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Optimum granularity level of modular product design architecture
CIRP Annals - Manufacturing Technology 62 (2013) 151–154
Contents lists available at SciVerse ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
Optimum granularity level of modular product design architecture Tarek AlGeddawy, Hoda ElMaraghy (1)* Intelligent Manufacturing Systems (IMS) Centre, University of Windsor, Canada
A R T I C L E I N F O
A B S T R A C T
Keywords: Product Module Granularity
In modular architectures, Design Structure Matrix (DSM) is used to cluster product components into modules with minimum interfaces externally and maximum internal integration between components. However, DSM is a flat connectivity map that does not capture the layered nature of the product structure. Hierarchical clustering (cladistics) is proposed to automatically build product hierarchical architecture from DSM. The resulting clustering tree represents product architecture while its depth represents its granularity. The optimum granularity level and number of modules are determined, indicating the potential product and process platforms. A case study of automobile body-in-white of 38 components is used to demonstrate the capabilities and superior results quality of the presented technique. ß 2013 CIRP.
1. Introduction Products architecture defines the functions of its components and the topology of their interfaces. Products architecture facilitates further detailed design, testing, and planning of its manufacture and material supply chain of those components [1]. In an era characterized by proliferation of product variety and mass customization, establishing families of parts/products and product/process platforms are effective solutions for product design and manufacturing [2]. A modular architecture defines the appropriate product structure consisting of a group of modules with distinguishable functions and minimum interaction with the rest of the product [3]. Many types of modularity can be identified [4,5] including: (1) bus modularity where all modules are connected to a single common module, (2) sectional modularity where product variants are built from specific combinations of modules having a unified interface, (3) scalable modularity where some scalable components are combined with standard components. The depth of the architecture hierarchy of components, modules and subassemblies defines its level of detailed description or granularity (Fig. 1). It has important implications on all subsequent activities throughout the product life cycle. Shared
Fig. 1. Different levels of product architecture granularity.
* Corresponding author. 0007-8506/$ – see front matter ß 2013 CIRP. http://dx.doi.org/10.1016/j.cirp.2013.03.118
common product modules across many product variants, known as product platforms, capitalize on commonality and similarity to approach the economy of scale while offering a range of differentiated variants to enable economies of scope. Success in achieving these objectives depends on the appropriate identification of common and different modules and their interactions. The appropriate level of aggregation and granularity should, therefore, be carefully considered when families of products are formed [6]. Chiriac et al. [7] analyzed many product architectures with one and two levels of granularity to identify the effect on the quality of product modularity. They concluded that modularity has a unidirectional relationship with granularity and indicated a need to investigate the appropriate granularity level for a given product design to optimize system modularity. This paper introduces a new model capable of determining the appropriate level of granularity for a product design, as well as the structure of its architecture based on the interactions among its components. The model also includes a new clustering tool to group components into modules in a hierarchical structure which reveals product architecture. 2. Product modularity incorporation Product components are usually grouped into modules that are assembled using a specific design architecture to facilitate future design changes, product variety management, mass customization and manufacturing processes using delayed product differentiation [8]. The Design Structure Matrix (DSM) is the most common tool used to represent interactions among components (component-based DSM) in a product [9]. DSM elements are usually represented by binary numbers where ‘1’ indicates interaction and ‘0’ indicates lack of it. Grouping product components into modules can be accomplished by clustering DSM into blocks consisting mostly of ‘1’ elements. There are few techniques to cluster DSM for modularity, which differ mainly in the clustering objective. Coordination cost minimization is one of the first clustering methods [10] in which each DSM element is placed in an individual cluster, then components are
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T. AlGeddawy, H. ElMaraghy / CIRP Annals - Manufacturing Technology 62 (2013) 151–154
coordinated across modules to minimize the cost of being inside and outside a cluster. The maximum number of components in a cluster was predetermined to prevent forming large clusters and optimization was performed using simulated annealing. Clustered DSM can be compared to a targeted DSM topology using another objective function called Minimal Description Length (MDL) [11] which finds mismatching elements between the two topologies. The objective of clustering was to minimize MDL using GAs where chromosomes are formulated to represent components combinations in clusters generations. The number of clusters is determined a priori based on the DSM structure. Clustering Efficiency (CE) index is another clustering objective that evaluates a weighed count of zero elements inside clusters and the non-zero elements outside clusters using neural network optimization for clusters generation with a predefined number of clusters otherwise the model would form fewer clusters than desired [12,13]. Measures other than clustering can be used for quantifying efficiency of modularity and alternative designs evaluation. Modularity performance is a normalized index [14], with value from 0 to 1. It is used to compare number of interfaces, connections and dependencies among the product components to the minimum and maximum possible number of interfaces. A value of ‘0’ indicates a fully integrated design, while modularity improves as it approaches ‘1’. Another similar modality index is more detailed as it counts the interactions between the composed modules taking into consideration intra-relationships between components in a module and components of the other modules [7]. It was also modified to count inter-relationships among components within modules [15]. A components similarity approach was used to present a relative modularity measure [16] in which the ratio of the sum of similarities within modules to the total similarity in the whole DSM matrix is added to the ratio of the sum of dependencies within modules to the total dependency. The concept of the smoothness of product change from one product generation to another was introduced through a coupling index, which is indirectly related to quantifying modularity [17] which measures the strength of relationships among product modules. The stronger the coupling, the more difficult are changes, and hence more modularity is needed to weaken the existing components’ coupling. The previous review of clustering techniques and modularity measures reveals two points: (1) The objective function for DSM clustering is related to the interactions inside and outside the resulting clusters. Chiriac et al. [7] compared many modularity indices, and results were similar for the same product. Therefore, modularity indices with the simplest formulation would be preferable. In this paper, a simpler formula of the clustering efficiency (CE) index [12] is adopted. (2) DSM clustering techniques reveal only one dimensional modules formation, even when compared to bus modularity architecture. Yu et al. [11] imposed bus architecture on the clustering process by utilizing former designer knowledge. Hence, the true nature of product architecture and its granularity is difficult to recognize using only clustered DSM, especially for large complex systems [13], without human input. This paper introduces a new DSM clustering technique for modularity. It finds an optimal granulated modular and hierarchical architecture without imposing any modularity structure or predefining the number of modules or number of components per module. 3. Product architecture granularity model The new model adopts hierarchal clustering to best divide a DSM into modular architecture. Cladistics, a classification tool extensively used in Biology [18,19], reveals the evolution hypothesis and speciation scheme of a studied group of entities. Cladistics was
first introduced to the world of artifacts and used to reveal the evolution and co-development of products and manufacturing systems by ElMaraghy et al. [20]. This powerful computational analysis results in useful graphical clusters representation called cladogram (Fig. 2), which shows how different entities can be grouped based on the commonality and differentiation of their characters. A handful of specialized software are dedicated for cladogram construction such as Hennig86, PAUP, NONA, PeeWee and Phylip that can cluster large data sets very fast [21]. NONA is used in this paper for cladogram construction. Cladogram construction, however, has to be modified for use in DSM clustering. In the original cladistics techniques, clustering is based on entities characters, while a DSM represents relationships and connections among entities. The existence of relationships between components will be considered their characters/features to be used for cladistics clustering. For correct results, the selfrelationships of components to themselves are taken into consideration by the ‘1’ diagonal elements of the original DSM in Fig. 2. A cladogram would reveal the proposed hierarchal architecture of such components starting with a common root where the whole product appears and ending with cladogram terminals of individual components. The long inclined line at the left hand side of the cladogram, at each branching node, represents the beginning of a new granularity level. The example in Fig. 2 results in possibly three granularity levels below each branching node. This excludes the lowest node at which individual components appear since it does not represent useful modularity information. The only useful information for product architecture construction is the topology of the cladogram. The distribution of characters/connections on the cladogram was the result of the parsimony analysis; however it is not useful for further granularity analysis of the product architecture. To determine the optimum granularity level on a cladogram, a simple modularity index is used to specify the depth of the cladogram topology equivalent to the granularity level corresponding to the best modularity index. The developed modularity index (MI) has the same premise of the clustering efficiency (CE) index [12], both aim to reduce the number of blank ‘0’ cells inside obtained clusters, and the ‘1’ cells outside them. However the MI results in integers that can be easily understood compared to the very small fractions that result from using CE. In the particular used case study in this paper, the body-in-white, MI = 2/CE, when CE weight factors are taken equal to 0.5. The MI is the sum of the number of intra-relationships among modules and the number of missed inter-relationships among components of these modules. MI is expressed as: MI ¼ I þ Z
(1)
where I is the number of ‘1’ elements in the DSM outside developed clusters, and Z is the zero elements of those clusters (referred to as Sin and Sout in [12]). The smallest MI corresponds to the best clustering. MI value changes according to the granularity level of the formed clusters. In the example shown in Fig. 2, the first granularity level divides product components into two branches and consequently two clusters/modules – module {C,D,E,F,A} and module {B}. When DSM is re-shuffled to reflect component rearrangement at the cladogram terminals, the boundaries of clustered modules can be defined and MI can then be calculated. For level 1, MI = 10 since there are 2 intra-relationships between the two modules and 8 non-existing inter-relationships inside the modules. The second level scores MI = 6 based on three modules: {C,D,E}, {F,A} and module {B}. The last level scores MI = 10 based on four modules: {C,D}, {E}, {F,A} and module {B}. The shown example in Fig. 2 has an optimum granularity level of 2 since it has the least MI = 6. The best architecture can then be extracted from the cladogram at the optimum granularity level, which is the granularity map of the analyzed product (Fig. 2). Level 2 illustrates the hierarchical relationship between the three resulting clusters. Module {C,D,E} and module {F,A} are assembled to form subassembly {C,D,E,F,A} to which module {B} is added later. This product architecture decomposition is shown in Fig. 2.
T. AlGeddawy, H. ElMaraghy / CIRP Annals - Manufacturing Technology 62 (2013) 151–154
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5. Results and discussion The DSM of the BIW has been used to construct a cladogram using NONA cladistics software. The resulting cladogram has a length of 127 steps and shown in Fig. 5. The information of cladogram length is not useful later in granularity analysis, however the shortest length would ensure having the most parsimonious cladogram and the best topology that would serve as a granularity map and design architecture. Cladogram topology in Fig. 5 shows 10 possible levels of granularity between the top root level and the terminal level of individual components. The arrangement of product components at the terminals of the cladogram is used to re-shuffle component arrangement at header row and column of the DSM of BIW. The new ordered DSM is shown in Fig. 6. Fig. 2. The DSM clustering model steps.
4. Automotive body-in-white case study This case study was published in [12,14] to evaluate modularity measures and clustering technique which uses neural networks for optimization. An automobile body-in-white (BIW) is a structure consisting of large number of metal parts to be welded in preparation for subsequent painting (Fig. 3). The DSM representing relationships among BIW components (Table 1) is shown in Fig. 4. Components in the DSM are listed in alphabetical order. Selfrelationships of components are indicated with ‘1’ elements and used as input to cladistics analysis.
Fig. 5. Resulting cladogram showing the different architecture granularity levels and component modules of the BIW case study.
Fig. 3. Automobile body-in-white (BIW).
Fig. 6. New clustered and ordered body-in-white DSM using cladistics showing the optimum granularity level modules.
Fig. 4. The body-in-white DSM. Adapted from [12].
Table 1 Body-in-white components. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Adapter A-Pillar Roof Rail Adapter B-Pillar Roof Rail A-Pillar Inner A-Pillar Inner
15 16 17 18
A-Pillar Reinforcement Back Panel Back Panel Side Body Side B-Pillar Channel Cowl Cross track Rear Floor Dash Cross Member Dash Panel
19 20 21 22 23 24 25 26 27 28
Adopted from [12].
Floor Panel Front Header Front Side Rail Front Suspension Housing Heel kick Rear Floor Panel Rear Floor Side Rear Header Rear Panel Inner Lower Rear Panel Inner Upper Rear Side Floor Rear Side Rail Rear Side Rail Centre Rear Side Rail Front
29 30 31 32
Reinforcement Rocker Rear Rocker Roof Bow Roof Panel
33 34 35 36 37 38
Roof Rail Seat Cross member Front Seat Cross member Rear Shotgun Spare Wheel Well Wheelhouse
To determine the best granularity level, Modularity Index (MI) is calculated for each possible granularity level presented by cladogram topology. The ordered DSM is used to draw cluster boundaries at each level to identify the ‘1’ elements outside cluster boundaries and the ‘0’ elements inside those boundaries. Table 2 shows the calculated MI for each level along with I and Z numbers of ‘1’ and ‘0’ elements. Results show that level 6 scores the least MI = 160, hence the optimum granularity level is 6 with 9 modules: {36,1,11,3,4}, {9,2,35,34}, {30,8,29,28,25,19}, {27,15}, {38,23,24}, {17,14,18,13,10}, {26, 21,5,7,6}, {20,12,37} and finally module {33,32,31,16,22}. Cladogram topology (Fig. 5) can be dissected at level 6 (Fig. 7) to produce the architecture and granularity map of the desired BIW. It can be converted to a product architecture layout similar to the Bill-of-Material (BOM) tree (Fig. 8) by adding nodes of subassemblies at each level to illustrate unions of component modules. Modules {38,1,11,3,4} and {9,2,35,34} exist at the end Table 2 Modularity indices at each body-in-white granularity level. Level
1
2
3
4
5
6
7
8
9
10
Z I MI
872 12 884
498 38 536
320 60 380
234 76 310
116 102 218
40 120 160
34 132 166
14 148 162
2 162 164
2 194 196
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Fig. 7. The dissected cladogram used to generate the architecture map of the bodyin-white case study.
Fig. 8. The body-in-white architecture showing best granularity level and its modules.
adding and switching modules. Interactions among components are the main reason for grouping components into modules. The objective of components clustering is to maximize component interconnection within each module and minimize interactions between modules. A clustering method using cladistics analysis, a hierarchical classification tool commonly used in biology, has been developed to: (1) find the architecture structure of analyzed product design, (2) group product components into the best number of modules, and (3) identify the best product modular granularity level which minimizes the overall interactions between modules and subassemblies at all granularity levels. Unlike the flat un-structured modules resulting from DSM analysis, the new method also defines the hierarchical relationship between the clustered modules. A body-in-white (BIW) case study analyzed using the new clustering method showed: (1) hierarchal clustering of products reveals their architecture, (2) the new hierarchical clustering model determines the best product modular granularity level, (3) hierarchical clustering is superior to earlier clustering methods, and (4) the relationship between modularity measures and granularity level is not unidirectional as proposed earlier in literature. Modularity improves as granularity increases up to a point where few components exist in each module, and then it deteriorates with further increase in modularization and granularity. References
Fig. 9. Relationship between product structure modularity and granularity level for the BIW case study.
of the tree indicating that these are core modules with the most relationships with other modules. Hence, they have the least probability of change over product generations and the highest probability of being a platform for this product for multiple generations. In general, the assembly processes of core modules are the process platform of the product, while other modules at the higher granularity levels are assembled later following a delayed differentiation pattern for customizing products. The clustering efficiency (CE) results of this example [12] could be converted to MI equal to 202, which is higher than the 160 obtained in the cladogram based method. This shows that clustering results using the proposed method are superior to the latest models in the literature, in addition to its ability of determining the whole product design architecture. A quick analysis of MI values across all possible granularity levels shows that both very coarse or very fine clustering granularity do not result in good modularity measures. A U-shape correlation between granularity level and modularity index is found as illustrated in Fig. 9 for the analyzed BIW case study. This result is not in agreement with the conclusion drawn by Chiriac et al. [7], stating that modularity has a uni-directional proportional (decreasing or increasing) relationship with granularity level. This might be because Chiriac et al. did not exceed two product granularity levels, hence, drawing a general conclusion regarding such relationship is not justified. Modularity seems to decrease at high granularity levels, after level 6 in the BIW case study. 6. Conclusions Products architecture represents the main design of its components layout and their interaction. A modular architecture is very useful in designing product variants especially for mass customization. It facilitates customizing variants by removing,
[1] Ulrich KT, Eppinger SD (2012) Product Design and Development, 5th ed. McGraw-Hill Irwin, Boston415. [2] ElMaraghy H (2009) Changing and evolving products and systems – models and enablers. in ElMaraghy H, (Ed.) Changeable and Reconfigurable Manufacturing Systems, Springer-Verlag, London25–45(Chapter two). [3] Simpson TW, Siddique Z, Jiao J (2007) Product Platform and Product Family Design Methods and Applications, vol. xi. Springer, New York; London 548. [4] Ulrich K, Tung K (1991) Fundamentals of product modularity. Issues in design manufacturing/integration. American Society of Mechanical Engineers 39(1):73–79. [5] Tseng MM, Jiao J, Merchant ME (1996) Design for mass customization. CIRP Annals – Manufacturing Technology 45(Compendex):153–156. [6] Xuehong D, Jianxin J, Tseng MM (2001) Architecture of product family: fundamentals and methodology. Concurrent Engineering Research and Applications 9(Copyright 2002, IEE):309–325. [7] Chiriac N, Holtta-Otto K, Lysy D, Eun Suk S (2011) Level of modularity and different levels of system granularity. Journal of Mechanical Design 133(10):101007. (10 pp). [8] AlGeddawy T, ElMaraghy H (2011) Product variety management in design and manufacturing: challenges and strategies. Proceeding of the 4th International Conference on Changeable, Agile, Reconfigurable and Virtual Production (CARV2011), Montreal, Canada. [9] Eppinger SD, Browning TR (2012) Design structure matrix methods and applications. Engineering Systems, vol. xii. MIT Press, Cambridge, MA 334. [10] Thebeau RE (2001) Knowledge management of system interfaces and interactions for product development processes. System Design and Management, Massachusetts Institute of Technology. [11] Tian-Li Y, Yassine AA, Goldberg DE (2007) An information theoretic method for developing modular architectures using genetic algorithms. Research in Engineering Design 18(2):91–109. [12] Pandremenos J, Chryssolouris G (2011) A neural network approach for the development of modular product architectures. International Journal of Computer Integrated Manufacturing 24(10):879–887. [13] Sharman DM, Yassine AA (2004) Characterizing complex product architectures. Systems Engineering 7(1):35–59. [14] Pandremenos J, Chatzikomis C, Chryssolouris G (2009) On the quantification of interface design architectures. Asian International Journal of Science and Technology in Production and Manufacturing Engineering 2(3):41–48. [15] Guo F, Gershenson JK (2004) A comparison of modular product design methods based on improvement and iteration. 2004 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference, September 28, 2004–October 2, 2004American Society of Mechanical Engineers, Salt Lake City, UT, United States. [16] Gershenson JK, Prasad GJ, Allamneni S (1999) Modular product design: a lifecycle view. Journal of Integrated Design and Process Science 3(4):13–26. [17] Martin M, Ishii K (2002) Design for variety: developing standardized and modularized product platform architectures. Research in Engineering Design 13(4):213–235. [18] Kitching IJ, Forey PL, Humphries CJ, Williams DM (1998) Cladisitcs: The Theory and Practice of Parsimony Analysis, Second edition. Oxford University Press, The Systematics Association. [19] Hennig W (1966) Phylogenitic Systematics, University of Illinois Press, Urbana. (republished in 1999). [20] ElMaraghy H, AlGeddawy T, Azab A (2008) Modelling evolution in manufacturing: a biological analogy. CIRP Annals – Manufacturing Technology 57(1):467–472. [21] Nixon KC (1999) The parsimony ratchet, a new method for rapid for rapid parsimony analysis. Cladistics 15(1):407–414.
Contents lists available at SciVerse ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
Optimum granularity level of modular product design architecture Tarek AlGeddawy, Hoda ElMaraghy (1)* Intelligent Manufacturing Systems (IMS) Centre, University of Windsor, Canada
A R T I C L E I N F O
A B S T R A C T
Keywords: Product Module Granularity
In modular architectures, Design Structure Matrix (DSM) is used to cluster product components into modules with minimum interfaces externally and maximum internal integration between components. However, DSM is a flat connectivity map that does not capture the layered nature of the product structure. Hierarchical clustering (cladistics) is proposed to automatically build product hierarchical architecture from DSM. The resulting clustering tree represents product architecture while its depth represents its granularity. The optimum granularity level and number of modules are determined, indicating the potential product and process platforms. A case study of automobile body-in-white of 38 components is used to demonstrate the capabilities and superior results quality of the presented technique. ß 2013 CIRP.
1. Introduction Products architecture defines the functions of its components and the topology of their interfaces. Products architecture facilitates further detailed design, testing, and planning of its manufacture and material supply chain of those components [1]. In an era characterized by proliferation of product variety and mass customization, establishing families of parts/products and product/process platforms are effective solutions for product design and manufacturing [2]. A modular architecture defines the appropriate product structure consisting of a group of modules with distinguishable functions and minimum interaction with the rest of the product [3]. Many types of modularity can be identified [4,5] including: (1) bus modularity where all modules are connected to a single common module, (2) sectional modularity where product variants are built from specific combinations of modules having a unified interface, (3) scalable modularity where some scalable components are combined with standard components. The depth of the architecture hierarchy of components, modules and subassemblies defines its level of detailed description or granularity (Fig. 1). It has important implications on all subsequent activities throughout the product life cycle. Shared
Fig. 1. Different levels of product architecture granularity.
* Corresponding author. 0007-8506/$ – see front matter ß 2013 CIRP. http://dx.doi.org/10.1016/j.cirp.2013.03.118
common product modules across many product variants, known as product platforms, capitalize on commonality and similarity to approach the economy of scale while offering a range of differentiated variants to enable economies of scope. Success in achieving these objectives depends on the appropriate identification of common and different modules and their interactions. The appropriate level of aggregation and granularity should, therefore, be carefully considered when families of products are formed [6]. Chiriac et al. [7] analyzed many product architectures with one and two levels of granularity to identify the effect on the quality of product modularity. They concluded that modularity has a unidirectional relationship with granularity and indicated a need to investigate the appropriate granularity level for a given product design to optimize system modularity. This paper introduces a new model capable of determining the appropriate level of granularity for a product design, as well as the structure of its architecture based on the interactions among its components. The model also includes a new clustering tool to group components into modules in a hierarchical structure which reveals product architecture. 2. Product modularity incorporation Product components are usually grouped into modules that are assembled using a specific design architecture to facilitate future design changes, product variety management, mass customization and manufacturing processes using delayed product differentiation [8]. The Design Structure Matrix (DSM) is the most common tool used to represent interactions among components (component-based DSM) in a product [9]. DSM elements are usually represented by binary numbers where ‘1’ indicates interaction and ‘0’ indicates lack of it. Grouping product components into modules can be accomplished by clustering DSM into blocks consisting mostly of ‘1’ elements. There are few techniques to cluster DSM for modularity, which differ mainly in the clustering objective. Coordination cost minimization is one of the first clustering methods [10] in which each DSM element is placed in an individual cluster, then components are
152
T. AlGeddawy, H. ElMaraghy / CIRP Annals - Manufacturing Technology 62 (2013) 151–154
coordinated across modules to minimize the cost of being inside and outside a cluster. The maximum number of components in a cluster was predetermined to prevent forming large clusters and optimization was performed using simulated annealing. Clustered DSM can be compared to a targeted DSM topology using another objective function called Minimal Description Length (MDL) [11] which finds mismatching elements between the two topologies. The objective of clustering was to minimize MDL using GAs where chromosomes are formulated to represent components combinations in clusters generations. The number of clusters is determined a priori based on the DSM structure. Clustering Efficiency (CE) index is another clustering objective that evaluates a weighed count of zero elements inside clusters and the non-zero elements outside clusters using neural network optimization for clusters generation with a predefined number of clusters otherwise the model would form fewer clusters than desired [12,13]. Measures other than clustering can be used for quantifying efficiency of modularity and alternative designs evaluation. Modularity performance is a normalized index [14], with value from 0 to 1. It is used to compare number of interfaces, connections and dependencies among the product components to the minimum and maximum possible number of interfaces. A value of ‘0’ indicates a fully integrated design, while modularity improves as it approaches ‘1’. Another similar modality index is more detailed as it counts the interactions between the composed modules taking into consideration intra-relationships between components in a module and components of the other modules [7]. It was also modified to count inter-relationships among components within modules [15]. A components similarity approach was used to present a relative modularity measure [16] in which the ratio of the sum of similarities within modules to the total similarity in the whole DSM matrix is added to the ratio of the sum of dependencies within modules to the total dependency. The concept of the smoothness of product change from one product generation to another was introduced through a coupling index, which is indirectly related to quantifying modularity [17] which measures the strength of relationships among product modules. The stronger the coupling, the more difficult are changes, and hence more modularity is needed to weaken the existing components’ coupling. The previous review of clustering techniques and modularity measures reveals two points: (1) The objective function for DSM clustering is related to the interactions inside and outside the resulting clusters. Chiriac et al. [7] compared many modularity indices, and results were similar for the same product. Therefore, modularity indices with the simplest formulation would be preferable. In this paper, a simpler formula of the clustering efficiency (CE) index [12] is adopted. (2) DSM clustering techniques reveal only one dimensional modules formation, even when compared to bus modularity architecture. Yu et al. [11] imposed bus architecture on the clustering process by utilizing former designer knowledge. Hence, the true nature of product architecture and its granularity is difficult to recognize using only clustered DSM, especially for large complex systems [13], without human input. This paper introduces a new DSM clustering technique for modularity. It finds an optimal granulated modular and hierarchical architecture without imposing any modularity structure or predefining the number of modules or number of components per module. 3. Product architecture granularity model The new model adopts hierarchal clustering to best divide a DSM into modular architecture. Cladistics, a classification tool extensively used in Biology [18,19], reveals the evolution hypothesis and speciation scheme of a studied group of entities. Cladistics was
first introduced to the world of artifacts and used to reveal the evolution and co-development of products and manufacturing systems by ElMaraghy et al. [20]. This powerful computational analysis results in useful graphical clusters representation called cladogram (Fig. 2), which shows how different entities can be grouped based on the commonality and differentiation of their characters. A handful of specialized software are dedicated for cladogram construction such as Hennig86, PAUP, NONA, PeeWee and Phylip that can cluster large data sets very fast [21]. NONA is used in this paper for cladogram construction. Cladogram construction, however, has to be modified for use in DSM clustering. In the original cladistics techniques, clustering is based on entities characters, while a DSM represents relationships and connections among entities. The existence of relationships between components will be considered their characters/features to be used for cladistics clustering. For correct results, the selfrelationships of components to themselves are taken into consideration by the ‘1’ diagonal elements of the original DSM in Fig. 2. A cladogram would reveal the proposed hierarchal architecture of such components starting with a common root where the whole product appears and ending with cladogram terminals of individual components. The long inclined line at the left hand side of the cladogram, at each branching node, represents the beginning of a new granularity level. The example in Fig. 2 results in possibly three granularity levels below each branching node. This excludes the lowest node at which individual components appear since it does not represent useful modularity information. The only useful information for product architecture construction is the topology of the cladogram. The distribution of characters/connections on the cladogram was the result of the parsimony analysis; however it is not useful for further granularity analysis of the product architecture. To determine the optimum granularity level on a cladogram, a simple modularity index is used to specify the depth of the cladogram topology equivalent to the granularity level corresponding to the best modularity index. The developed modularity index (MI) has the same premise of the clustering efficiency (CE) index [12], both aim to reduce the number of blank ‘0’ cells inside obtained clusters, and the ‘1’ cells outside them. However the MI results in integers that can be easily understood compared to the very small fractions that result from using CE. In the particular used case study in this paper, the body-in-white, MI = 2/CE, when CE weight factors are taken equal to 0.5. The MI is the sum of the number of intra-relationships among modules and the number of missed inter-relationships among components of these modules. MI is expressed as: MI ¼ I þ Z
(1)
where I is the number of ‘1’ elements in the DSM outside developed clusters, and Z is the zero elements of those clusters (referred to as Sin and Sout in [12]). The smallest MI corresponds to the best clustering. MI value changes according to the granularity level of the formed clusters. In the example shown in Fig. 2, the first granularity level divides product components into two branches and consequently two clusters/modules – module {C,D,E,F,A} and module {B}. When DSM is re-shuffled to reflect component rearrangement at the cladogram terminals, the boundaries of clustered modules can be defined and MI can then be calculated. For level 1, MI = 10 since there are 2 intra-relationships between the two modules and 8 non-existing inter-relationships inside the modules. The second level scores MI = 6 based on three modules: {C,D,E}, {F,A} and module {B}. The last level scores MI = 10 based on four modules: {C,D}, {E}, {F,A} and module {B}. The shown example in Fig. 2 has an optimum granularity level of 2 since it has the least MI = 6. The best architecture can then be extracted from the cladogram at the optimum granularity level, which is the granularity map of the analyzed product (Fig. 2). Level 2 illustrates the hierarchical relationship between the three resulting clusters. Module {C,D,E} and module {F,A} are assembled to form subassembly {C,D,E,F,A} to which module {B} is added later. This product architecture decomposition is shown in Fig. 2.
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153
5. Results and discussion The DSM of the BIW has been used to construct a cladogram using NONA cladistics software. The resulting cladogram has a length of 127 steps and shown in Fig. 5. The information of cladogram length is not useful later in granularity analysis, however the shortest length would ensure having the most parsimonious cladogram and the best topology that would serve as a granularity map and design architecture. Cladogram topology in Fig. 5 shows 10 possible levels of granularity between the top root level and the terminal level of individual components. The arrangement of product components at the terminals of the cladogram is used to re-shuffle component arrangement at header row and column of the DSM of BIW. The new ordered DSM is shown in Fig. 6. Fig. 2. The DSM clustering model steps.
4. Automotive body-in-white case study This case study was published in [12,14] to evaluate modularity measures and clustering technique which uses neural networks for optimization. An automobile body-in-white (BIW) is a structure consisting of large number of metal parts to be welded in preparation for subsequent painting (Fig. 3). The DSM representing relationships among BIW components (Table 1) is shown in Fig. 4. Components in the DSM are listed in alphabetical order. Selfrelationships of components are indicated with ‘1’ elements and used as input to cladistics analysis.
Fig. 5. Resulting cladogram showing the different architecture granularity levels and component modules of the BIW case study.
Fig. 3. Automobile body-in-white (BIW).
Fig. 6. New clustered and ordered body-in-white DSM using cladistics showing the optimum granularity level modules.
Fig. 4. The body-in-white DSM. Adapted from [12].
Table 1 Body-in-white components. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Adapter A-Pillar Roof Rail Adapter B-Pillar Roof Rail A-Pillar Inner A-Pillar Inner
15 16 17 18
A-Pillar Reinforcement Back Panel Back Panel Side Body Side B-Pillar Channel Cowl Cross track Rear Floor Dash Cross Member Dash Panel
19 20 21 22 23 24 25 26 27 28
Adopted from [12].
Floor Panel Front Header Front Side Rail Front Suspension Housing Heel kick Rear Floor Panel Rear Floor Side Rear Header Rear Panel Inner Lower Rear Panel Inner Upper Rear Side Floor Rear Side Rail Rear Side Rail Centre Rear Side Rail Front
29 30 31 32
Reinforcement Rocker Rear Rocker Roof Bow Roof Panel
33 34 35 36 37 38
Roof Rail Seat Cross member Front Seat Cross member Rear Shotgun Spare Wheel Well Wheelhouse
To determine the best granularity level, Modularity Index (MI) is calculated for each possible granularity level presented by cladogram topology. The ordered DSM is used to draw cluster boundaries at each level to identify the ‘1’ elements outside cluster boundaries and the ‘0’ elements inside those boundaries. Table 2 shows the calculated MI for each level along with I and Z numbers of ‘1’ and ‘0’ elements. Results show that level 6 scores the least MI = 160, hence the optimum granularity level is 6 with 9 modules: {36,1,11,3,4}, {9,2,35,34}, {30,8,29,28,25,19}, {27,15}, {38,23,24}, {17,14,18,13,10}, {26, 21,5,7,6}, {20,12,37} and finally module {33,32,31,16,22}. Cladogram topology (Fig. 5) can be dissected at level 6 (Fig. 7) to produce the architecture and granularity map of the desired BIW. It can be converted to a product architecture layout similar to the Bill-of-Material (BOM) tree (Fig. 8) by adding nodes of subassemblies at each level to illustrate unions of component modules. Modules {38,1,11,3,4} and {9,2,35,34} exist at the end Table 2 Modularity indices at each body-in-white granularity level. Level
1
2
3
4
5
6
7
8
9
10
Z I MI
872 12 884
498 38 536
320 60 380
234 76 310
116 102 218
40 120 160
34 132 166
14 148 162
2 162 164
2 194 196
154
T. AlGeddawy, H. ElMaraghy / CIRP Annals - Manufacturing Technology 62 (2013) 151–154
Fig. 7. The dissected cladogram used to generate the architecture map of the bodyin-white case study.
Fig. 8. The body-in-white architecture showing best granularity level and its modules.
adding and switching modules. Interactions among components are the main reason for grouping components into modules. The objective of components clustering is to maximize component interconnection within each module and minimize interactions between modules. A clustering method using cladistics analysis, a hierarchical classification tool commonly used in biology, has been developed to: (1) find the architecture structure of analyzed product design, (2) group product components into the best number of modules, and (3) identify the best product modular granularity level which minimizes the overall interactions between modules and subassemblies at all granularity levels. Unlike the flat un-structured modules resulting from DSM analysis, the new method also defines the hierarchical relationship between the clustered modules. A body-in-white (BIW) case study analyzed using the new clustering method showed: (1) hierarchal clustering of products reveals their architecture, (2) the new hierarchical clustering model determines the best product modular granularity level, (3) hierarchical clustering is superior to earlier clustering methods, and (4) the relationship between modularity measures and granularity level is not unidirectional as proposed earlier in literature. Modularity improves as granularity increases up to a point where few components exist in each module, and then it deteriorates with further increase in modularization and granularity. References
Fig. 9. Relationship between product structure modularity and granularity level for the BIW case study.
of the tree indicating that these are core modules with the most relationships with other modules. Hence, they have the least probability of change over product generations and the highest probability of being a platform for this product for multiple generations. In general, the assembly processes of core modules are the process platform of the product, while other modules at the higher granularity levels are assembled later following a delayed differentiation pattern for customizing products. The clustering efficiency (CE) results of this example [12] could be converted to MI equal to 202, which is higher than the 160 obtained in the cladogram based method. This shows that clustering results using the proposed method are superior to the latest models in the literature, in addition to its ability of determining the whole product design architecture. A quick analysis of MI values across all possible granularity levels shows that both very coarse or very fine clustering granularity do not result in good modularity measures. A U-shape correlation between granularity level and modularity index is found as illustrated in Fig. 9 for the analyzed BIW case study. This result is not in agreement with the conclusion drawn by Chiriac et al. [7], stating that modularity has a uni-directional proportional (decreasing or increasing) relationship with granularity level. This might be because Chiriac et al. did not exceed two product granularity levels, hence, drawing a general conclusion regarding such relationship is not justified. Modularity seems to decrease at high granularity levels, after level 6 in the BIW case study. 6. Conclusions Products architecture represents the main design of its components layout and their interaction. A modular architecture is very useful in designing product variants especially for mass customization. It facilitates customizing variants by removing,
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