Product Specification Analysis for Modular Product Design Using Big Sales Data

Abstract

Big data on product sales are an emerging resource for supporting modular product design to meet diversified customers’ requirements of product specification combinations. To better facilitate decision-making of modular product design, correlations among specifications and components originated from customers’ conscious and subconscious preferences can be investigated by using big data on product sales. This study proposes a framework and the associated methods for supporting modular product design decisions based on correlation analysis of product specifications and components using big sales data. The correlations of the product specifications are determined by analyzing the collected product sales data. By building the relations between the product components and specifications, a matrix for measuring the correlation among product components is formed for component clustering. Six rules for supporting the decision making of modular product design are proposed based on the frequency analysis of the specification values per component cluster. A case study of electric vehicles illustrates the application of the proposed method.

1 Introduction

Innovative product design is essential for global competition among manufacturers because the lifecycle performance of a product is highly influenced by the quality of product design solutions [1, 2]. Compared with the technology-driven mode of product design based on manufacturers’ technical abilities, the market-driven mode of product design can rapidly respond to market changes with the required product specifications [3,4,5].

The required changes in product specifications and their combinations can be achieved through adaptations of the physical components. In the past decades, various types of product structures have been proposed to develop modular products to satisfy the changing market requirements, such as mass manufactured products, mass customized products, reconfigurable products, upgradeable products, open architecture products, and adaptable products [6,7,8]. A comparison of the different types of products is presented in Table 1 [8]. It was observed that these modular products consist of the following modules and interfaces.

• Common module: Common modules are designed and manufactured by manufacturers using mass production methods [9, 10]. Those shared by different products are typically considered platforms in a product family.

• Customized module: Customized modules are designed and manufactured by the original equipment manufacturer (OEM) using mass customization methods for customer choice during the purchasing process [11].

• Personalized module: Personalized modules are designed and manufactured to satisfy the personalized requirements of the customers. They can be designed by customers and/or purchased from a third-party vendor.

• Adaptable interface: Adaptable interfaces are components and their relationships to the interface can be easily adapted in the product operation stage to satisfy different requirements [12, 13].

Table 1 Types of products with different modules

To better satisfy the changing customer/market requirements of product specifications, there is a need to support the design decisions of common, customized, and personalized modules and their interfaces. In the past decades, many research efforts have been devoted to modular design methods (such as module-based product family design, platform design, and modular design for mass customization) for better product variety, reduced production costs, and shortened lead time. Different approaches, such as the design structure matrix method and modular function deployment method, have been proposed for product modularization. Various metrics (such as the component shape, materials, and manufacturing capability) for modularity evaluation have been proposed for modular product design [14]. To identify common modules shared by a product family, platform and product family design have been proposed by researchers. Methods for customized module determination have also been developed in modular design for mass customization.

Despite progress in modular product design, it was observed that most of the existing methods focused on identifying common (platform) and customized modules. Few studies have been conducted on the identification and design of personalized modules and adaptable interfaces for connecting personalized modules. In addition, existing methods tend to use independence and/or similarity based on considerations of component geometry, materials, assembly, disassembly, etc. for product modularity. Unambiguous functional correlation analysis among components remains a less regarded topic in product modularization [15]. It was observed that the prediction and incorporation of diversified market preferences on product specification combinations have rarely been studied to support modular design decisions.

Customers and markets have different preferences for product specification combinations. Design decisions on different types of modules (i.e., common, customized, personalized modules) and their interfaces to satisfy various customer requirements need to be carried out based on market preference analysis. The correlations between specifications can effectively reflect customer and market preferences for product specification combinations. Generally, relationships among product specifications may have three categories: Independent, normal, and strong. These relationships are illustrated in Figure 1.

Figure 1

Relationships among specifications

To better facilitate the design of different types of modular products to satisfy diversified changeable requirements, specification correlations originating from customer/market preferences should be investigated for design decision-making of physical components by considering specification-component relationships [16]. However, there is a lack of research on the correlations between product specifications for product modularity [17, 18]. Although existing methods for customer preference analysis (such as individual judgment, expert meeting, brainstorming, Delphi method, and Kano method) have been widely used, owing to their strong applicability and good interpretability, the following limitations have been observed:

• The dataset used is not large enough because only a limited number of customers can participate in the interview, and only parts of the customers provide useful feedback or comments on the product. This results in an insufficient reflection of customer preferences in the marketplace.

• Product specification correlations originating from both conscious and subconscious customer preferences were not fully considered. Because most existing methods focus on analyzing customer preferences for certain functions and/or features of a product, few studies have investigated specification correlations originating from customer preferences and their combinations.

Big data on product sales are valuable sources for mining relationships among product specifications. Specification relations originating from customers’ conscious and subconscious preferences are embedded in big data on product sales. Related research has demonstrated that sales data can provide critical guidance for product design and development [16, 19]. This study proposes a method for the correlation analysis of product specifications and components using big sales data to support modular product design. In this study, the sales data of target products are collected and used to reflect customer preferences. Specification correlations were obtained according to the sales and specification values. Additionally, four types of relations between specifications and components were defined so that designers could categorize these relations according to different design requirements. According to the correlations of the product components, different combinations of components were obtained using a hierarchical clustering algorithm. Component combinations are used to support design decision making for the updating/development of products.

2 Proposed Method

Product specifications in the functional domain were designed to meet customer requirements. The physical components are designed to support the specifications required by customers. Correlations among product specifications are the basis of component design and reconfiguration. According to statistical analysis based on the collected product data, a method for measuring correlations among product specifications is proposed based on the following assumptions:

• (1) Product sales data, such as the number of product sales and combinations of product specifications, can be obtained through market surveys.

• (2) Correlations among product specifications can originate from the customers’ conscious and subconscious preferences.

• (3) The correlations among product specifications originating from customer preferences are embedded in the product sales data.

Based on these three assumptions, a framework is proposed for modular product design decision support through the quantification of correlations among product specifications, as shown in Figure 2.

Figure 2

Framework of the proposed method

The method associated with this framework is illustrated in Figure 3. The proposed method comprises five phases. In Phase 1, the sales data, product specifications, and their values are obtained through a market survey, and these data are processed to support the search for specification correlations. In Phase 2, a specification correlation matrix is formed to measure the correlations among product specifications. The matrix reflects customer preferences when searching using sales data. In Phase 3, four relations between product components and specifications are identified to satisfy different design requirements. Based on the relations between specifications and components, the correlations of product components are determined in Phase 4. Using the component correlations, the components are clustered into different groups using a hierarchical clustering method in Phase 5. Additionally, a frequency analysis of the corresponding specification values per component cluster is conducted to obtain the characteristics of each cluster. Finally, rules for supporting the decision making of modular product design are formed based on the component clustering results.

Figure 3

Five phases of the proposed method

2.1 Data Collecting and Preprocessing

In this step, a market survey is conducted to acquire relevant data for each product instance. The market survey was implemented by accessing the official websites of these products and other database platforms. The survey output included various products and their sales data, specifications, and values.

Following data collection, the data were preprocessed. Screening of non-relevant specifications can be performed manually to meet the scope and objectives of the investigation. Consequently, the redundant specifications can be removed. Furthermore, a dimensionality reduction operation may be performed by removing entries in product instances and specifications to reduce the large amount of useless data [20, 21].

In this study, supposed m product instances are collected, and the sales number of products is modelled as follows:

$$\varvec{N} = [N_{{1}} , \, \ldots ,N_{m} ],$$

(1)

where N_i represents the sales of the ith product and i =1, 2, …, m.

Within the collected datasets, it is assumed that n specifications are considered for the correlation analysis, and the specifications can be modelled as follows:

$$\varvec{S} = [S_{{1}} , \, \ldots ,S_{n} ],$$

(2)

where S_i (i=1, …, n) denotes the ith specification.

To simplify the calculation, the values of each product specification need to be digitized/discretized in the data preparation for correlation searching. For example, for battery cell shapes (S_i), a value of 1 or 2 can be assigned to represent the shape of a cylinder or square, respectively.

2.2 Correlations among Product Specifications

In this step, correlations among product specifications are calculated using the collected big sales data. Generally, correlations between two specifications originating from customers’ conscious and subconscious preferences can be linear or nonlinear.

The correlation between two variables can be described using correlation coefficients. The Pearson correlation coefficient [22] and Spearman rank correlation coefficient [23] are commonly used to measure the linear and nonlinear relationships between two variables, respectively. The values of the correlation coefficient varied between −1 and 1.

In this study, correlation coefficients are required to measure correlations between specifications, considering customer preferences through big data on product sales. The correlations among all the n specifications can be obtained using the following matrix M_S:

$${{\varvec{M}}}_{{\varvec{S}}}=\left[\begin{array}{cccc}1& {\rho }_{{S}_{1}{S}_{2}}& \dots & {\rho }_{{S}_{1}{S}_{n}}\\ {\rho }_{{S}_{1}{S}_{2}}& 1& \dots & {\rho }_{{S}_{2}{S}_{n}}\\ \dots & \dots & \dots & \dots \\ {\rho }_{{S}_{1}{S}_{n}}& {\rho }_{{S}_{2}{S}_{n}}& \dots & 1\end{array}\right],$$

(3)

where ${\rho }_{{\it{S}}_{i}{\it{S}}_{j}}$ is the correlation between S_i and S_j, i, j = 1, 2, …, n. n is the number of product specifications.

2.3 Specifications and Components Relations

Product specifications are physically realized by the components. The relationships between the components and specifications of a product are required for the investigation of component correlations.

In logic and mathematics, necessary and sufficient are used to describe the conditional relationship between the two statements. If the truth of statement A guarantees the truth of statement B, then A is sufficient to B, and B is necessary for A. On this basis, four types of relations between product specifications and components are considered, as follows.

• (1) Neither sufficient nor necessary. The component is relatively independent of the specification, which means that specification changes do not cause component changes, and component changes do not cause specification changes.

• (2) Sufficient and unnecessary. The component is affected by multiple specifications, which means that specification changes will cause a component change, but the component change does not necessarily cause a specification change.

• (3) Necessary but not sufficient. The specification is affected by multiple components, which means that specification changes do not cause a component change; however, component changes will cause a specification change.

• (4) Sufficient and necessary. The specification only affects the component, and the component is only affected by the specification.

To achieve different design requirements or objectives, the above four types of relations between product specifications and components must be transferred into influential (I) and non-influential (N). The following three scenarios related to the design objective were considered for the relationship transformation:

• (a) Scenario 1: The design objective is to minimize the number of changing components while satisfying the specification changes. For example, the modular design of an open architecture product satisfies changeable specification requirements. In this situation, the relations of types 2 and 4 are defined as influential (I), whereas 1 and 3 are non-influential (N) when changes in specifications are known. This scenario is applicable to the condition that the priority target is to meet the changeable requirements of the product specifications.

• (b) Scenario 2: The design objective is to minimize the number of specifications that could be influenced by the required adaptations of the components. For example, the modular design of products for upgrading or replacing required components. In this situation, the relations of types 3 and 4 are defined as influential (I), whereas 1 and 2 are non-influential (N) when changes in components are known. This scenario is applicable under the condition that the priority target is to facilitate the required upgrading or adaptations of certain product components.

• (c) Scenario 3: The design objective is to maximize the adaptation capability to satisfy unknown changes in both the specifications and components. For example, the modular design of adaptable products satisfies potential changes in both product specifications and components. In this situation, the relations of types 2, 3, and 4 are defined as influential (I) and type 1 as non-influential (N) when changes in the components and specifications are unknown. This scenario is applicable under the condition that potential changes in both specifications and components should be considered.

The relation transfers based on different design objectives and their application conditions are summarized in Table 2.

Table 2 Relation transfer based on different design objectives

In this study, a matrix M_R is proposed to model the transferred relations of the product specifications and components as follows:

$${{\varvec{M}}}_{{\varvec{R}}}={\left[{r}_{ij}\right]}_{m\times n},$$

(4)

where r_ij represents the relationship between the ith specification and jth component. r_ij uses I and N to represent the influential and non-influential relationships between the ith specification and jth component, respectively.

2.4 Correlations among Product Components

Component correlations matrix M_C can be formed based on the correlations of specifications M_S and specification-component relations M_R. A computational method is proposed to map specification correlations in the customer domain to component correlations in the physical domain. Component correlations can be used for decision making in the design of physical product structures.

In this study, we assume that t is the number of components considered in the design, and specifications S_p, …, S_q are influenced by components C_x, x=1, …, t, p≠q, p, q∈ [1, n]$.$ Specifications S_u, …, S_v are influenced by physical components C_y, y=1, …, t, u≠v, u, v∈ [1, n].

The correlations between components C_x and C_y can be determined based on the correlations among specifications S_p, …, S_q and S_u, …, S_v. In this study, the correlations between components C_x and C_y are defined by the mean values of the correlations among related specifications S_p, …, S_q and S_u, …, S_v. Therefore, the correlations between the components C_x and C_y can be determined by

$${\rho }_{{C}_{x}{C}_{y}}=\frac{\sum_{j=u}^{v}\sum_{i=p}^{q}{\rho }_{{S}_{i}{S}_{j}}}{(q-p)\times (v-u)},$$

(5)

where x, y=1, …, t, p≠q, u≠v, p, q, u, v = 1, 2, …, n; n denotes the number of specifications considered in the design.

According to Eq. (5), the correlation among the components can be modelled by the correlation matrix M_C as follows:

$${{\varvec{M}}}_{{\varvec{C}}}=\left[\begin{array}{cccc}1& {\rho }_{{C}_{1}{C}_{2}}& \dots & {\rho }_{{C}_{1}{C}_{t}}\\ {\rho }_{{C}_{1}{C}_{2}}& 1& \dots & {\rho }_{{C}_{2}{C}_{t}}\\ \dots & \dots & \dots & \dots \\ {\rho }_{{C}_{1}{C}_{t}}& {\rho }_{{C}_{2}{C}_{t}}& \dots & 1\end{array}\right],$$

(6)

Obviously, the matrix has the following properties:

• It is a symmetric matrix, which indicates non-direction in the component correlations.

• The values of the diagonal elements are equal to one, which reflects the correlations between the components themselves.

2.5 Components Clustering and Frequency Analysis

Product components can be clustered to obtain rules and implications for design decisions using the formed matrix of the product component M_C. The clustering results formed the component groups.

In this step, a hierarchical clustering method is used to cluster the components. Hierarchical clustering is an unsupervised learning method that supports data clustering without the target attributes. The data were evaluated to determine some intrinsic structures of the data. Hierarchical clustering hierarchically decomposes a given dataset into a tree using two schemes: Cohesive and split. Aggregated hierarchical clustering is a bottom-up approach. Split hierarchical clustering is contrary to agglomerated hierarchical clustering [24, 25].

The result of hierarchical clustering is a set of components as a significant basis for product design reorganization. Components can be designed in the same module when their correlations are high, for a convenient solution for design improvement. For convincing design decision support, clustering results should be analyzed to meet the scope of applications.

In the frequency analysis, a specification group i (Figure 4) can be obtained according to the clustering result and specification/component relations, which is a set of all specifications related to the components in cluster i.

Figure 4

Searching for specification groups

Frequency analysis searches for each specification in cluster i according to the collected data. Kurtosis is used to measure the degree of data aggregation to reflect the distribution of the specification values. The kurtosis of each specification can be obtained through frequency analysis. A large kurtosis value means that the specification values are relatively concentrated, which can be considered a dominant specification. However, a small kurtosis value indicates a high divergence in the specification values. In this sense, medium and small kurtosis values should be considered for customized and personalized modules, respectively.

Using this concept, two thresholds t₁ and t₂ are empirically defined based on the designers’ experience, where t₁ > t₂. Clusters can then be defined for different types based on the following rules.

• (1) If all kurtosis in this cluster is larger than a predefined threshold value t₁, the cluster can be considered a common module.

• (2) If the kurtosis in the cluster has a value among the predefined threshold values t₁ and t₂, the cluster can be considered a customized module.

• (3) If the kurtosis in the cluster has a value less than the predefined threshold value t₂, the cluster can be considered a personalized module.

2.6 Rules for Supporting Decision-Making of Modular Product Design

A product module forms a unit of components with a particular function [26]. In other words, some elements of a product are combined to realize specific functions. Customized modules can be changed according to customer requirements, but the options are limited. For a personalized module, users can add modules according to their personalized requirements. Open adaptable interfaces allow third-party modules from different sources to meet the customers’ changeable requirements [13].

Components with different characteristics should be structured into different modules [27]. Therefore, different design decisions can be made for the components in each cluster according to the kurtosis of all the specifications in different clusters.

In this study, the following rules are proposed to support modular design decisions based on the clustering results.

• a) Components in the same cluster are recommended to be grouped into one module.

• b) Components in different clusters are recommended not to be grouped into the same module.

• c) If all kurtosis in a cluster is larger than a predefined threshold value t₁, the cluster should be formed as a common module.

• d) If the kurtosis in the cluster has a value between the predefined threshold values t₁ and t₂, it is suggested that the cluster form a customized module.

• e) If the kurtosis in the cluster has a value less than the predefined threshold value t₂, the cluster is suggested to be a personalized module.

• f) Adaptable interfaces are suggested to connect customized and personalized modules with the common module.

Considering the diversity of products in the market, the proposed rules can be used to support the design decisions for different types of products as shown in Figure 5.

Figure 5

Applications of the rules

3 Case Study

Electric vehicles (EVs) have attracted significant attention worldwide in the application of green technology. In recent years, a significant number of EVs has emerged in the market. Although EVs show promise in the automotive market, increasing demand and fast upgrades cause chaotic challenges in the EV market. For design upgrading, the lack of consideration of customer preferences is a concern, and it is particularly important to build upgrading rules of EVs based on customer preferences. In this research, the proposed method is used for the update of EV components to support design decision-making in EV renewal.

A typical structure of an EV is shown in Figure 6, which illustrates the functional modules of the vehicle [28]. To meet diversified customer requirements, EVs should be well designed with adaptability using a modular or open architecture. The design support of EVs based on the correlations among the product specifications is illustrated using the proposed method.

Figure 6

Typical structure of EVs

3.1 Data Collection and Preprocess of EVs

Using an online search, 31 different types of EVs were identified. Data including sales and specification values of the EVs were collected. It should be noted that only sales in the Chinese market in 2018 were recorded. The data were obtained from the official websites of these products. Some of the collected datasets are listed in Table 3.

Table 3 Collected data sets

The specifications of EVs were then obtained by evaluating and analyzing the existing EVs in the market. Considering that partial specifications have the same characteristics without details of the data, 15 were selected after data preprocessing for analysis. Additionally, as listed in Table 4, the values of the 15 specifications were discretized.

Table 4 Product specifications and values

3.2 Calculation of Specification Correlations

In this study, the specification distributions and correlations were obtained according to the collected data described in Section 3.1. Pairwise correlations among the 15 specifications were calculated in a 15×15 matrix ${{\varvec{M}}}_{{\varvec{s}}}$ as partially shown below for specifications S₁ to S₁₅. As shown in ${{\varvec{M}}}_{{\varvec{s}}}$, for example, the correlation between S₂ and S₆ is 0.93, which means that the probability of S₂ and S₆ changing together is very high, according to the customer preferences.

$${{\varvec{M}}}_{{\varvec{s}}}=\left[\begin{array}{ccccccccccccccc}1& 0.40& 0.74& 0.45& 0.27& 0.48& 0.48& 0.38& 0.01& 0.18& 0.61& 0.18& 0.27& 0.13& 0.19\\ 0.40& 1& 0.55& 0.55& 0.62& 0.93& 0.63& 0.39& 0.30& 0.04& 0.75& 0.30& 0.03& 0.27& 0.56\\ 0.74& 0.55& 1& 0.62& 0.65& 0.60& 0.61& 0.45& 0.15& 0.28& 0.78& 0.48& 0.07& 0.18& 0.58\\ 0.45& 0.55& 0.62& 1& 0.77& 0.64& 0.88& 0.78& 0.08& 0.10& 0.83& 0.29& 0.34& 0.12& 0.49\\ 0.27& 0.62& 0.65& 0.77& 1& 0.68& 0.86& 0.30& 0.45& 0.14& 0.77& 0.23& 0.13& 0.26& 0.67\\ 0.48& 0.93& 0.60& 0.64& 0.68& 1& 0.73& 0.41& 0.24& 0.15& 0.74& 0.27& 0.04& 0.16& 0.64\\ 0.48& 0.63& 0.61& 0.88& 0.86& 0.73& 1& 0.58& 0.26& 0.08& 0.84& 0.23& 0.27& 0.16& 0.52\\ 0.38& 0.39& 0.45& 0.78& 0.30& 0.41& 0.58& 1& 0.31& 0.01& 0.58& 0.34& 0.47& 0.07& 0.33\\ 0.01& 0.30& 0.15& 0.08& 0.45& 0.24& 0.26& 0.31& 1& 0.31& 0.25& 0.12& 0.24& 0.14& 0.14\\ 0.18& 0.04& 0.28& 0.10& 0.14& 0.15& 0.08& 0.01& 0.31& 1& 0.38& 0.20& 0.12& 0.15& 0.15\\ 0.61& 0.75& 0.78& 0.83& 0.77& 0.74& 0.84& 0.58& 0.25& 0.38& 1& 0.49& 0.30& 0.03& 0.51\\ 0.18& 0.30& 0.48& 0.29& 0.23& 0.27& 0.23& 0.34& 0.12& 0.20& 0.49& 1& 0.20& 0.06& 0.47\\ 0.27& 0.03& 0.07& 0.34& 0.13& 0.04& 0.27& 0.47& 0.24& 0.12& 0.30& 0.20& 1& 0.04& 0.27\\ 0.13& 0.27& 0.18& 0.12& 0.26& 0.16& 0.16& 0.07& 0.14& 0.15& 0.03& 0.06& 0.04& 1& 0.03\\ 0.19& 0.56& 0.58& 0.49& 0.67& 0.64& 0.52& 0.33& 0.14& 0.15& 0.51& 0.47& 0.27& 0.03& 1\end{array}\right].$$

(7)

3.3 Relation Modeling of Specifications and Components

The major components considered in this design are listed in Table 5. A list of components is formed by analyzing the structures of the sample EVs. The characteristics of each component are then analyzed to identify the relationships between the components and specifications, as shown in Table 6. In this case study, Scenario 2, which is summarized in Table 2, was considered. Therefore, the transferred relation matrix M_R can be obtained from Table 6.

Table 5 Components of an EV

Table 6 Specifications-components relation matrix

$${{\varvec{M}}}_{{\varvec{C}}}=\left[\begin{array}{cccccccccccccccccccccccc}1& 0.61& 0.62& 0.62& 0.62& 0.67& 0.67& 0.67& 0.63& 0.64& 0.64& 0.64& 0.64& 1& 0.68& 1& 1& 1& 0.64& 0.64& 0.64& 0.64& 0.62& 0.62\\ 0.61& 1& 0.67& 0.67& 0.67& 0.66& 0.66& 0.66& 0.65& 0.64& 0.64& 0.64& 0.64& 0.61& 0.57& 0.61& 0.61& 0.61& 0.64& 0.64& 0.64& 0.64& 0.67& 0.67\\ 0.62& 0.67& 1& 1& 1& 0.67& 0.67& 0.67& 0.66& 0.65& 0.65& 0.65& 0.65& 0.62& 0.58& 0.62& 0.62& 0.62& 0.65& 0.65& 0.65& 0.65& 1& 1\\ 0.62& 0.67& 1& 1& 1& 0.67& 0.67& 0.67& 0.66& 0.65& 0.65& 0.65& 0.65& 0.62& 0.58& 0.62& 0.62& 0.62& 0.65& 0.65& 0.65& 0.65& 1& 1\\ 0.62& 0.67& 1& 1& 1& 0.67& 0.67& 0.67& 0.66& 0.65& 0.65& 0.65& 0.65& 0.62& 0.58& 0.62& 0.62& 0.62& 0.65& 0.65& 0.65& 0.65& 1& 1\\ 0.67& 0.66& 0.67& 0.67& 0.67& 1& 1& 1& 0.65& 0.66& 0.66& 0.66& 0.66& 0.67& 0.62& 0.67& 0.67& 0.67& 0.66& 0.66& 0.66& 0.66& 0.67& 0.67\\ 0.67& 0.66& 0.67& 0.67& 0.67& 1& 1& 1& 0.65& 0.66& 0.66& 0.66& 0.66& 0.67& 0.62& 0.67& 0.67& 0.67& 0.66& 0.66& 0.66& 0.66& 0.67& 0.67\\ 0.67& 0.66& 0.67& 0.67& 0.67& 1& 1& 1& 0.65& 0.66& 0.66& 0.66& 0.66& 0.67& 0.62& 0.67& 0.67& 0.67& 0.66& 0.66& 0.66& 0.66& 0.67& 0.67\\ 0.63& 0.65& 0.66& 0.66& 0.66& 0.65& 0.65& 0.65& 1& 0.64& 0.64& 0.64& 0.64& 0.63& 0.62& 0.63& 0.63& 0.63& 0.64& 0.64& 0.64& 0.64& 0.66& 0.66\\ 0.64& 0.64& 0.65& 0.65& 0.65& 0.66& 0.66& 0.66& 0.64& 1& 1& 1& 1& 0.64& 0.60& 0.64& 0.64& 0.64& 1& 1& 1& 1& 0.65& 0.65\\ 0.64& 0.64& 0.65& 0.65& 0.65& 0.66& 0.66& 0.66& 0.64& 1& 1& 1& 1& 0.64& 0.60& 0.64& 0.64& 0.64& 1& 1& 1& 1& 0.65& 0.65\\ 0.64& 0.64& 0.65& 0.65& 0.65& 0.66& 0.66& 0.66& 0.64& 1& 1& 1& 1& 0.64& 0.60& 0.64& 0.64& 0.64& 1& 1& 1& 1& 0.65& 0.65\\ 0.64& 0.64& 0.65& 0.65& 0.65& 0.66& 0.66& 0.66& 0.64& 1& 1& 1& 1& 0.64& 0.60& 0.64& 0.64& 0.64& 1& 1& 1& 1& 0.65& 0.65\\ 1& 0.61& 0.62& 0.62& 0.62& 0.67& 0.67& 0.67& 0.63& 0.64& 0.64& 0.64& 0.64& 1& 0.68& 1& 1& 1& 0.64& 0.64& 0.64& 0.64& 0.62& 0.62\\ 0.68& 0.57& 0.58& 0.58& 0.58& 0.62& 0.62& 0.62& 0.62& 0.60& 0.60& 0.60& 0.60& 0.68& 1& 0.68& 0.68& 0.68& 0.60& 0.60& 0.60& 0.60& 0.58& 0.58\\ 1& 0.61& 0.62& 0.62& 0.62& 0.67& 0.67& 0.67& 0.63& 0.64& 0.64& 0.64& 0.64& 1& 0.68& 1& 1& 1& 0.64& 0.64& 0.64& 0.64& 0.62& 0.62\\ 1& 0.61& 0.62& 0.62& 0.62& 0.67& 0.67& 0.67& 0.63& 0.64& 0.64& 0.64& 0.64& 1& 0.68& 1& 1& 1& 0.64& 0.64& 0.64& 0.64& 0.62& 0.62\\ 1& 0.61& 0.62& 0.62& 0.62& 0.67& 0.67& 0.67& 0.63& 0.64& 0.64& 0.64& 0.64& 1& 0.68& 1& 1& 1& 0.64& 0.64& 0.64& 0.64& 0.62& 0.62\\ 0.64& 0.64& 0.65& 0.65& 0.65& 0.66& 0.66& 0.66& 0.64& 1& 1& 1& 1& 0.64& 0.60& 0.64& 0.64& 0.64& 1& 1& 1& 1& 0.65& 0.65\\ 0.64& 0.64& 0.65& 0.65& 0.65& 0.66& 0.66& 0.66& 0.64& 1& 1& 1& 1& 0.64& 0.60& 0.64& 0.64& 0.64& 1& 1& 1& 1& 0.65& 0.65\\ 0.64& 0.64& 0.65& 0.65& 0.65& 0.66& 0.66& 0.66& 0.64& 1& 1& 1& 1& 0.64& 0.60& 0.64& 0.64& 0.64& 1& 1& 1& 1& 0.65& 0.65\\ 0.64& 0.64& 0.65& 0.65& 0.65& 0.66& 0.66& 0.66& 0.64& 1& 1& 1& 1& 0.64& 0.60& 0.64& 0.64& 0.64& 1& 1& 1& 1& 0.65& 0.65\\ 0.62& 0.67& 1& 1& 1& 0.67& 0.67& 0.67& 0.66& 0.65& 0.65& 0.65& 0.65& 0.62& 0.58& 0.62& 0.62& 0.62& 0.65& 0.65& 0.65& 0.65& 1& 1\\ 0.62& 0.67& 1& 1& 1& 0.67& 0.67& 0.67& 0.66& 0.65& 0.65& 0.65& 0.65& 0.62& 0.58& 0.62& 0.62& 0.62& 0.65& 0.65& 0.65& 0.65& 1& 1\end{array}\right].$$

(8)

3.4 Component Correlations

The component correlations are searched based on the specification correlation matrix M_S and relation matrix M_R.

In this case, 24 components were identified, and the correlation matrix of the components ${{\varvec{M}}}_{{\varvec{C}}}$ (as shown in Eq. (8)) was obtained using Eq. (6). The results of the component correlations provide a basis for component clustering. The values in ${{\varvec{M}}}_{{\varvec{C}}}$ reflect the probability of the clustered components based on the customer preferences.

3.5 Component Clustering and Frequency Analysis

Hierarchical clustering was conducted based on the correlation matrix, M_C. In this process, every item in the matrix is replaced by the difference between the original value and 1.

As shown in Figure 7, different component clusters can be obtained when different thresholds are selected. Considering the existing product structure, when the threshold is lower than 0.5, the clustering results can satisfy the physical constraints of the product components to the greatest extent. When the threshold is greater than 0.5, C₂ (drive motor) and C₉ (battery pack) are clustered into the same cluster. This is inconsistent with the existing design. Therefore, in this case study, the threshold is set to 0.4. The clustering results and corresponding specification groups are listed in Table 7.

Figure 7

Results of component clustering

Table 7 Component clusters of EVs

As illustrated in Table 7, high correlations among the components were observed in the same cluster. In Cluster 1, the results showed that C₁₀, C₁₁, C₁₂, C₁₃, C₁₉, C₂₀, C₂₁, and C₂₂ should be formed in a module. However, in the existing design of EVs, C₁₀, C₁₁, C₁₂ C₁₃, are structured in a module, and C₁₉, C₂₀, C₂₁, and C₂₂ are designed in a module. This is because the correlations among the specifications were not properly evaluated in the original design. In cluster 2, C₃, C₄, C₅, C₂₃, and C₂₄ can form a module. From Table 7, it can be observed that C₂₃ and C₂₄ should be separated from this cluster when considering the physical structure. In cluster 3, C₁, C_14, C₁₆, C₁₇ and C₁₈ were physically related. This demonstrates the rationality of the existing design of EVs.

In Figure 7, the distances between the components in clusters 1, 2, 3, and 4 are zero, which means that these components should not be clustered into different clusters, regardless of the threshold. In industry, sufficient specification data must be collected for product design to improve the accuracy of the proposed method. To better support the design decision, a specification frequency analysis was conducted as shown in Figure 8. In this analysis, the number of samples was determined based on the sales of different types of products.

Figure 8

Part of specification frequency analysis

The kurtosis of the 15 specifications is obtained as shown in Figure 9. For the clusters, if all kurtosis values in a specification group are larger than t₁, the components in this cluster should be designed as a common module. If there is kurtosis in the specification between t₁ and t₂, the components in this cluster can be designed as a customized module. If the kurtosis of the specification is less than t₂, the components in this cluster should be designed as personalized modules.

Figure 9

Kurtosis of all specifications

3.6 Modular Design Decision Support of EVs

According to the cluster analysis results in Section 3.5, the clusters of the components were divided into three categories: Common, customized, and personalized modules as illustrated in Table 9. Additional modular product design recommendations of EVs are presented in Table 10.

Table 9 Cluster analysis results

Table 10 Decision support of modular EV design

From Table 10, it can be observed that recommendations 1, 2, 4, and 6 are consistent with the existing design, which proves the effectiveness of the proposed method. However, it is obvious that recommendation 3 does not fit the existing design of EVs, because C₆, C₇, and C₈ are not designed as common components. Based on the analysis results, C₆, C₇, and C₈ should be redesigned as common components or grouped into a common module. Compared with the existing design of EVs that does not include a personalized module, recommendation 5 suggests that a personalized module should be designed to satisfy the personalized requirements of the vehicle in the marketplace.

It is worth mentioning that the design recommendations summarized in Table 10 may be unsuitable for the design modifications of a specific existing product because the physical constraints of the manufacturer technique capability also need to be considered. Additionally, metrics related to the component geometry, materials, assembly, and disassembly should be considered for product modularity evaluations in real modular product design practices. Integrations of the newly proposed method with existing modular design methods must be carried out for modular product design.

4 Discussions and Conclusions

Increasing market driving and technology development require a rapid response of products to meet market and customer requirements through product specification combinations. Specification relations originating from customer conscious and subconscious preferences can be embedded in the big sales data. To better facilitate various types of modular product designs to satisfy the changeable market/customer requirements, relations among product specifications should be evaluated using big data on product sales. In this study, a framework and associated method were proposed to support modular product design decisions based on the correlation analysis of product specifications and components using the big sales data. Correlations among product specifications were identified by analyzing product sales data. By considering the components and specification relations, a matrix for measuring the correlation among the product components was formed for component cluster analysis. Frequency analysis of the corresponding specification values per component cluster was performed to evaluate the dominance of the component clusters. Six rules for supporting the decision making of modular product design were proposed based on the frequency analysis results. A case study of EVs was used to illustrate the proposed method. The contributions of this study are summarized as follows.

• The newly proposed specification correlation can reflect customer conscious and subconscious preferences for product specification combinations using big sales data.

• The correlations of components originating from customers/market preferences with product specifications are identified by defining the relationship between specifications and components.

• The proposed method can accurately and comprehensively determine the correlation degree of product specifications and components from big sales data analysis, rather than defining the correlation degree using small amounts of data from experts and/or customers.

• The six rules proposed for supporting design decision marking can potentially facilitate axiomatic design, adaptable design, product family design, product platform design, and open architecture product design.

Although the effectiveness of the newly proposed method has been illustrated using a case study of EVs, in addition to specification correlations, other metrics such as the size, shape, and materials of components for product modularity evaluations should be considered for industrial applications. Additionally, the accuracy of the design recommendations provided by the proposed method is highly influenced by the following factors, which should be considered.

• (1) Quality of collected data. For a given category of products with certain similarities, a comprehensive market survey should be conducted to obtain the number of product sales and combinations of product specifications.

• (2) Calculation of correlation coefficients. The relationships among product specifications due to customer preferences could be linear and nonlinear. Both linear and nonlinear correlation coefficients should be considered in practice for the correlation analysis of the product specifications.

• (3) Design objection-related scenario selection. The selection of the three types of design scenarios provided in Section 2.3 should be conducted based on specific design objectives for the relation transformation.

• (4) The determination of thresholds t₁ and t₂ in Section 2.5. In the proposed work, two thresholds, t₁ and t₂, were defined empirically based on the designers’ experience. Inappropriate value determination of t₁ and t₂ can lead to inappropriate recommendations for common, customized, and personalized modules.

Nevertheless, this work provides the first attempt at specification analysis using big sales data to support modular product design decisions. More research and application efforts are necessary to facilitate further product design using big sales data. Future research activities in this research scope include but are not limited to the followings:

• Investigation of evolution trends of product specifications in the market using historical data on product sales.

• Calculating functional correlations among product specifications to better facilitate decoupling strategy planning for a complex product or system.

• The effects of physical constraints of both the component features and manufacturer technique capability make the proposed method more specific for design decision support.