries. Additionally, a minimum number ofstrongly undesired entries should be included in the sub-matrices of the block diagonalsuitability matrix. These two matrices describe interactions between components and thesuitability of combining components into a single module. As with other methods, suit-ability could be extended to represent similarity or any life-cycle constraint. Matrixentries are typically 0 or 1 for interaction (although they could be scaled) and a, e, o, andu (representing strongly desired to strongly undesired) for suitability. These actions aresubject to three constraints—empty modules are not allowed, the number of componentsin a module cannot exceed the upper bound, and the total cost of the components cannotexceed a total budget. The decomposition approach adopted in this method involves thetransformation of the interaction and suitability matrices based on triangularizing theinteraction matrices, analysis of the corresponding suitability matrix for ‘goodness’, andcombination of components into a new product. This iterative process allows for theremoval of a component from a module if it is incompatible, the formation of new mod-ules from this process, or the duplication of components if it is ‘strongly desired’ in twomodules simultaneously.

Huang and Kusiak’s method for grouping components is different from others insome significant ways. While they use two matrices, one is a constraint matrix.


Although this means that the interaction matrix contains less information, it is a sim-pler way to include constraints in the process. They have opted for a manual processwith a very simple set of procedures. This allows for an easy implementation, evenwith more complex products. However, they do not clearly spell out when to makedeletions 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 system-atically, is surprisingly rare in modularity research.

Allen and Carlson-Skalak (1998) developed a design methodology for evolution-ary 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 func-tionality. Allen and Carlson-Skalak’s method leads to a measure of disassembly mod-ularity in only a few simple steps. However, it is not a redesign method since it offersno 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 involvedare identification of modules of previous product generations, identification of thefunction structure with respect to the company’s structure, the development of a pro-duct’s system function structure, and calculation of metrics to indicate the modularityof the product. Their measure of modularity, number of modules/number of parts, issimilar to Ishii et al.’s (1995) commonality measure. These steps are iterated to verifyand update information from previous steps. After the development of architecture andsub-teams for the previous generation product, the architecture will have to be appliedto new products to yield the ‘design’.

Gu et al. (1997) state that product modularization may be applied in differentforms. Different modularization scenarios have different impacts on the life-cyclecharacteristics of a product. A product could be modularized to enhance assembly,reusability, etc. The effect of modularization on functions can be represented by func-tional interactions among components in terms of exchanges of materials, energy, andsignals, or spatial and geometric relationships. The geometric relationships includeattachment, positioning, motion, and containment. In work by similar researchers, thegoal of Sosale et al. (1997) is to develop a modular design method to assist in group-ing components into easily detachable modules such that they can be easily reused orremanufactured. Material compatibility has to be considered for recycling in additionto ease of disassembly. Modular design can be approached in two ways: 1) form mod-ules based on each objective separately and then make trade-off decisions between dif-ferent modular configurations or 2) modularize a product based on a weighted averageobjective. Their design method has three phases.

Problem definition: this includes identification of type and characteristics of designproblems, decomposing the problem into sub-problems, and determining theobjectives of modularization.

Interaction analysis: as described earlier, each modular design requires a set offactors to be considered. To evaluate the interactions for the objective, valuesare assigned to each objective. An interaction matrix, having the interactionvalues between components, is constructed. These values are then scaled to liebetween 0 and 10. A weighted average is then calculated for the interactions forany two components.

Module formulation: an algorithm is then implemented to cluster the componentsinto modules such that the component–component interactions within a moduleare maximized. If two components are not separable at all, they are considered


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

The outstanding facet of this work is that it is specifically designed to accommo-date multiple life-cycle elements simultaneously. The use of a weighted objective func-tion at once adds definition and increased subjectivity to the method. This is on top ofthe already subjective nature of the interaction ratings. The goal of the design methodis to maximize the interactions within a module. However, it should be questionedwhether maximizing intra-module interactions is a more relevant goal than minimizinginter-module interactions. In addition, the notion of similarity is missing. The algo-rithm appropriately accounts for design constraints by treating component–componentinseparability. However, component–component incompatibility is not considered.

For Gershenson et al. (1999), creating modular products involves comparing thecomponent tree and process graphs of a product and making sure that, at each levelof detail, the product’s components are as independent from one another as possiblefor each level of detail of the life-cycle processes. If a dependency does occur, itshould 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 elim-inating components or modules, rearranging components or modules, or changingcomponent attributes. Elimination is the simplest process. Reconfiguration is the shift-ing of components to other modules to increase the total relative modularity. Redesignis the changing of component attributes to reduce outside similarities and dependen-cies or increase inside similarities and dependencies. Each step of the method is con-trolled by their previously discussed total relative modularity measure. A designermoves from elimination to redesign and from least modular components to most mod-ular 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 isnot 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 iterativedesign approach. This approach allows for few or many design changes, all of which aremoving towards a more modular product. However, this strength is also a significantweakness. 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 toreduce the design time. Another unique element is the inclusion of elimination—ofmodules and components—to increase modularity. This signals that the design methodwould fit in well with other design for X methods that stress allowing elimination.

Hillstrom (1994) sets the design task of optimizing modularity. The task ofdetermining the optimum number of modules is a complex task, which is influencedby 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.


This method of identifying modules consists of using quality function deploymentanalysis to make sure the right product specifications are attained, then modulecreation, analysis of interfaces, and module selection to organize the product, andfinally design for assembly analysis of each module to minimize cost. While there areno rules for module creation, the next step is to design the module interfaces accordingto the principles of independence in axiomatic design. Based on functional analysis, adecision as to whether a proposed solution is functionally acceptable is made. Theremaining solutions are filtered to obtain the best possible solutions. The number ofsurfaces contained in the interface, form, and tolerances associated with each surfaceprovide a measure of the information content. This can be used to choose a better orsimpler design. Relative cost can be related to interface complexity, and is used as ameasure for comparing different solutions in the framework of axiomatic design.This heuristic application of traditional axiomatic (independence) design combinedwith a qualitative measure of ‘goodness’ based on axiomatic design (information con-tent) is novel but lacks the functionality of most of the previously described methodsand never realizes the stated goal of optimization.

Stone et al. (1998), based on Little et al. (1997) and McAdams et al. (1999), put for-ward a heuristic method to identify modules from a functional description of a product’sarchitecture. 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 functionstructure diagram to identify: 1) dominant flows—a set of sub-functions a flow passesthrough from system entry/flow initiation to system exit/flow conversion; 2) branchingflows—a set of sub-functions making a parallel function chain associated with a branchedflow; and 3) conversion-transmission flows—a set of sub-functions responsible for thetransition 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 betweenmodules. These lead to a quantified device-function matrix using weighted customerrequirements. This work is unique for its structure in module identification. This workstops at function-based modules but similar function structure diagrams can be developedfor other life-cycle processes. However, we would still be left with a heuristic approach tomodular design that is not easily quantified. Expansions to this work (Zamirowski andOtto 1999, Dahmus et al. 2000) have centered on portfolio architecting—the design ofa product family by using modular and integrative assemblies. Although beyond thescope of this paper, their method utilizes a qualitative modularity matrix to examine com-monalities across a platform and look for modular opportunities. Their improved methodintegrates customer needs analysis as a basis for tradeoffs on the goodness of portfoliodecisions. A limited move towards portfolio optimization that incorporates the uncer-tainty 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 spacecraftplatforms 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, Gonzalez-Zugasti 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 elementsof 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 designmethods there is quite a bit of commonality. All modular design methods have a


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 ofpossibilities. Clearly, checking all feasible designs is important, as is a method opento multiple life-cycle modularity criteria.

One problem with nearly all of the described modular design methods is that theyrequire a considerable amount of information that is not always readily available, espe-cially at the point where modular design considerations are most effective. Therefore,all of these methods work best in well structured and information intensive productdevelopment environments. All of these methods also require significant amounts ofinformation input, calculation, and manipulation. Therefore, they are only reasonableas computer implementations. One other issue is that methods that give a single, finalresult do not take into account the minor design changes that are necessary to accom-modate each reconfiguration and their impact on dependencies. That is, often thedesign changes are more complex than simply moving components into new modules.In addition, the feasibility of these individual changes is often not accounted for inmethods that seek a singular, optimal configuration. Lastly and most importantly, noneof the design methods has shown an improved design by any independent measure-ment, and most cannot guarantee improved modularity. However, a solid foundationexists upon which to build modular design methods.

5. DiscussionThis 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 dif-ficult to fully understand each work. Despite the brief descriptions, one can find nearconsensus on some points and disagreement on others.

Overall, there is a significant lack of consensus in modularity measures and mod-ular product design methods. Whatever consensus there is exists due to a commonunderstanding 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 dif-ferent ways of accomplishing similar tasks.

Areas of consensus, or at least significant similarity, are based in representation, theoverall structure of the modularity measure, and the normalization of the measure.Matrix-based methods represent the relationships between components as a first steptowards measuring modularity and grouping components into modules. Typically, thematrices have rows and columns that represent components. Occasionally, additionalcolumns that represent life-cycle processes are added. The contents of thesematrices—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 therelationships differs from one representation to another as well. Most use a single matrixto represent dependencies. Some use two matrices to represent dependencies and simi-larities. 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


versus those relationships with components outside the module is common. However,the types of dependencies (design dependencies, functional connections, assembly con-nections, disassembly connections, etc.) vary among researchers. Similarity, when it isconsidered, is not so easily corralled. Similarity is usually used to denote a like proces-sing or the ability to be processed in a like manner. This can be for specific life-cycleprocesses (material compatibility for recycling) or any life-cycle process.

Typically, independence and similarity are measured separately but corres-pondingly. Usually, a measure is the number of dependencies (or similarities) thatoccur between components in the same module as a percentage of the total numberof dependencies (or similarities) in the whole product or system. Occasionally, thestrength of those relationships is accounted for in the measure as well.

While there are several areas of consensus, there are also several aspects of themodularity measures and modular design methods that are parallel, if not conflicting.These aspects include how the design method is implemented, the role of the measurein the design method, and representation’s impact on the inclusion of multiple life-cycle stages.

As mentioned in the discussion of modular design methods, the goal of somedesign methods is to optimize the modularity while for others the goal is to improvethe modularity. The difference between the two is critical in implementation. While alldesigners would like to optimize the modularity, the methods for optimization pre-sented 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 designchange or their stepped nature would allow for it. Can feasibility be included into theoptimization methods? Perhaps that is possible if the optimization is semi-automatic.

This disagreement between optimization and improvement brings to light anotherquestion on the specifics of the implementation of modular design methods. What isthe role of the modular design measure? Nearly every research group tackling modu-larity has proposed some sort of measure of modularity. Most have discussed whatmakes a product more modular. Some have proposed systematic modular designmethods to improve product modularity. Some of these methods include the modulardesign method as a guide for improving modularity and some use guidelines toimprove the modularity. The big reason for the disagreement is the amount of infor-mation and work that goes into calculating the modularity measures. Again, there isa way to achieve consensus if the measures can be automated, especially if they areautomated from standard product descriptions.

The last major area of disagreement is over the inclusion of life-cycle issues in themeasure and design of modular products. The question here is one of representation aswell as measure. Can the same representation and measurements be used to includeany life-cycle issue of interest? Some have measured each life-cycle issue separatelyand then weighted and combined them. Some have used very different definitions ofdependencies and other variables of interest depending upon the life-cycle issue ofinterest. In the end, it comes down to finding a single way to define and accommodateall the information needed. No method has a definition of variables that cleanly andeasily spans the life-cycle. Considerably more time should be placed on the definitionsof at least dependence and similarity to achieve this. As described previously, eachmeasure or method may have varying benefits and efficiencies. Clearly, the overridingproblem is that most methods are worked on in isolation. There is a strong need tocompare and/or connect the various methods.


The lack of a true consensus in any of these foundation areas points to the centralmatter of this paper—there is an obvious need for further research in product modu-

larity. Some aspects lacking consensus or utilization in the current works include:

1. a widespread definition for modularity that takes into account aspects of a pro-duct other than its function and perhaps one life-cycle aspect;

2. a concentration on methods for designing modular products;3. modularity measure that takes into account the above two points as well as

being useful to a designer; and4. a more object method of measuring dependence and similarity relationships.

Due to the immature nature of modularity and the need for rigor in itsdefinition, considerable research effort has been put into conveying thedefinitions.

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

6. ConclusionsWhile much has changed in modularity research in the 17 years since the indepen-

dence axiom, some questions remain unanswered. Ulrich and Tung (1991) ask severalresearch 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 ofthe utility, incorporation, and information content of modular design. Experimentationin the design process will be a common theme among successful works.

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