J. Cent. South Univ. (2016) 23: 623-636

DOI: 10.1007/s11771-016-3108-y

A bottom-up method for module-based product platform development through mapping, clustering and matching analysis

ZHANG Meng(张萌)¹, LI Guo-xi(李国喜)¹, CAO Jian-ping(曹建平)²,

GONG Jing-zhong(龚京忠)¹, WU Bao-zhong(吴宝中)¹

1. College of Mechatronic Engineering and Automation, National University of Defense Technology,

Changsha 410073, China;

2. Naval Aeronautical and Astronautical Institute, Qingdao 266041, China

 Central South University Press and Springer-Verlag Berlin Heidelberg 2016

Abstract: Designing product platform could be an effective and efficient solution for manufacturing firms. Product platforms enable firms to provide increased product variety for the marketplace with as little variety between products as possible. Developed consumer products and modules within a firm can further be investigated to find out the possibility of product platform creation. A bottom-up method is proposed for module-based product platform through mapping, clustering and matching analysis. The framework and the parametric model of the method are presented, which consist of three steps: (1) mapping parameters from existing product families to functional modules, (2) clustering the modules within existing module families based on their parameters so as to generate module clusters, and selecting the satisfactory module clusters based on commonality, and (3) matching the parameters of the module clusters to the functional modules in order to capture platform elements. In addition, the parameter matching criterion and mismatching treatment are put forward to ensure the effectiveness of the platform process, while standardization and serialization of the platform element are presented. A design case of the belt conveyor is studied to demonstrate the feasibility of the proposed method.

Key words: product platform development; bottom-up method; mapping; clustering; matching

1 Introduction

Today, the focus of manufacturing has been shifting from mass production to mass customization. Diversification and individuation of products are becoming more and more important to gain market share and customers. Many companies are being faced with a challenge, namely, providing increased product variety for the marketplace with as little variety between products as possible in order to maintain the requisite economies of scale and scope needed to remain profitable [1]. Product platform designing is an effective way of resolving this dilemma by allowing highly differentiated products to be developed around a platform while targeting individual products to distinct market segments [2–3]. The platform strategy provides the conventional product design with two tasks: product platform design and platform-based product derivation. The former seeks to develop a collection of the common technical features as a platform, and the latter enables faster and cheaper development of multiple variants based on the platform to satisfy a variety of market niches [4]. Variant products make use of the product platform as the starting point and then add or remove components to change features of the base product [5]. Product platform helps to enhance competition power, promote sustainable development and improve innovative ability [6].

There are three types of product platform concepts: module-based (modular) [7–9], scale-based (scalable) [1, 10–11] and module-scale-based (flexible) [12–14] platform. Module-based platforms are those where products share common modules but have different functionalities. The modular platform is used to create variants through configuration of existing modules. The main task of module-based platform designing is to identify the shared modules in some correlative products. In modular platform-based product derivation, modules are added, substituted, and/or removed to make unique products. Scale-based platforms are those where products share the functionality but are all at different performance levels. The primary problem of scalable platform planning is to determine platform parameters and scaling variables within a product family. In scalable platform-based product derivation, scaling variables are used to stretch or shrink the product platform in one or more dimensions to satisfy a variety of customer needs [1]. Module-scale-based platform is a mixture of module-based platform and scale-based platform, which possesses their advantages simultaneously but is difficult to be modelled and developed.

Researchers have done much work on the product platform development over the past decade. There are several methods for designing a product platform, including the design for variety (DFV) method [15], the composite design method [16], the product platform concept exploration method (PPCEM) [1], the function based modularization approach towards platform design [17], the quantitative optimization approach towards multiple platform design [18–19], and so on. SIMPSON et al [1] categorised these approaches into two types: top-down (proactive platform) and bottom-up (reactive redesign). The top-down approach is used to develop a family of products when starting with a product platform and its derivatives, while the bottom-up approach redesigns and/or consolidates an existing group of products around a platform. The top-down approach is more business-oriented and the bottom-up approach is more technically oriented [20]. Another way to characterise the two approaches is that the top-down approach commences at the conceptual design stage and the bottom-up approach at the detailed design stage [21].

In this work, the bottom-up approach is focused on to develop module-based product platforms. In the literature, researchers approach modular platform design from many viewpoints. SIDDIQUE and ROSEN [22], for example, proposed a method to design a product platform from an existing group of products by comparing commonalities in the assembly process. FARRELL and SIMPSON [23] employed the PPCEM in a bottom-up approach to leverage redesign effort over a highly customised product line. QIN et al [24] presented a framework of layered constructing platform architecture and an approach to capture platform elements through analysing the commonality and standardization on a set of existing products. MOON et al [3] developed a method for identifying a product platform along with variant and unique modules in a product family using data mining and fuzzy clustering techniques. CORMIER et al [25] developed a formal design method, which may be useful for both the top- down platforming approach and the bottom-up approach. QU et al [26] described a scientific and effective decision to assist product development practitioners and managers with major decision activities in the process of platform product development. TURNER et al [27] explored a bottom-up approach and created a platform based on the solution to the individually optimised product line.

In this work, a new bottom-up method for module- based product platform development through mapping, clustering and matching analysis is proposed. The method can construct a platform by redesigning an existing family of products and their modules. This method is conducted in three steps: (1) mapping parameters from existing products to functional modules, (2) clustering the modules within module families based on the parameters to construct module clusters, and selecting the satisfactory module clusters based on commonality, and (3) matching the parameters of the module clusters to the functional modules so as to capture platform elements.

2 Methodology for module-based product platform designing

2.1 Modular platform development framework

Since established companies, where modularity strategy has been implemented for a period of time, usually have existing collections of modules already designed for previous products that need to be considered for potential use in the variants, as well as the resources to design new version of the same modules or modules with new functionality [28], the bottom-up method for modular product platform designing should both utilise existing modules and specify new ones according to the customers’ requirements.

In this work, we consider product families that have a modular architecture already determined. That is to say, the topological breakdown of all functions into sub-groups that will serve as modules is specified. The designed distinct modules have been grouped into module families, while the previous products have been formed in product families. We consider products that are composed of a set of known modules connected by compatible interfaces.

The framework of module-based platform development is shown in Fig. 1. Some definitions are proposed so as to readily describe and understand, as follows:

Definition 1: Generic product family (GPF) is a group of products with the same or similar functionality, which are designed and produced in the traditional production mode by firms.

Definition 2: Segmented product family (SPF), which can be obtained by grouping all products of a GPF in accordance with the market segments, consists of some products that could be covered with a product platform.

The GPF, naturally formed in the production process, is a collection of products that are not planned in advance, and it is difficult to be covered with one platform. The SPF is a subset of the GPF, where products and new ones can be developed based upon the same platform. There are apparent differences of performance among various SPFs.

Fig. 1 Framework of modular product platform design

Definition 3: Functional module (FM) is function oriented, while a structural module family (MF) contains several modules with the same or similar functionality. The relationship between FM and MF is one-to-one. Each module of a given MF is an instance of the relevant FM. The FM may have multiple instances. The different instances provide the sizes and capabilities that are required by the desired product variety.

Definition 4: Module cluster (MC), which is a subset of the MF, can be created by clustering modules within the MF. There are marked differences of performance among various MCs.

Suppose that the product family is determined by a set of characteristic parameters. In the same way, the FM, MF, MC and the module can also be described by a group of parameters. In this work, we assume that parameters in the same set have no relevance to each other.

As shown in Fig. 1, the framework has two inputs, one output and three units. The Input 1 is a certain SPF that is obtained by partitioning the GPF based on requirements, and the Input 2 is the whole MFs that are formed from a set of distinct modules due to the functionality. The output of this framework is the product platforms. The platform i in Fig. 1 represents the platform of SPFi. The three units are the mapping unit, the clustering unit and the matching unit.

1) The mapping unit extracts the characteristic parameters of SPFi from Input 1 and maps these parameters from SPFi to the correlative FMs. The parameters of FMs are obtained and output to the matching unit.

2) The clustering unit groups the modules within each MF from Input 2 into several MCs through clustering analysis. The parameters of these MCs are output to the matching unit.

3) The matching unit receives two types of the parameters from the mapping unit (the parameters of FMs) and the clustering unit (the parameters of MCs). According to the predefined matching criterion, the matching unit determines whether they can make a match or not. If it works, the matching results need to be adopted to capture platform elements; otherwise, some mismatching treatment could be considered. There are two alternative ways: (1) re-iterating of the procedures of the mapping unit and the clustering unit, and (2) re-designing some new products and modules to deal with the mismatching induced for lack of existing resources.

2.2 Parametric model of method

In this work, suppose the expression “A=B” means that A consists of the elements of B, “A : B” represents that A can be described by the elements of B, and  indicates that B is the value of the parameters of A.

Let S denote a family of n₁ products, i.e., S={p₁, p₂, …,Each product of SPF can be characterised by a set of n₂ parameters, i.e., S:{t₁, t₂,…, where  represents the ith parameter of the products. The “parameters–products” matrix  can be set up, where q_ij denotes the value of the ith parameter of product According to the predefined modular product architecture, the FMs related to SPF can be described aswhere  represents the jth FM, and n₃ is the number of FMs. Similarly, F_j can also be expressed using a set of k_j parameters, i.e.,where  represents the kth parameter of F_j. The parameters of the products can be mapped to that of FMs. For instance, p_i is tried to map to F_j, where and   is the value of the kth parameter of F_j, which is retrieved by mapping from p_i. Consequently, the “products–FMs’ parameters” matrix can be established by mapping the parameters from products in SPF to FMs in turn.

The set of modules can be classified into n₃ MFs, i.e., has the same parameters with F_j, viz,  For each M_j, its modules can be grouped into c_j MCs, i.e., where  is the ith MC of M_j. Due to may be expressed using the parameters of M_j, i.e.,  comprises ofmodules, i.e.,  whereis the lth module of Consequently, all modules of  constitute the “modules–parameters” matrix where  is the value of the kth parameter of the lth module of

The parametric model of the proposed method is shown in Fig. 2.

(1) Mapping unit

Step 1–2: Take the product  from the matrix and map it to all relevant FMs. Given i from 1 to n₁, all products of SPF are mapped.

Step 3–4: Get F_j from the above FMs and constitute the matrix For the parameter  the values obtained from different products distribute in a range, viz, . Given j from 1 to n₃, the value ranges of each FM’s parameters are obtained.

(2) Clustering unit

Step 1′: Extract M_j from MS and group its modules into c_j MCs through clustering analysis. Given j from 1 to n₃, each MF is analysed.

Step 2′–3′: Construct the matrix  for  of M_j. The values of parameter of the distinct modules ofalso stay in a range, i.e., . Given i from 1 to c_j, the value ranges of each MC’s parameters are gotten.

(3) Matching unit

Step 1′′: Match the two kinds of intervals from the mapping unit and the clustering unit.

3 Parameter mapping from SPF to FMS

Figure 3 describes the relationships among the SPF (with a modular architecture), FMs and MFs. Each product is a configuration of modules from different MFs. During the mapping process from the SPF to FMs lies the design knowledge, the design experience and even the designer’s preference. Therefore, the mapping is complex and nonlinear.

Fig. 2 Parametric model of this proposed method

Fig. 3 Relationships among SPF, FMs and MFs

For can be retrieved through mapping analysis. Generally, the mapping process may be expressed by the matrix A, as shown in Fig. 4.

Let A^j denote the mapping matrix of F_j, where and then,

There are a variety of mapping patterns of A^j, including the direct mapping, the empty mapping and the general mapping: (1) Direct mapping refers that the parameter relationship between the SPF and the FM is one-to-one. This means that one product parameter isonly relevant to one FM parameter. In this situation, A^j is a diagonal matrix. (2) The empty mapping indicates that there is no relationship between the product parameters and the FM’s parameters. At this time, A^j is a zero matrix. (3) The general mapping includes the dispersion mapping (1:N), the aggregate mapping (N:1), the conjugate mapping and the indirect mapping (M:N), and then A^j is a general matrix. In practice, the parameter mapping from products to FMs is a mixture of the aforementioned mapping patterns.

Fig. 4 Matrix of parameter mapping from p_i to FMs

Due to the complexity and uncertainty of the mapping process, it is hardly to find out the matrix A. Consequently, how to express and (or) simulate A is the key factor in the mapping unit. A matrix, linear essentially, cannot be used to describe the nonlinear process. That is, the matrix A shown in Fig. 4 is unable to express the parameter mapping process from products to FMs. In this work, we consider using the artificial neural network to deal with the problem. By training with a large number of samples, a network structure that is approximately equivalent to the matrix A can be obtained, as shown in Fig. 5.

Fig. 5 Parameter mapping model based on neural network

4 Parameter clustering within MFs

4.1 Module clustering based on fuzzy c-means algorithm

The fuzzy c-means (FCM) algorithm, which is fuzzy clustering method containing an objective function, regards the clustering problem as a constrained nonlinear programming problem, and can group the objects (data, or points) in a space into clusters by optimization such that objects within a cluster are similar to each other and objects in different clusters have a high degree of dissimilarity. By randomly initializing the membership matrix, FCM is trying to optimise the objective function as follows [29]:

              (1)

s.t.               (2)

where is the membership matrix, n is the size of samples;represents c cluster centers, and 2≤c≤n; the sign “” denotes the Euclidean distance; m is the weighted index, and m≥1. There are several advantages of this algorithm, including self-learning, robustness and others.

 is a collection of modules with the same or similar functionality, viz,   where s_j is the size of the collection. Since can be expressed in the same way and characterised by the differences among distinct modules, i.e., modules clustering within a given MF can be implemented based on these parameters. As the contributions of the various parameters of the module are uneven, we take the method of interval grey numbers to calculate the weight of each parameter [30–31]. The obtained weight set is denoted by where 1.

The weighted Euclidean distance is adopted to describe the contribution to clusters. According to W^j, the diagonal positive definite matrix of the weighted Euclidean distance is determined as follows:

                  (3)

Consequently, the distance between the value vector of the parameters of and the cluster center vector  of the cluster is expressed as follows:

 (4)

whereand

The objective function is adapted as follows:

                (5)

where c_j is the number of the clusters, and 1≤c_j≤s_j.

The process of modules clustering based on FCM is carried out in five steps:

Step 1: Determine the values of the parameters of each modules of M_j, constitute the “modules– parameters” matrix  and compute the weight set W^j with the approach of interval grey numbers.

Step 2: Normalise the matrix X using Eq. (6), and then get a standardised matrix :

                        (6)

      (7)

Step 3: Initialise the FCM algorithm, give initial values to c_j, U and the convergence threshold ξ. Aiming to optimise the objective function shown in Eq. (5), implement the algorithm until the convergence condition is met.

Step 4: Calculate the final U and V according to c_j, where is the center of the cluster  that belongs to the optimal clusters  Determine the value range of the parameter  of :

Step 5: Analyse the clustering results further to determine whether or not it corresponds with the actual business of firms. If not, repeat the process of clustering analysis.

4.2 MCs selection based on commonality

The MCs clustered in above section are not necessary to be the platform elements, but the ones with a high commonality degree could be. The MCs that satisfy a given commonality threshold should be formally expressed:

                       (8)

where M^* is the set of MCs that have the potential to become the platform elements,  is the module cluster, “f (·)” denotes the commonality function, and ε is the commonality threshold.

MCs selection is the process of selecting the MCs that satisfy the Eq. (8) from the set of MCs obtained in Section 4.1. The commonality of the modules in the product family takes on two aspects: (1) the number of the module in use (called the depth index), and (2) the range of the module in use (called the breadth index). In order to expand the scope of the product platform, the MC in which any module satisfies the conditions (1) or (2) can be considered to put into the product platform. The depth index and the breadth index of are defined as follows:

                (9)

                 (10)

where  is the number of the hth module of  that is in use. Let  if the hth module of  is the component of product p_i, and  if it is not. And N(·) denotes the total number of the modules of the MC.

During the product platform process, ε differs in consideration of various factors. In this work, a general method is given for determining ε according to the Pareto law: Computing f₁(·) and f₂(·) for each MC and sorting the results in descending order, and then the first 20% of the MCs are potential to be platform elements.

The process of MCs selection based on commonality includes three steps:

Step 1: Forcomputeand  The matrix is obtained. Given and  then

Step 2: Reorder the elements of F₁ and F₂, and attain two ordered vectors:  and where   and

Step 3: Extract the MCs that correspond to the first 20% elements of  and That is to say, given ifthen  And  denotes the rounding-up operation.

5 Parameter matching between FMS and MCs

5.1 Procedure of distance-based parameter matching

The parameter matching is the process of comparing the parameters of FMs with those of the selected MCs to form a product platform corresponding to SPF. The parameter matching unit is the key to combine the parameter mapping unit with the parameter clustering unit. In fact, the parameters of FMs are regarded as the constraints that are applied to amend the parameters of the selected MCs, and the product platform will be developed based on the amendments.

The parameter matrixes of FMs and MCs are shown in Fig. 6. We regard these parameters as the points in a k_j-dimensional space, and then the parameter matching is transformed into the matching of the spatial points.

To measure the matching degree between two sets of points, the reciprocal of the distance between two specific elements of the two sets can be considered. In this work, we use the maximum distance function to define the matching degree between two sets:

                   (11)

                  (12)

where S₁ and S₂ are two sets of points in n-dimensional space, is divided into m groups according to a certain rule, the ith group is expressed as (a_i, b_i), and  and  are two points. d_∞(·) denotes the maximum distance between two points, and a_ij and b_ij are the values of the jth dimension of the point a_i and b_i, respectively. D(S₁, S₂) represents the matching degree between S₁ and S₂.

  

(a)                                     (b)

Fig. 6 Parameters matrixes of FMs (a) and MCs (b)

Intuitively, the matching degree between two sets is determined by the overlap of them. However, the parameter matching between FMs and MCs only takes an underlying trend. The parameters between them do not usually match completely, even mismatch sometime. There are three reasons: (1) the information incompleteness of the products and the modules due to their expressions with the characteristic parameters, (2) the computational bias of the neural network and the fuzzy clustering method, and (3) the subjective uncertainties caused by designers’ participation during the platform development. Therefore, when the intersection operation of the parameters of FMs and MCs is directly performed, an empty set is likely to be obtained and the original trend of matching may be ignored. In order to deal with such a problem, a method based on the bounding volume (BV) is proposed, which includes four steps: (1) expanding the parameter of FMs and MCs, and constructing their bounding volumes, (2) extracting the overlap between the two BVs (), (3) grouping the elements within the overlap, and (4) calculating the matching degree by Eq. (11).

The expanding way of the parameter of the  dimension is expressed as  . In the same way, each dimension can be expanded, and then a BV in the k_j-dimensional space, which covers all of the points, is finally constructed. The establishment of the BV converts the parameters from discrete variables to continuous ones. We denote the overlap of the parameters of FMs by S₁ and the part of the parameters of MCs by S₂.

To ensure the rationality of the matching analysis, a grouping rule is given: Taking a point of S₁ as benchmark, looking for the nearest point of S₂ to it, and grouping them together. When the grouping operation is completed, we regard the grouped points of S₂ as a new set, viz, Calculate the matching degree between S₁ and S₂ using Eq. (11). If the threshold of the matching degree is met,  is substituted for the original parameters of the MCs. We put these MCs into the product platform of SPF.

Given n₁=10, and k_j=2, that is, SPF includes ten products, has five modules, and F_j and  can be described with two parameters. The above process can be described in Fig. 7.

5.2 Matching criterion and mismatching treatment

There are two types of the parameter matching operation: (1) the local matching, and (2) the global matching. The former is the matching between the FM and the MC, and the latter is the sum of the local matching of all FMs and MCs, which indicates the effectiveness of the platform process. For the local matching, when the matching degree is greater than a certain matching threshold,  we consider that the local matching is successful. The matching threshold δ can be determined through experiments or by experts. There are several different cases of the local matching:

(1) Mismatching between FM and MC   then

(2) Matching between FM and MC   and

(3) Matching between FM and MC   and

The global matching can determine whether or not the whole matching succeeds. If the degree of the global matching is greater than a given threshold value, we consider that the global matching is valid. The global matching degree G is defined as

                    (13)

Consequently, when each of the local matching and the global matching exceed their threshold values, the generated platform is considered satisfactory. The rule can be expressed as follows:

                      (14)

where η is the threshold of the global matching.

Fig. 7 Diagram of parameter matching process:

If the obtained platform fails according to the matching criterion, the mismatching treatment should be taken into account. In general, there are two ways: (1) re-building the platform by adjusting the relevant parameters and iterating the construction process, and (2) re-designing the modules of the MCs in order to meet the matching requirements.

5.3 Standardization and serialization

In this work, the platform element appears as the subset of the MC, viz,  which may include several modules. To ensure the commonality of platform elements and further find out the potential product variants, it is necessary to take into account standardization and serialization of modules of  as shown in Fig. 8. By analysing the values of the parameters of each module of  the parameter set is rearranged. The new set is   where the values of the first k parameters are similar and the values of the last k_j–k parameters are distinct. That is to say, in the k_j-dimensional space, the projections on the ith (1≤i≤k) dimension of the modules of  are densely distributed, while the projections on the (k+i)th (1≤i≤k_j–k) dimension are sparsely distributed. Therefore, standardization or commonization should be carried out for the first k parameters, and serialization or customization should be implemented for the last k_j–k parameters.

Obviously, when k is equal to k_j, the platform element becomes a standard module; when k is equal to zero, all parameters of the platform element can be customised according to the parameter series.

Fig. 8 Standardization and serialization of platform element

6 Case study

In this section, a case study illustrating how to apply the proposed method to develop a product platform for ten stationary belt conveyors is presented. The belt conveyor is the most widely used handing equipment of aggregate for the concrete mixer. Figure 9 shows a typical conveyor which contains sixteen parts.

There are a lot of belt conveyor products in the company. By analysing these products according to the functionality, a GPF can be established. Various SPFs could be obtained through grouping the products of the GPF in accordance with the market segments. We focus on one of the SPFs to develop the corresponding product platform,  The belt conveyor can be characterised by three parameters: belt width (mm), belt speed (m/s) and belt conveying capacity (m³/h), which are denoted by t₁, t₂ and t₃ in turn. The “parameters–products” matrix, denoted by is shown in Table 1.

Generally, the stationary belt conveyors can be divided into nine modules according to the function and the structure, which are the belt module, the driver module, the transmission roller module, the commutation roller module, the idler module, the tensioner module, the discharger module and the sweeper module. We denote the functional module by the sign  and the relevant module family by

The threshold values in this work are problem- dependent and currently determined heuristically. In the example, the threshold values are chosen as follows: ξ=10^–6, ε₁=ε₂=0.65, δ=8 and η=6.

The product platform for SPF can be developed through the mapping, clustering and matching analysis. Here, we focus on the process of capturing platform elements to illustrate the proposed methodology.

6.1 Parameter mapping

The artificial neural network is used for the parameter mapping from SPF to F_i. Here, we take the commutation roller module (F₄) as an example, whose parameters are diameter (mm) and maximum carrying capacity (N) that are denoted by  and  respectively.

The network structure will be obtained by training with a large number of samples. The existing belt conveyor products and the relevant commutation roller modules are considered as the samples. Figure 10 shows the training process of the BP neural network.

Inputting the data in Table 1 into the obtained network, the parameter values of F₄ can be computed that is mapped from the parameters of the products of SPF. Consequently, the “products–FMs” parameter matrix, denoted by is established, as listed in Table 2.

6.2 Parameter clustering

There are eleven commutation roller modules of the M₄ in the company. The modules of M₄ can be described using the same parameters with F₄. The “modules– parameters” matrix, denoted byis shown in Table 3.

The clustering analysis is performed on the family of commutation roller modules to realise classification of the optimization solutions. FCM is the clustering tool and the method of interval grey numbers is used to calculate the weight of the parameters. The result of the clustering analysis is shown in Fig. 11, and similarity clusters are as follows:   and

Fig. 9 Sketch structure of a typical stationary belt conveyor:

Table 1 Parameter values of products of SPF

Fig. 10 Training process of neural network

Table 2 Parameter values of F₄ calculated through mapping analysis

Table 3 Parameter values of modules of M₄

Fig. 11 Result of clustering analysis

The obtained MCs should be determined whether or not their commonality degree meets the given threshold value. Using Eqs. (9) and (10) to calculate the values of the depth index and the breadth index that are listed in Table 4, a set of the satisfactory MCs can be selected, which is denoted by

Table 4 Commonality degree of MCs

6.3 Parameter matching

The matching analysis is now carried out to capture the platform element by analysing the parameter matching degree between FM and MC. Here  is chosen to illustrate the matching process.

Step 1: Normalization. The data prepared for the matching analysis need to be normalised. The standardised “products–FMs’ parameter matrix of F₄ is listed in Table 2 and the “modules–parameters” matrix of  is given in Table 5.

Table 5 Parameter values of  calculated through clustering analysis

Step 2: BV construction. The parameters of F₄ and  both locate within the  plane. Expand the parameters and construct the BVs. The expanding way of the parameters is expressed as Consequently, the BV of the parameters of F₄ can be established that is [0,1]×[0,1], and the BV of the parameters ofis [0.0606,0.3030]×[0.2247,0.5753]. Figure 12 shows the diagram of the BV construction of the parameters of F₄ and

Fig. 12 Diagram of BV construction and intersection operation

Step 3: Intersection operation. Extract the overlap between the two BVs. The intersection is Then, S₁ and S₂ are gotten, where andThe intersection operation is shown in Fig. 12.

Step 4: Grouping. The elements within the overlap are matched according to the grouping rule. The grouping results are as follows:      Therefore,  

Step 5: Calculating the matching degree. The maximum distance of each group is computed, as given in Table 6. The greatest value is 0.1208 that belongs to the group Then, the matching degree between S₁ and S₂ is calculated as follows:

Table 6 Maximum distance of each group

Step 6: Decision-making. Since  and  the local matching between S₁ and S₂ is successful according to the matching criterion. Therefore, we consider that  can be treated as a platform element.

Step 7: Standardization and serialization. The modules of  are different alternatives for designing product variants. It is necessary to take into account standardization and serialization of modules of  based on the preferred number series. In this example, the modules of  are well designed and do not need to be standardised or serialised.

The parameter mapping, clustering and matching operations should be continued until all FMs and MCs are performed. Finally, a product platform scheme is generated. The global matching degree of the obtained platform should be computed by Eq. (12). The rule expressed by Eq. (13) is used to determine whether or not the platform is valid. According to the result, corresponding treatment is considered.

7 Conclusions

1) Aiming at the development of product platforms during the transformation of firms from the traditional production mode to the platform-based mode, a bottom-up modular platform formulation methodology is presented, offering a complete methodological framework for developing product variants suitable for mass customization. This computational approach utilises the mapping, clustering and matching analysis, helping designers to capture the platform elements for modular product family. The BP neural network model is applied for parameter mapping from products to FMs. An adapted FCM-based clustering algorithm is used for modules clustering to constitute MCs. The commonality degree of each MC is considered as an index to select the satisfactory MCs. A distance-based matching algorithm is used to analyse and compute the matching degree between FMs and MCs so as to determine the platform elements. The example of product platform development of a family of belt conveyors is used to illustrate the method. By comparing the proposed method with that given in previous studies, we show that such a method can redesign existing resources around platforms according to the market inches, and be able to achieve a trade-off between the commonality requirements from mass production and the performance requirements from diversified markets, making the developed platform more representative and reasonable.

2) This work focuses on developing a coherent methodology for product platform development, thus the proposed method has been preliminarily applied, tested and validated. Limitations exist in several aspects. And this work may be developed further in the future in the following way: (1) Concrete applications of the platform method should be refined in practice. Since the assumptions are too strong, an adaptation to the method should be made by considering the practical situation so as to enhance and widen the applications of the method. (2) Each step in the method currently relies on threshold values, such as the convergence threshold ξ, the commonality threshold ε, the local matching threshold δ and the global matching threshold η. Rigorous analysis for determining the threshold values in the method is required to replace the heuristics way.

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(Edited by YANG Bing)

Foundation item: Project(9140A18010210KG01) supported by the Departmental Pre-research Fund of China

Received date: 2014-11-27; Accepted date: 2015-05-07

Corresponding author: ZHANG Meng, PhD; Tel: +86–18673150714; E-mail: z.mengdr@gmail.com