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Functional requirements analysis-based method for product platform design in axiomatic design.

1. Introduction

In today's highly competitive and volatile market, a major competitive advantage for any company is the ability to bring products to market faster. Mass customization is a manufacturing approach to produce customized products based on requirements of individual customers with near mass production efficiency [1]. The product family design based on product platform can rapidly respond to customer individual needs. Product platforms can be classified into two categories: modular platforms and scalable platforms [2]. A modular platform is a collection of components to be shared by all the products in a product family. Different functions in this family are achieved by adding, removing, or substituting attachment modules to/from the platform. A scalable platform is modeled by scalable variables that can satisfy different requirements by being changed. There exists much subjectivity in assigning artificially the type of product platform assigned in advance. It is difficult for the designers to distinguish the modules and scalable platform. Simultaneously, this division for product family can't meet the needs of market segment for the company. So, in this paper, the modular and scalable product platforms are unified as generalized parametric product platform in the view of axiomatic design.

Scholars around the world have devoted considerable efforts to product platform and family design. [3] developed a six-step robust design framework for product family formation. [4] presented a single-stage approach for optimizing a platform and the resulting family of products based on one or more scaling variables. [5] pointed out that the market segmentation grid was useful for both platform development and product family consolidation. [6] introduced the customizability measure to evaluate mass customized designs and their impact to customers and manufacturers. [7] developed an information system to integrate design and manufacturing activities in mass customization. [8] developed a scalable product platform robust design framework that can assist companies in creating product platforms quickly and efficiently. [9] used parametric design to achieve a scalable platform and introduced commonality measures to evaluate product platform and family design.

At present, the existing design methods for product platform don't consider how to make the product better meet customer individual needs from the view of customer needs, so as to ensure the rationality of the design decomposition. Different customer needs drive the difference of function-structure for product, and the variation of customer needs affect the customization degree of product, so the different product in product family should have the different functional requirements (FRs) which are expressed by corresponding characteristic attributes. However, the study on FRs for product from the view of customer needs is little. It is not enough to only analyze customer needs, since the needs for customer to product is that to product function. The designed product should have certain functional requirements, which may be affected by customer needs and design parameters (DPs). This paper analyzes the functional requirements of product in the view of customer needs firstly.

2. Functional requirements analysis of product design

The diversity of products is determined by different customer needs. The function for product in product family are similar, but to meet user's individual requirements, the FRs for product should have certain diversity which include functional diversity and performance diversity, which can be achieved by relevant product structure. The functional diversity is achieved by adding, modifying or removing one or more modules. The performance diversity is achieved by adjusting one or more DPs of product platform, or designing different structures to meet performance requirements.

Kano model proposed by Kano in Japan is customer satisfaction model relating to product quality. This model classifies product quality into the basic, work and surprise quality according to the relationship between product quality and customer satisfaction degree [9]. The classification contributes to understanding, analysis and arrangement of customer needs. It aims to help enterprise to find entry point of improving customer satisfaction degree, helping enterprise to know customer needs in different levels, then identifying factors of great concern to satisfy customer, through distinguishing and managing different customer needs.

Considering the link between customer needs and product quality characteristics, the FRs for product are classified into basic functional requirements, expectable functional requirements and adjunctive functional requirements based on the model of customer satisfaction presented by Kano, as shown in figure 1. It describes product function type of current market and predicted future market, and point out needs direction for the current and future development of product platform.


2.1 Basic functional requirements

For customers, the basic functional requirements are indispensable for one product, which are common functions of all products developed based on product platform in existing product family. If the product doesn't have such functions or these functions are good enough, it will cause the customer's strong dissatisfaction. When the product has these functions, the customer' complaints can be eliminated, but the customer's satisfaction degree isn't increased. For customers, these are basic functions that product should have. The basic functional requirements fully describe the nature and content of product platform defined by enterprise.

2.2 Expectable functional requirements

The expectable functional requirements are those the customers expect, but not necessary. The more the expectable functional requirements of products, the larger the customer's satisfaction degree. When these FRs are not enough, the customers may be not pleased. These FRs are often paid close attention by customers, competitor and enterprise in the growth stage of product, which reflects product competitiveness. In mass customization mode, the basic functional requirements can't fully meet the customer's individual requirements, and the expectable functional requirements can meet the market by increasing product functions on the bases of product platform.

2.3 Adjunctive functional requirements

The adjunctive functional requirements provide some fully unexpected product attributes to the customer, which may give a pleasant surprise to the customers.. However, the customers don't complain when products don't have such functions or these functions are not good enough. The customer will be satisfied when products have such FRs, and the customers' loyalty index will be improved. It is necessary to define reasonably the adjunctive functional requirements for the upgrade of product platform, which are also the development power of product platform. These FRs are usually developed latent customer needs and increase extra price of product.

Since the customer's needs characteristics are dynamic factors, they may be changed with time, technology and market segmentation. The FRs reflect different hierarchy customer needs for product functions, therefore, they will move downward in model with the development of time. When a new product is developed, it must have the basic functional requirements. Once the product is accepted by the customer gradually, the parts of expectable functional requirements may be converted into basic functional requirements, and some adjunctive function may be converted into expectable functional requirements when product in mature period.

3. Decomposition process of product design using axiomatic design and design structure matrix

Axiomatic design offers a scientific base for design and improves design activities by providing the designer with a theoretical foundation based on logical and rational thought processes and tools [10]. The approach views the design process as a series of mappings among customer, functional, physical, and process domains. Every domain is characterized by its element, viz., customer needs (CNs), functional requirements, design parameters and process variables (PVs). Product family design based on product platform should map among these domains. The current product platform design method usually starts with mapping analysis between FRs and physical parameters. Then product modularization structure is determined, and the sharing strategy of product platform parameters is identified by clustering algorithm and optimization method.

Based on axiomatic design, the relationship between FRs and DPs can be described with the following equation

FR = [A] DP (1)

where DP = [[[DP.sub.1], [DP.sub.2],..., [DP.sub.n]].sup.T], FR = [{[FR.sup.b], [FR.sup.e], [FR.sup.a]}.sup.T] = [{[FR.sub.1], [FR.sub.2],... [FR.sub.n]}.sup.T]. [FR.sup.b], [FR.sup.e] and [FR.sup.a] are respectively basic functional requirements, expectable functional requirements and adjunctive functional requirements. [A] is design matrix. The rearrangement process of the design matrix aims to transform the design matrix into a triangular or diagonal form.

Axiomatic design postulates a zigzagging process for FR-DP mapping. However, it can't capture the interactions among the design parameters in design process. The design structure matrix is a popular representation and analysis tool for system modeling, especially for purposes of decomposition and integration [11]. A DSM displays the relationships between components of a system in a compact, visual, and analytically advantageous format. The matrix contains a list of all constituent subsystems/ activities and the corresponding information exchange and dependency patterns. DSM provides a powerful technique for the analysis of design, but it is fully known only for products that have already been designed. Because of the complementarities of axiomatic design and DSM, the decomposition problem would be better modeled as a co-evolution of design matrix and DSM [12]. The processes of the proposed decomposition are illustrated in figure 2

Step 1. Construct the design matrix. Firstly, the FRs of the system is described, and the DPs corresponding to each FR are selected according to independence axiom. Then the relationships between FRs and DPs are established. After the expression of functional requirements and selection of design parameters, the design matrix of the FR-DP hierarchy is constructed based on these FRs and DPs.

Step 2. Establish transition matrix. In each row of design matrix, the DP that has the largest influence on this FR is chosen to replace corresponding FR. Then the corresponding transition matrix is established.

Step 3. Construct the DSM. The rows and columns of transition matrix are exchanged so that all dominant elements appear on the main diagonal, and the elements corresponding to the design parameters with the coupling relationship should be as possible as laid in lower triangular position. Thus the DSM is constructed, that is, a DSM derived only from the functional view of the product.

4. Product platform design

Product platform is the basis of product family development. Its structure can be defined according to basic functional requirements for product family in whole market. The design process of product platform includes: analyze customer needs, determine the FRs vector, mapping between function domain and physical domain, transform axiomatic design matrix into design structure matrix, seek cluster piece of DPs by clustering analysis algorithm, and then identify a kind of coupling design with minimum dependence degree according to coupling analysis among DPs. The product diversity is achieved by adding, modifying, removing and adjusting the DPs which constitute product and meet basic functional requirements. The functional diversity are embodied by adding, modifying and removing one or more DPs; the performance diversity are embodied by adjusting operationymagnifying or reducing one or more DPs. Product platform is structured by determining basic structure, characteristic parameters and value range, and adjusting function-performance.

4.1 Definition of basic design parameters, common platform parameters and individual parameters

Product function-performance requirements for different customers are different, the needs diversity promote product diversification, thus drive FRs diversity, which may cause product physical structure diversity. In the view of product meeting customer needs, each DP should correspond to certain FRs. The DPs which can achieve basic functional requirements of product family are defined as basic design parameters. The DPs which have same value and influence on product performance diversity smaller or negligible among different products in product family are defined as common platform parameters, which reflect expectable functional requirements with commonality to different products in product family. The DPs which have different value, and have important effect on product performance diversity are defined as individual parameters, which can be customized according to customer needs to gain individual product, and reflect customer expectable functional requirements and adjunctive functional requirements for customers to products individualization in product family.

Product platform is the aggregation of basic design parameters, common platform parameters and individual parameters. It can meet customer various requirements using the configuration of existing design parameters, the product meeting customer individual requirements can be fast designed and don't increase or increase only a small number of production cost by changing the customization parameters, when existing design parameters combination don't meet customer individual requirements.

The key to constructing product platform is that basic design parameters, common platform parameters and individual parameters in product platform are distinguished and determined from DPs. On condition that customer various requirements are satisfied, determine reasonably the customization point of product family, enhance the generality of product as far as possible, reduce complexity and cost of product design, shorten production cycle, meet customer individual requirements furthest by changing the least design. At the same time, the DPs are integrated furthest on the basis of keeping the independence of FRs. If common platform parameters are too much, product will be a light hierarchical configuration design, so it's difficult to satisfy customer individual requirements; If common platform parameters are too little, product will be a deeper hierarchical customized design, so it's nicely to satisfy customer individual requirements, but product redundancy derived by product platform will increase, and cost of production will also increase.

4.2 Identify product platform parameters

When product platform is designed by applying axiomatic design method, the requirements analysis and functional decomposition for product are firstly doing, and then axiomatic design matrix is established, which represents the mapping between FRs in functional domain and DPs in structural domain. When the design matrix is diagonal, each of the FRs can be satisfied independently by means of one DP. Such a design is called an uncoupled design. Other form of the design matrix is called decoupled or coupled design, which shows that there exists the relation among DPs and results in coupling among FRs. Here, the independent DPs and coupling parameters vectors should be distinguished by using partition operation method, and the relation among them is identified. The elements of design matrix in axiomatic design is indicated by the form of Boolean that contains too little information and doesn't/t show the degree of functional coupling (strong or weak), therefore it can't provide necessary information for further analysis of coupling design. In this section, the design matrix is transformed into design structure matrix by considering the influence degree of DPs to FRs, and then platform parameters are identified by clustering analysis. The detail process is introduced as following.

(1) In product design, the CNs for product are essentially needs to product functions. Considering the advantages of quality function deployment (QFD) in transforming customer needs into functional performance and guiding robust design and quality assurance of products, the CNs can be mapped into FRs for product using QFD. Then the FRs for product are analyzed based on the Kano model and fuzzy clustering analysis method to identify three types of FRs, [FR.sup.b], [FR.sup.e] and [FR.sup.a].

(2) Applying axiomatic design principles to map FRs into DPs. After each hierarchy mapping are resolved completely, the coupling correlation among FRs can be identified according to the influence of DPs on FRs, then design matrix is established.

Suppose the number of FRs is n, in which the number of basic functional requirements, expectable functional requirements and adjunctive functional requirements are p, q and r (p + q + r = n) respectively, [FR.sup.b] = [{[FR.sub.1], [FR.sup.2],...,[FR.sub.p]}.sup.T], [FR.sup.e] = [{[FR.sub.p+q+1],...,[FR.sub.n]}.sup.T], [FR.sup.a] = [{[FR.sub.p+q+1],...,[FR.sub.n]}.sup.T], then the relation between FRs and DPs can be written as


Since the basic functional requirements of any product in product family are same, the corresponding DPs achieving these FRs can be shared in product family, which is defined as basic design parameters [DP.sup.b]. [DP.sup.b] should not vary with the change of other DPs other than the influence of basic design parameters, namely

[partial derivative][FR.sup.b.sub.k]/[partial derivative][DP.sup.q + r.sub.t] = 0, k = 1,..., p, t = p + 1,...n (3)

Then, [FR.sup.b] [right arrow] [DP.sup.b] is transform into [DP.sup.b] [left and right arrow] [DP.sup.b] using the proposed methods in section 2. The cluster analysis is applied, and the coupling blocks among DPs in [DP.sup.b] are acquired. These coupling blocks will be regarded as common modules of product platform. Other DPs need to be further subdivided. If all were regarded as individual parameters, it means that sharing parameters of product platform will be less, the product generality will drop, redundancy will increase, and the cost will increase.

(3) Due to dynamic characteristics of customer needs, the FRs will move down in the model, parts of expectable functional requirements with commonality ([FR.sup.e]) may be changed into basic functional requirements. Therefore, the DPs ([DP.sup.e']) achieving these FRs can be defined as common platform parameters, denoted as [DP.sup.p].

If one expectable functional requirement ([FR.sub.i] C [FR.sup.e,]) is only influenced by corresponding design parameter and basic design parameters, namely

[partial derivative][FR.sup.e,.sub.k]/[partial derivative][DP.sup.e + a.sub.t] = 0, i = p + 1,..., q,j = p + 1,... n, i = [not equal to] j (4)

Then the DPs responding to these FRs can be regarded as common platform parameters. When the design satisfies independent axiom, it is easy to identify common platform parameters according to eq. (4). If the design is coupled, the common platform parameters will be too little due to difficulty to satisfying strictly eq. (4). Here, the design parameter [DP.sup.e'] can be regarded as individual parameter, then the relation degree among DPs corresponding [FR.sup.e'] is analyzed.

(4) The interactions should be quantified to describe strengths of relationships between design parameters. The quantification can be different by the design problems. In this paper, a four-point scale (0, 3, 6 and 9) based on the functional and structural interface relations analysis is introduced, as shown in Table 1. After the interactions have been quantified, the next step is to count the total relation degree.

Reading across a row reveals what other DPs the DP in that row provides to; scanning down a column reveals what other DPs the DP in that column depends on. That is, reading down a column reveals input information, while reading across a row indicates output information. The total of each row represents the influence of the corresponding DP fed by other DPs, while the total of each column represents the influence of the corresponding DP on other DPs. The smaller the total relation degree of row parameters, the less the dependence on other DPs. The larger the total relation degree of column parameters, the more the influence on other DPs. So, the DPs satisfying the above two terms can be regarded as common platform parameters.

Then the sharing strategy can be identified in product platform by clustering analysis, thus the design scheme on product family based on product platform is obtained.

(5) Other DPs are considered as individual parameters. Parts of them are determined due to independent influence of performance diversity among different products in product family, another are due to achieving product adjunctive functional requirements. The individual module for product can be obtained by clustering analysis to these individual parameters.

5. Case study

The electro-hydraulic drum brakes is mainly used for various mechanisms deceleration and stop/braking of various lift, belt transport, port handing, metallurgical and building machinery. Its main function is to achieve stopping and adjusting running speed of mechanism, as shown in figure 3.

5.1 Customer needs analysis of brake and functional requirements--design parameters mapping


According to current market demands of brake, the using experiences of customer and the understanding of designer, customers needs to the brake function, performance, quality are different, such as the needs of equalizing the clearance of brake shoes, needing additional heater in occasions which environmental temperature is lower, and indicate whether brake is properly release or closed, etc. But from the view of statistics, the customer needs to parts of performance parameters have a certain generality, such as braking, brake-releasing, brake shoes aligning and adjusting brake moment, etc, in which braking and brake-releasing are the basic requirements of brake. Based on axiomatic design, FRs and DPs of brake are decomposed according to zigzagging mapping, as shown in table 2 and table 3. Every level needs independent functional analysis in decomposable process. The design matrix is established according to the relationship of FRs and DPs in every level, which is arranged as shown in table 4.

5.2 Functional requirements classification for brake

The customer requirements to product are firstly summarized by customer needs, market research and customer feedback. Then the important degree of each is determined. The relation among FRs and the common requirements for product are analyzed, and the dynamic characteristics of FRs are determined. Thus according to functional requirements decomposition (Table 2), the FRs are classified as three types.

(1) Basic functional requirements: [FR.sup.b] = [{[FR.sub.1], [FR.sub.21], [FR.sub.22]}.sup.T]. These FRs are necessary to brake.

(2) Expectable functional requirements: [FR.sup.e] = [{[FR.sub.23], [FR.sub.31], [FR.sub.32], [FR.sub.33], [FR.sub.35], [FR.sub.44]}.sup.T]. These FRs are those the customers expect, but not necessary. At present, [FR.sub.23], [FR.sub.31], [FR.sub.32], [FR.sub.33] and [FR.sub.35] are certain common requirements which most customers expect, and may be classified as basic functional requirements in some way.

(3) Adjunctive functional requirements: [FR.sup.a] = [{[FR.sub.24], [FR.sub.34], [FR.sub.41], [FR.sub.42], [FR.sub.43], [FR.sub.45], [FR.sub.46]}.sup.T]. These FRs can meet individual requirements of different customers, where [FR.sub.34] and [FR.sub.43] can be also regarded as expectable functional requirements due to being needed by more and more customers. Of course, in addition to these, there are other adjunctive functional requirements, such as extending ascend or descend time for brake pull rod.

5.3 Identify brake platform parameters

According to basic functional requirements of brake and eq. (3), the dominant DPs affecting basic functional requirements can be lined out alone from DPs vector. The DPs contained by gray area in figure 6 are denoted as DP = [{[DP.sub.1], [DP.sub.21], [DP.sub.22]}.sup.T]. For those DPs correspond to expectable functional requirements with commonality, [DP.sub.23], [DP.sub.31] and [DP.sub.33] can be easily determined by using equation (4) as common platform parameters. Since [DP.sub.32] and [DP.sub.35] could not strictly satisfy equation (4), the relation degree among DPs corresponding [FR.sup.e] should be analyzed, as shown in Table 5.

From Table 5, except that [DP.sub.23], [DP.sub.31] and [DP.sub.33] are already common platform parameters, [DP.sub.35] have the smallest row total relation degree, so it can be added into common platform parameters vector. Other DPs are all regarded as individual parameters, which mainly affect the individual requirements of customers for brake. Thus [DP.sup.p] = [{[DP.sub.23], [DP.sub.31], [DP.sub.33], [DP.sub.35]}.sup.T]. In DPs respond to [FR.sup.e], [DP.sub.32] is mainly depended on [DP.sub.33]0 (common platform parameter) and doesn't affect other DPs. When the customer's needs are changed with time, technology and market segmentation, [DP.sub.33] may be transferred to common platform parameter. The design parameters and platform parameters are shown in figure 4.


6. Conclusions

Mass customization is a manufacturing approach to develop product families to increase variety, while keeping production costs low. The key to a successful product family is the product platform, from which the individual product is derived either by adding, removing, or substituting one or more modules to the platform, or by scaling the platform in one or more dimensions to target specific market niches. In this paper, from the view of customer needs, the FRs for products are classified into basic functional requirements, expectable functional requirements and adjunctive functional requirements. For different type of FRs, according to independent axiom, the dominant DPs are identified. The DPs only achieving basic functional requirements are defined as basic design parameters, while the DPs only achieving expectable functional requirements with commonality and only influenced by corresponding design parameter and basic design parameters, or have the small row and large column total relation degree are regarded as common platform parameters. Then the design scheme on product family based on product platform is determined. Finally, a product platform on electro-hydraulic drum brakes is developed, which achieve the diversity requirements and can fast respond to the customer.

Received: 28 March 2012, Revised 7 June 2012, Accepted 14 June 2012

7. Acknowledgment

This work was supported by the National Natural Science Foundation of China under the Grant No. 51165007. The authors would like to thank the reviewers for their valuable comments and suggestions.


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Xianfu Cheng

School of Mechanical and Electronical Engineering

East China Jiaotong University


Postal 330013


Author Biography

Xianfu Cheng received the MS degree in Mechanical Engineering from Wuhan University of Technology in 2000, and the PhD degree in School of Mechanical Science and Engineering at Huazhong University of Science and Technology in 2007. He is currently an associate professor in East China Jiaotong University. His research interests are in the areas of design theory and methodology, mass customization, robust design.
Table 1. The design relation matrix

DP       A           B           C           D           E

A        --          BA          CA          DA          EA
B        AB          --          CB          DB          EB
C        AC          BC          --          DC          EC
D        AD          BD          CD          --          ED
E        AE          BE          CE          DE          --
Total    [A.sub.s]   [B.sub.s]   [C.sub.s]   [D.sub.s]   [E.sub.s]

DP       Total

A        [A.sub.R]
B        [B.sub.R]
C        [C.sub.R]
D        [D.sub.R]
E        [E.sub.R]

Table 2. The functional requirements decomposition of electro-
hydraulic drum brakes

[FR.sub.1], Close brake           [FR.sub.2] Release brake

[FR.sub.11] Provide brake force   [FR.sub.21] Afford open brake force

[FR.sub.12] Increase force        [FR.sub.22] Connect braking element

[FR.sub.13] Deliver force         [FR.sub.23] Open brake manually
[FR.sub.14] Increase rub          [FR.sub.24] Heat

[FR.sub.15] Connect two brake
[FR.sub.16] Support and locate

[FR.sub.1], Close brake           [FR.sub.3] Adjust

[FR.sub.11] Provide brake force   [FR.sub.31] Adjust brake moment

[FR.sub.12] Increase force        [FR.sub.32] Adjust clearance of
                                    brake shoes

[FR.sub.13] Deliver force         [FR.sub.33] Align brake shoes

[FR.sub.14] Increase rub          [FR.sub.34] Equalize brake shoes

[FR.sub.15] Connect two brake     [FR.sub.35] Adjust compensate for
  arms                              wear

[FR.sub.16] Support and locate

[FR.sub.1], Close brake           [FR.sub.4] Display

[FR.sub.11] Provide brake force   [FR.sub.41] Display signal of
                                    closing brake

[FR.sub.12] Increase force        [FR.sub.42] Display signal of
                                    releasing brake

[FR.sub.13] Deliver force         [FR.sub.43] Display wear limit

[FR.sub.14] Increase rub          [FR.sub.44] Display brake moment

[FR.sub.15] Connect two brake     [FR.sub.45] Display whether brake is
  arms                            properly closed

[FR.sub.16] Support and locate
                                  [FR.sub.4] Display whether brake is
                                  properly released

Table 3. The design parameters hierarchy of electro-hydraulic
drum brakes

DP electro-hydraulic brakes

[DP.sub.1] Closing brake device   [DP.sub.2] Releasing brake device

[DP.sub.11] Brake spring          [DP.sub.21] Thruster
[DP.sub.12] Brake arms            [DP.sub.22] Set square
[DP.sub.13] Brake shoes           [DP.sub.23] Hand release lever
[DP.sub.14] Brake lining          [DP.sub.24] Heater
[DP.sub.15] Brake pull rod
[DP.sub.16] Foot log

[DP.sub.1] Closing brake device   [DP.sub.3] Adjust device

[DP.sub.11] Brake spring          [DP.sub.31] Moment adjusting nut
[DP.sub.12] Brake arms            [DP.sub.32] Threads compensation
[DP.sub.13] Brake shoes             jacket of brake pull rod
[DP.sub.14] Brake lining          [DP.sub.33] Brake shoe aligning
[DP.sub.15] Brake pull rod        [DP.sub.34] Clearance balancing
[DP.sub.16] Foot log              [DP.sub.35] Lining-wear
                                    self-compensation device

[DP.sub.1] Closing brake device   [DP.sub.4] Display device

[DP.sub.11] Brake spring          [DP.sub.41] Close limit-switch
[DP.sub.12] Brake arms            [DP.sub.42] Release limit-switch
[DP.sub.13] Brake shoes           [DP.sub.43] Lining-wear limitation
[DP.sub.14] Brake lining          limit-switch
[DP.sub.15] Brake pull rod        [DP.sub.44] Brake moment gage rod
[DP.sub.16] Foot log              [DP.sub.45] Inferior limit-switch
                                  [DP.sub.46] Superior limit-switch

Table 4. Design matrix of electro-hydraulic drum brakes

D                         [DP.sub.1]                  [DP.sub.2]
P/FR           11    12   13    14    15    16    21    22    23    24

[FR.sub.11]     1
[FR.sub.12]          1
[FR.sub.13]          1     1
[FR.sub.14]                1     1
[FR.sub.15]          1                 1
[FR.sub.16]                                  1
[FR.sub.21]                                        1
[FR.sub.22]          1                 1                 1
[FR.sub.23]                                        1           1
[FR.sub.24]                                                          1
[FR.sub.31]     1
[FR.sub.33]                1
[FR.sub.32]                1           1           1
[FR.sub.34]                1                 1
[FR.sub.35]     1                      1           1
[FR.sub.44]     1

D                     [DP.sub.3]               [DP.sub.3]
P/FR           31   33   32   34   35   41   42   43   44   45   46

[FR.sub.31]    1
[FR.sub.33]         1
[FR.sub.32]         1    1
[FR.sub.34]         1    1    1
[FR.sub.35]              1         1
[FR.sub.41]                             1
[FR.sub.42]                                  1
[FR.sub.43]                                       1
[FR.sub.44]    1                                       1
[FR.sub.45]                                                 1
[FR.sub.46]                                                      1

Table 5. Design relation matrix of the DPs

DP            [DP.sub.23]   [DP.sub.31]   [DP.sub.32]   [DP.sub.33]

[DP.sub.23]       --             0             0             0
[DP.sub.31]        0            --             0             0
[DP.sub.32]        0             0            --             6
[DP.sub.33]        0             0             0            --
[DP.sub.35]        0             0             0             0
[DP.sub.44]        0             6             0             0

Total              0             6             0             6

DP            [DP.sub.35]   [DP.sub.44]   Total

[DP.sub.23]        0             0          0
[DP.sub.31]        0             0          0
[DP.sub.32]        0             0          6
[DP.sub.33]        0             0          0
[DP.sub.35]       --             0          0
[DP.sub.44]        0            --          6

Total              0             0

Figure 2. The construction process of design structure matrix

Design Matrix

DP/FR        [DP.sub.i]   [DP.sub.j]   [DP.sub.k]

[FR.sub.l]      1             1
[FR.sub.j]                     1
[FR.sub.k]                                 1

Transition Matrix

DP/                     [DP.sub.i]   [DP.sub.j]   [DP.sub.k]

[FR.sub.l] [DP.sub.i]      1             1
[FR.sub.j] [DP.sub.i]                    1
[FR.sub.k] [DP.sub.k]                                1


DP/DP        [DP.sub.i]   [DP.sub.j]   [DP.sub.k]

[DP.sub.i]      1            1
[DP.sub.i]                      1
[DP.sub.k]                                     1
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Author:Cheng, Xianfu
Publication:Journal of Digital Information Management
Article Type:Report
Date:Oct 1, 2012
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