# Research on Designing an Industrial Product-Service System with Uncertain Customer Demands

Authors: Fei Zhang; Liecheng Jia; Weizhen Han
Journal: Complexity
 (2021)

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## Abstract

The industrial product-service system (iPSS) is a kind of system engineering methodology, integration scheme, and business model to realize service value by adding intangible services in the whole life cycle. However, the design of the system involves many difficulties such as uncertain customer demands, strong subjectivity of the experience design, and long debugging times. Methods for solving upper problems are therefore essential. This paper presents a design model that integrates an improved affinity propagation (AP) clustering algorithm, quality function development (QFD), and axiomatic design (AD). The entire process of designing an iPSS can be split into three steps. First, uncertain customer demands is determined and standardized. Second, the functions of the product-service system are investigated. Finally, the structures of the system are determined. This paper examines the example of the control service of an iPSS for a water heater tank capping press. An improved AP clustering algorithm is used to determine standardized customer demands, the proposed QFD, and an AD integration model to initially establish a mapping between the customer demands domain and the function domain and clarify the design focus. Next, a QFD- and AD-integrated model is constructed to establish a mapping between the function domain and the structure domain and optimize the control scheme through the quality of its risk prediction. Finally the paper verifies that the upper process and methods can guide the design process effectively in production applications.


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## Body

## 1. Introduction

The Made in China 2025 policy lists intelligent manufacturing as one of China’s five key projects and presents a comprehensive plan to develop the intelligent manufacturing industry [1]. In 2006, the Weishang factory cooperated with Yuanfang Software Company to carry out the first furniture informatization renovation in China, and in 2016, it was awarded as the only smart manufacturing demonstration base in the home furnishing industry [2]. At the same time, Sinopec Jiujiang Branch integrated modern information technology and established a digital monitoring and optimization system, covering the entire process of “management, production, operation, and warehousing,” becoming a sample of intelligent transformation of process-oriented manufacturing [3]. Zhejiang Toman Machinery Co., Ltd. introduced intelligent manufacturing technology in 2013 to improve product quality and production efficiency. Since 2014, Toman has used self-developed systems to provide SMEs (small and medium-sized enterprises) with customized solutions, such as TM-e (a production management system) and TM-SPC (a quality control system). Toman has transformed from an equipment manufacturer to a production system integrator [4]. With the continuous development of intelligent manufacturing in practice, a variety of different themes have emerged. These themes include the Internet of things [5], big data manufacturing [6], cloud manufacturing [7], and digital twin [8], which play a positive role in guiding the technological upgrading of the manufacturing industry. For example, Jiang et al. [9–11] developed a new MATLAB toolbox, the data-based key performance indicator-oriented fault detection toolbox (DB-KIT), for evaluating the influence of the detected faults on systems behavior, reviewed the key scientific issues in the design and implementation of soft sensors in modern industry, and also proposed a research route centered on the construction of performance evaluation system and performance-oriented fault diagnosis methods. Su and Yu [12] constructed a spatial econometric model with geographical proximity as the spatial weight to study the effect of spatial agglomeration of new energy industries on regional pollution control performance. The development of the intelligent manufacturing industry has driven the rapid development of the industrial product-service system (iPSS) in China. Zhu et al. [13] comprehensively considered processing time, cost, and quality and proposed a machining capability model for quantifying and measuring machining capabilities of an mt-iPSS (industrial product-service system of a machine tool). Based on the tool-based industrial product-service system, Sun et al. [14] further studied the tool delivery method in the iPSS, established a cutting tool demand prediction model and a tool delivery model, and proposed a novel cutting tool service model. Ding et al. [15] discussed the multiobjective resource scheduling problem in the operation phase of iPSS, used an improved NSGA-II algorithm to solve the multiobjective problem including comprehensive customer satisfaction degree, resource utilization efficiency, and product-service cost, and verified the feasibility with a case of China Yufeng Electric Power Company. Leng et al. [16] proposed the concept of a cost-effective industrial product-service system for oil sands mining (om-iPSS). Haeberle et al. [17] proposed a method of systematically establishing service parameters to enhance the effectiveness of industrial service systems for establishing new services. However, there is no analysis and research on how the service parameters can be obtained from customer needs. Industrial electronic control systems constitute the control core of the iPSS of complete equipment. Usually, the control system’s design is based on customer demands. The designer creates a control system’s software and hardware design based on personal experience and professional knowledge. However, this design method is inadequate. First, customers are restricted by the professional’s knowledge and resource conditions, customers’ demands are often unclear and hard to determine, and the method involves too many ambiguities and uncertainties. Second, designers have different levels of experience and lack scientific theory to guide the design process. Therefore, when customer demands are uncertain, it is difficult for the designer to deliver a good product/service. It is, therefore, critical that the iPSS of complete equipment be provided with accurate information about customer demands to quickly design a satisfactory control system.Quality function deployment (QFD) and axiomatic design (AD) are product design methods driven by customer demand that have been widely used in other product design fields. For example, Chang et al. [18] applied QFD theory to electric vehicles and provided an effective and scientific development tool for electric vehicle manufacturers. Wang et al. [19] used QFD theory to solve a multiobjective decision problem in a collaborative supply chain network. Han et al. [20] applied QFD theory to the field of augmented reality design, achieving collaborative customer innovation and improving customer satisfaction. Avikal et al. [21] constructed a new method based on the fuzzy Kano model and QFD theory for designing the exterior of a sport utility vehicle. The project QFD tool developed by Chao et al. [22] was used by an electronics company in Japan to engage in semiconductor projects and business model development to help deploy solution elements and resources. Vinodh et al. [23] considered environmental factors at various stages of QFD and proposed the QFDE method, which was applied to the Indian rotary switch manufacturing organization to achieve an environmentally conscious design in the early stages of product development. The SOFRAGRAF Company used QFD for the design of hand tools, staplers, nailing machines, etc. [24] In addition, QFD was used to design university textbooks and improve the quality of courses. Rainstar University in Scottsdale, Arizona, applied QFD to the redesign of higher education courses. [25] Liu et al. [26] established a conceptual design process model by applying the theory of inventive problem solving and AD to the innovative design of the manipulator. Tamayo et al. [27] combined AD and a design structure matrix to determine customer demands at the conceptual design stage of a manufacturing system. Goo et al. [28] introduced independence and failure modes in AD to improve the reliability of the product design process. Pétursson et al. [29] used AD to complete the research and development of shape-memory alloy spring static test equipment. Bae et al. [30] used independent axioms to define the relationship between hard points and suspension geometries and improve suspension system design and proposed a sequential kinematics design of suspension system based on the axiomatic design (AD). Lo and Helander [31] developed a method based on AD to identify couplings and make recommendations to eliminate couplings. This method was applied to the design of adjustable microscope workstations and the design of manual SLR (single-lens-reflex) cameras. Durmusoglu and Kulak [32] developed a method of designing efficient office operations using AD principles, which improves office operations and enhances business competitiveness by reducing customer delivery times. Ferrer et al. [33] proposed a two-stage method based on the AD method to define the structure of manufacturing knowledge and develop a knowledge-based DFM (Design for Manufacturing) application for connecting rod and internal combustion engine parts’ design.Given this background, QFD can clearly define the design focus of a product-service system, and the importance of customer demands can be transmitted by the house of quality (HoQ). However, QFD is based on an empirical design and lacks objective criteria; therefore, it is impossible to verify the rationality of the design process [34]. AD provides a set of scientific design methods and axioms that can verify this rationality, but there are no effective means to map between the customer demand domain and the function domain, and the design’s emphasis cannot be clearly defined. This paper, therefore, introduces a new method integrated with AP, QFD, and AD to design a control system for the iPSS of complete equipment.As shown in Figure1, the design model starts with an analysis of customer demands. It then uses an improved AP clustering algorithm to complete the cluster analysis of the original customer demands information. Next, it establishes a system for the functional HoQ to complete the mapping between the demand domain and the function domain. Finally, following AD theory, the function domain is mapped to the structure domain. Moreover, based on this, risk prediction of the HoQ is established to optimize the system structure. The proposed QFD and an AD integration model initially establish a mapping between the customer demand domain and the function domain and clarify the design focus.Figure 1
Design model integrating AP/QFD/AD, with functional requirements (FR), design parameters (DPs), and extended risk priority numbers (ERPNs).Moreover, in view of the vagueness, dispersion, and uncertainty of customer demands obtained from interviews and questionnaires, this paper proposes an AP clustering algorithm based on a weighted network. The algorithm uses an intuitionistic fuzzy decision matrix to quantify the correlation between demand nodes, uses a weighted network to determine the distribution density of demand nodes, and then determines the selection of initial deviation parametersP.This paper will take the control service design of an iPSS for a water heater tank capping press as example. The improved AP clustering algorithm will be used to determine standardized customer demands. Then the QFD and an AD integration model will be used to initially establish a mapping between the customer demand domain and the function domain and clarify the design focus. Finally, a QFD- and AD-integrated model will be constructed to establish a mapping between the function domain and the structure domain and optimize the control scheme through the quality of its risk prediction.


## 2. Cluster Analysis of Customer Demands

QFD and AD are driven by customer demands; thus, the accuracy of these demands is very important. Fuzzy or uncertain customer demands will affect the rationality and accuracy of the subsequent design process. However, due to limitations in professional knowledge, resource conditions, and so on, customers’ requirement descriptions have certain ambiguities and uncertainties. Therefore, to standardize customer demands, this paper proposes an AP clustering algorithm based on a weighted network for a cluster analysis of customer demands.


### 2.1. AP Clustering Algorithm Based on a Weighted Network

The basic idea of an AP clustering algorithm is to use all the data points as potential clustering centers and perform clustering on a similarity matrix of the data points [35]. The AP clustering algorithm has yielded good results in applications such as image processing, community detection, and fault diagnosis because of its strong clustering stability and lack of predefined information [36, 37]. Zhang proposed an improved K-means algorithm and an improved AP clustering algorithm to determine the modular configuration of service elements [38, 39]. However, research on the AP clustering algorithm in the processing of customer demand information is still lacking.In the AP clustering algorithm, responsibilityr (i, k) and availability a (i, k) represent two types of data object information [40]. As shown in Figure 2, r (i, k) describes the suitability of data object k as the clustering center of data object i. It also represents the message from i to k. The term A (i, k) describes the suitability of data object i as the clustering center of data object k. It also represents the message from k to i. At the end of the affinity propagation, the class representative point xi is determined to be xk, where k satisfies(1)argkminai,k+ri,k.Figure 2
AP clustering algorithm message transmission.The iterative process of the AP algorithm involves alternating the updates of two information sources. As shown in the following equation, when the sum of ther (i, k) and a (i, k) values of all the data points for any xi is calculated, the representative point of the class of xi is xk:(2)ri,k+ai,k=si,k+ai,k−maxk′≠kai,k′+si,k′.The AP algorithm refers to the message transmission of data points. Normally, a sample’s representativeness can be determined by its reliability and validity. If the change value ofa (i, k) and r (i, k) is the highest, then kx is a representative sample of ix. When the local a (i, k) and r (i, k) values no longer change, messaging will stop [41].Additionally, the AP clustering algorithm introduces a damping factorλ and a deviation parameter P. The factor λ has a value range [0, 1] and is used to adjust the convergence rate of the algorithm and the stability of the iterative process. Generally, λ = 0.5 is selected. When the iterative process has large oscillations, the value of λ can be accordingly reduced or increased. The parameter P has a value range [0, 1], which is the criterion for a data point i becoming a cluster center. The larger the value, the greater the probability of the point becoming a cluster center, and vice versa. When P is less than or greater than a certain threshold, the number of clusters will change [42]. Therefore, the AP clustering algorithm has certain limitations in terms of the initial bias [43].The steps of the AP clustering algorithm are as follows [44, 45].Step 1: use the Euclidean distance between data pointsi and j to calculate the similarity s (i, j):(3)si,j=−xi−xj2,i≠j.Step 2: assign an initial preference to each data point in the sample, where the value range ofP is [0, 1].Step 3: calculater (i, k), such that(4)ri,k←si,k−maxj≠ksi,j+ai,j.Step 4: calculatea (i, k), such that(5)ai,k←min0,rk,k+∑j≠i,kmax0,rj,k,(6)ak,k←∑j≠kmax0,rj,k.Step 5: updater (i, k) and a (i, k), respectively, according to(7)ri+1i,k=λ⋅rii,k+1−λ⋅ri+1ok1,λ∈0.5,1,(8)ai+1i,k=λ⋅aii,k+1−λ⋅ai+1ok1i,k,λ∈0.5,1.Step 6: if the number of iterations exceeds the maximum value or the number of consecutive iterations of the cluster center no longer changes, the calculation is stopped; otherwise, go to Step 3 to continue the calculation.According to the implementation steps of the AP clustering algorithm, two problems arise in the clustering of customer demands. The first is that the AP clustering algorithm uses the Euclidean distance to calculate the distance between two data points. The weight of each data point to the distance is the same by default, so the construction of the similarity matrix cannot truly reflect the correlation of the demands [46]. The second problem is that the initial P value is set manually, and the probability of each data point being a clustering center is the same, by default, which is obviously unreasonable.Considering these two problems, this paper introduces a weighted network AP clustering algorithm for the cluster analysis of customer demands. This method uses intuitionistic fuzzy sets to transform the correlation of demands into quantized data to construct a weighted complex network and a weighted network model of customer demands to determine the initialP value.Atanassov proposed the intuitionistic fuzzy set [47]. A weighted network can be used to describe complex correlations of nodes. It can clearly describe the interaction strengths of individuals, where the weights represent the connection tightness of the nodes in the network [44]. In a weighted network, V = v1,v2,…,vn represents the set of nodes, (vi, vij) represents the undirected edge between nodes vii and vij, and E ∈ {(vii, vij) : vii, vij ∈ V} is the undirected edge set. The term wij represents the weight of the undirected edge (vi, vj), and W = {wij : (vi, vj) ∈ E} is the weight set.In a weighted network, the weights of the nodes reflect the interrelations and importance of each node in the network. The interaction strengths of the nodes are measured by the weights of the edges. In addition, the weights of the edges are related not only to directly connected nodes but also to neighboring nodes. Generally, the higher the number of neighboring nodes, the greater the strength of the interactions of the nodes [48]. Therefore, a weighted network used to analyze the distribution density of customer demand nodes should consider not just one factor, but all other relevant factors as well. In the customer demand-weighted network model, five basic indicators reflect the connection density around the demand nodes [49, 50], as shown in Table 1.Table 1
Weighted network indicators.
IndicatorsDefinitionConnectivityNumber of edges to which a node is directly connected in a weighted networkWeighted degreeSum of the weights of all edges directly connected to nodes in a weighted networkWeighted aggregationDegree of aggregation around a node in a weighted networkAgglomeration coefficientDegree of connection between a node and its neighbors in a weighted networkWeighted network comprehensive eigenvaluesLocal distribution density around a node in a weighted networkAccording to the basic principles of an AP clustering algorithm based on a weighted network, the nodes are the customer demand units, the edges represent the correlations of the demand units, and the weights of the edges represent the similarities of the demand units. An undirected weighted network model of customer demand can thus be established. Therefore, the subjective influence of an initial deviation parameter determined by local density can be avoided in the AP clustering algorithm. The entire process can be described as follows:Step 1: construct an intuitionistic fuzzy decision matrix. Let CRi and CRj be any two customer demands. The decision maker evaluates the similarity uij and dissimilarity vij between CRi and CRj according to the intuitive fuzzy evaluation scale. The evaluation ranges of uij and vij are both [0, 1], and 0 ≤ uij + vij ≤ 1. Then, the decision maker’s intuitionistic fuzzy decision matrix Z for n demands is(9)Z=dijn×n=u11,v11u12,v12…u1j,v1ju21,v21u22,v22…u2j,v2j⋮⋮…⋮ui1,vi1ui2,vi2…unn,vnn,where the intuitionistic fuzzy numberdij = <uij, vij>.Step 2: solve the intuitionistic fuzzy similarity matrix. Let the intuitive fuzzy evaluation value between CRi and CRj be dij = <uij, vij>. The similarity, dissimilarity, and hesitancy distances between CRi and CRj, respectively, are as follows.Similarity distance:(10)d1ai,ak=∑j=1nuij−ukj22.Dissimilarity distance:(11)d2ai,ak=∑j=1nvij−vkj22.Hesitation distance:(12)d3ai,ak=∑j=1nπij−πkj22.The intuitive fuzzy similarity ofai and ak is described byρ (ai, ak) = <αij, βij> = <1 – d1 (ai, ak) – d3 (ai, ak), d2 (ai, ak)>:(13)D=ρijn×n=ρ11ρ12…ρ1jρ21ρ22…ρ2j⋮⋮…⋮ρi1ρi2…ρnn.Step 3: convert the intuitionistic fuzzy similarity matrix into a real matrix:(14)F=fijn×n=αij+η1−αij−βij,whereη is the satisfaction threshold, η ∈ [0, 1], such that(15)F=fijn×n=f11f12…f1jf21f22…f2j⋮⋮…⋮fi1fi2…fnn.Step 4: use the demand units as the nodes, the correlations of the demand units as the edges in the weighted network, and the similarities of the demand units as the weights of the edges to establish an undirected weighted network model of customer demands.Step 5: calculate the connectivity, weighted degree, weighted aggregation, clustering coefficient, and weighted network comprehensive eigenvalues of the nodes, respectively:(16)Di=vi,vj:vi,vj∈E,vi,vj∈V,whereDi represents the connectivity of node i;(17)WDi=∑vi,vj∈Ewij,where WDi represents the weighted degree of node i;(18)WKi=∑vj,vk∈Rwjk,where WKi represents the weighted aggregation degree of node i, with R = {(vj, vk) : (vi, vj) ∈ E, (vi, vk) ∈ E, (vi, vk) ∈ E, vi, vj, vk ∈ V};(19)WCi=2WKiWDiWDi−1,where WCi represents the aggregation coefficient of node i; and(20)WFi=βWCi+1−ηWDin,where WFi represents the weighted network’s comprehensive eigenvalue of node i, with β taking the value range of [0, 1] and n as the total number of nodes in the weighted network. Finally, by normalizing the integrated eigenvalues of the weighted network of nodes, the initial P of each demand is determined.Step 6: update the attraction and attribution values utilizing equations (4) to (8) until the stop condition is satisfied.


### 2.2. Cluster Analysis of Customer Demands for a Control Service System

To analyze customer demands, the example of a control service system for an iPSS for a water heater tank capping press is used. The capping press is for an enamel water tank liner of an air energy water heater, and it automatically presses the inner barrel and top cover in different diameters and lengths. The process flow diagram is depicted in Figure3. The equipment uses a programmable logic controller (PLC) as the control core, an ABB robot as the top cover automatic feeding device, and a touch screen as the human-computer interaction interface.Figure 3
The capping press process.
(a)(b)The determination of customer demands can be divided into two stages. The first is the interview stage. When the water heater manufacturer purchases equipment, the designer obtains the customer’s product and technical service demands by communicating with the customer group responsible for the purchase. After the interview, the questionnaire stage will be conducted. Use questionnaires to further obtain the use demands of maintenance personnel and operators.Finally, the customers’ demands for a control service system are categories into 35 types, as shown in Table2.Table 2
Customer demands for a control service system.
NumberNameNumberNameCr1Information storageCr19Reset promptCr2Parameter settingsCr20Operation monitoringCr3Boot operationCr21Information queryCr4Error alarmCr22Maintenance costCr5Accident detailsCr23Graphical button sizeCr6Workpiece informationCr24Picture colorCr7EconomicalCr25Failure machine stopCr8Button layoutCr26Line labelCr9Selection error promptCr27System upgradeCr10Part stabilityCr28Program structureCr11Part speciesCr29Program modificationCr12Full featuresCr30Part replacementCr13Login authenticationCr31Consistency checkCr14Three levels of login authorityCr32Clear interface markingCr15OperabilityCr33Equipment parameter queryCr16IntensityCr34Operation feedbackCr17Model switchingCr35Error resetCr18Error self-diagnosis——Furthermore, these customer demands can be clustered into subject categories. The design teams evaluate the similarity and dissimilarity of the demand units, and the evaluation results can be averaged, as shown in Table3.Table 3
Customer demands: evaluation results.
Cr1Cr2Cr3…Cr33Cr34Cr35Cr1(1, 0)(0.23, 0.72)(0.12, 0.76)…(0.32, 058)(0.16, 0.67)(0.10, 0.82)Cr2(0.23, 0.72)(1, 0)(0.71, 0.16)…(0.26, 0.60)(0.18, 0.69)(0.75, 0.12)Cr3(0.12, 0.76)(0.71, 0.16)(1, 0)…(0.12, 0.69)(0.34, 0.58)(0.67, 0.18)Cr4(0.08, 0.82)(0.23, 0.59)(0.12, 0.80)…(0.12, 0.72)(0.69, 0.23)(0.40, 0.48)……………………Cr32(0.18, 0.67)(0.32, 0.59)(0.24, 0.71)…(0.19, 0.68)(0.28, 0.64)(0.22, 0.58)Cr33(0.32, 058)(0.26, 0.60)(0.12, 0.69)…(1, 0)(0.09, 0.72)(0.15, 0.69)Cr34(0.16, 0.67)(0.18, 0.69)(0.34, 0.58)…(0.09, 0.72)(1, 0)(0.31, 0.64)Cr35(0.10, 0.82)(0.75, 0.12)(0.67, 0.18)…(0.22, 0.58)(0.31, 0.64)(1, 0)According to equations (10) to (14), the intuitionistic fuzzy similarity matrix D can be calculated as follows:(21)D=10.2430.1020.097…0.2030.3120.1340.1140.24310.7410.183…0.3020.2410.1770.7150.1020.74110.162…0.2260.1720.3050.6970.0970.1830.1621…0.1520.1810.6290.4070.2030.3020.2260.152…10.1890.2750.2230.3120.2410.1720.181…0.18910.0960.164⋮⋮⋮⋮…⋮⋮⋮⋮0.1340.1770.3050.629…0.2750.09610.3040.1140.7150.6970.407…0.2230.1640.3041.In the weighted network, the demand units are represented by the nodes, the correlations of the demand units are represented by the edges, and the similarities of the demand units are represented by the weights of the edges. An undirected weighted network model of customer demand can be built by selecting the Force Atlas layout in the Gephi software, as shown in Figure4.Figure 4
Undirected weighted network model of customer demands.In the undirected weighted network model of customer demand, the parameterβ is 0.5 according to equations (16) to (20). The calculation of the network attribute value of every node is shown in Table 4.Table 4
Eigenvalues of the weighted network nodes.
NodeDegreeWeighted degree WDWeighted aggregationAggregation coefficient WCWeighted network’s comprehensive eigenvaluesCr1356.3132.27.924.05Cr2358.9129.83.691.97Cr3358.1130.44.532.38Cr4357.4131.15.542.87Cr5358.0130.54.662.44Cr6358.5130.04.082.16Cr7355.5133.010.755.45Cr8358.2130.34.412.18Cr9357.0131.56.263.23Cr10357.8130.74.932.57Cr11358.4130.14.192.21Cr12357.3131.25.712.96Cr13356.8131.76.683.44Cr14356.2132.38.214.19Cr15359.9128.62.921.60Cr16359.8128.72.981.63Cr17359.7128.83.051.66Cr18358.1130.44.532.38Cr19358.2130.34.412.32Cr20358.8129.73.782.01Cr21359.6128.93.121.69Cr22356.3132.27.924.05Cr23357.3131.25.712.96Cr24357.9130.64.792.51Cr25357.2131.35.883.04Cr26357.2131.35.883.04Cr27358.7129.83.882.06Cr28356.7131.86.903.54Cr29356.5132.07.383.78Cr303510.2128.32.731.51Cr31356.4132.17.643.91Cr32359.2129.33.431.84Cr33357.1131.46.073.13Cr34358.7129.83.882.06Cr35359.2129.33.431.84Since the range of the initialP value in the AP clustering algorithm is [0, 1], the initial P value of the customer requirements Cr1, Cr2, …, Cr35 can be assumed to be p1,p2,…,p35. By adopting the normalization method to process the weighted network’s comprehensive feature value of each node, the initial P value of every customer demand can be obtained, as shown in Table 5.Table 5
InitialP value of every customer demand.
p1p2p3p4p5p6p7p8p9p10p11p120.890.170.310.480.330.2410.240.610.380.250.52p13p14p15p16p17p18p19p20p21p22p23p240.680.950.040.050.060.310.290.180.070.90.520.36p25p26p27p28p29p30p31p32p33p34p35—0.540.540.20.720.8000.850.130.580.20.13—To facilitate calculation and programming, 35 random coordinate points are set to correspond to customer demands Cr1, Cr2, …, Cr35. The values of the initial deviation parameters for every demand are shown in Table 5, where the maximum number of iterations is set to 500 and the number of consecutive iterations of the cluster center without a change is set to 50. The value of λ is set to 0.5 in Matlab R2014b. Figure 5 shows the results.Figure 5
Clustering of customer demands.
(a)(b)In Figure5, when λ = 0.5, after 40 iterations, the fitness value becomes stable at 22.20, indicating that the clustering center no longer changes and the value of λ is reasonable. There are nine clusters, where the dots represent demand items, demands in the same category are connected by straight lines, and different categories are displayed in various colors. According to the coordinate points corresponding to each demand, the customer demands displayed in Table 1 can be grouped into nine categories, {(Cr1, Cr13, Cr14), (Cr2, Cr3, Cr15, Cr16, Cr17, Cr35), (Cr4, Cr18, Cr19, Cr34), (Cr5, Cr6, Cr20, Cr21, Cr33), (Cr7, Cr22), (Cr8, Cr23, Cr24, Cr32), (Cr9, Cr25, Cr31), (Cr27, Cr10, Cr11, Cr26, Cr30), (Cr12, Cr28, Cr29)}. The customer demands for the control service system can then be divided into nine different subject categories, as shown in Table 6.Table 6
Architecture of customer demands.
Primary customer demandsSecondary customer demandsTertiary customer demandsCustomer demands for a control service systemInformation security,CR1Cr1, Cr13, Cr14Operability,CR2Cr2, Cr3, Cr15, Cr16, Cr17, Cr35Alarm prompt,CR3Cr4, Cr18, Cr19, Cr34Information query,CR4Cr5, Cr6, Cr20, Cr21, Cr33User-friendly interface,CR5Cr8, Cr23, Cr24, Cr32System program,CR6Cr12, Cr28, Cr29Error-proof design,CR7Cr9, Cr25, Cr31Maintainability,CR8Cr1, Cr10, Cr11, Cr26, Cr30Economy,CR9Cr7, Cr22


## 2.1. AP Clustering Algorithm Based on a Weighted Network

The basic idea of an AP clustering algorithm is to use all the data points as potential clustering centers and perform clustering on a similarity matrix of the data points [35]. The AP clustering algorithm has yielded good results in applications such as image processing, community detection, and fault diagnosis because of its strong clustering stability and lack of predefined information [36, 37]. Zhang proposed an improved K-means algorithm and an improved AP clustering algorithm to determine the modular configuration of service elements [38, 39]. However, research on the AP clustering algorithm in the processing of customer demand information is still lacking.In the AP clustering algorithm, responsibilityr (i, k) and availability a (i, k) represent two types of data object information [40]. As shown in Figure 2, r (i, k) describes the suitability of data object k as the clustering center of data object i. It also represents the message from i to k. The term A (i, k) describes the suitability of data object i as the clustering center of data object k. It also represents the message from k to i. At the end of the affinity propagation, the class representative point xi is determined to be xk, where k satisfies(1)argkminai,k+ri,k.Figure 2
AP clustering algorithm message transmission.The iterative process of the AP algorithm involves alternating the updates of two information sources. As shown in the following equation, when the sum of ther (i, k) and a (i, k) values of all the data points for any xi is calculated, the representative point of the class of xi is xk:(2)ri,k+ai,k=si,k+ai,k−maxk′≠kai,k′+si,k′.The AP algorithm refers to the message transmission of data points. Normally, a sample’s representativeness can be determined by its reliability and validity. If the change value ofa (i, k) and r (i, k) is the highest, then kx is a representative sample of ix. When the local a (i, k) and r (i, k) values no longer change, messaging will stop [41].Additionally, the AP clustering algorithm introduces a damping factorλ and a deviation parameter P. The factor λ has a value range [0, 1] and is used to adjust the convergence rate of the algorithm and the stability of the iterative process. Generally, λ = 0.5 is selected. When the iterative process has large oscillations, the value of λ can be accordingly reduced or increased. The parameter P has a value range [0, 1], which is the criterion for a data point i becoming a cluster center. The larger the value, the greater the probability of the point becoming a cluster center, and vice versa. When P is less than or greater than a certain threshold, the number of clusters will change [42]. Therefore, the AP clustering algorithm has certain limitations in terms of the initial bias [43].The steps of the AP clustering algorithm are as follows [44, 45].Step 1: use the Euclidean distance between data pointsi and j to calculate the similarity s (i, j):(3)si,j=−xi−xj2,i≠j.Step 2: assign an initial preference to each data point in the sample, where the value range ofP is [0, 1].Step 3: calculater (i, k), such that(4)ri,k←si,k−maxj≠ksi,j+ai,j.Step 4: calculatea (i, k), such that(5)ai,k←min0,rk,k+∑j≠i,kmax0,rj,k,(6)ak,k←∑j≠kmax0,rj,k.Step 5: updater (i, k) and a (i, k), respectively, according to(7)ri+1i,k=λ⋅rii,k+1−λ⋅ri+1ok1,λ∈0.5,1,(8)ai+1i,k=λ⋅aii,k+1−λ⋅ai+1ok1i,k,λ∈0.5,1.Step 6: if the number of iterations exceeds the maximum value or the number of consecutive iterations of the cluster center no longer changes, the calculation is stopped; otherwise, go to Step 3 to continue the calculation.According to the implementation steps of the AP clustering algorithm, two problems arise in the clustering of customer demands. The first is that the AP clustering algorithm uses the Euclidean distance to calculate the distance between two data points. The weight of each data point to the distance is the same by default, so the construction of the similarity matrix cannot truly reflect the correlation of the demands [46]. The second problem is that the initial P value is set manually, and the probability of each data point being a clustering center is the same, by default, which is obviously unreasonable.Considering these two problems, this paper introduces a weighted network AP clustering algorithm for the cluster analysis of customer demands. This method uses intuitionistic fuzzy sets to transform the correlation of demands into quantized data to construct a weighted complex network and a weighted network model of customer demands to determine the initialP value.Atanassov proposed the intuitionistic fuzzy set [47]. A weighted network can be used to describe complex correlations of nodes. It can clearly describe the interaction strengths of individuals, where the weights represent the connection tightness of the nodes in the network [44]. In a weighted network, V = v1,v2,…,vn represents the set of nodes, (vi, vij) represents the undirected edge between nodes vii and vij, and E ∈ {(vii, vij) : vii, vij ∈ V} is the undirected edge set. The term wij represents the weight of the undirected edge (vi, vj), and W = {wij : (vi, vj) ∈ E} is the weight set.In a weighted network, the weights of the nodes reflect the interrelations and importance of each node in the network. The interaction strengths of the nodes are measured by the weights of the edges. In addition, the weights of the edges are related not only to directly connected nodes but also to neighboring nodes. Generally, the higher the number of neighboring nodes, the greater the strength of the interactions of the nodes [48]. Therefore, a weighted network used to analyze the distribution density of customer demand nodes should consider not just one factor, but all other relevant factors as well. In the customer demand-weighted network model, five basic indicators reflect the connection density around the demand nodes [49, 50], as shown in Table 1.Table 1
Weighted network indicators.
IndicatorsDefinitionConnectivityNumber of edges to which a node is directly connected in a weighted networkWeighted degreeSum of the weights of all edges directly connected to nodes in a weighted networkWeighted aggregationDegree of aggregation around a node in a weighted networkAgglomeration coefficientDegree of connection between a node and its neighbors in a weighted networkWeighted network comprehensive eigenvaluesLocal distribution density around a node in a weighted networkAccording to the basic principles of an AP clustering algorithm based on a weighted network, the nodes are the customer demand units, the edges represent the correlations of the demand units, and the weights of the edges represent the similarities of the demand units. An undirected weighted network model of customer demand can thus be established. Therefore, the subjective influence of an initial deviation parameter determined by local density can be avoided in the AP clustering algorithm. The entire process can be described as follows:Step 1: construct an intuitionistic fuzzy decision matrix. Let CRi and CRj be any two customer demands. The decision maker evaluates the similarity uij and dissimilarity vij between CRi and CRj according to the intuitive fuzzy evaluation scale. The evaluation ranges of uij and vij are both [0, 1], and 0 ≤ uij + vij ≤ 1. Then, the decision maker’s intuitionistic fuzzy decision matrix Z for n demands is(9)Z=dijn×n=u11,v11u12,v12…u1j,v1ju21,v21u22,v22…u2j,v2j⋮⋮…⋮ui1,vi1ui2,vi2…unn,vnn,where the intuitionistic fuzzy numberdij = <uij, vij>.Step 2: solve the intuitionistic fuzzy similarity matrix. Let the intuitive fuzzy evaluation value between CRi and CRj be dij = <uij, vij>. The similarity, dissimilarity, and hesitancy distances between CRi and CRj, respectively, are as follows.Similarity distance:(10)d1ai,ak=∑j=1nuij−ukj22.Dissimilarity distance:(11)d2ai,ak=∑j=1nvij−vkj22.Hesitation distance:(12)d3ai,ak=∑j=1nπij−πkj22.The intuitive fuzzy similarity ofai and ak is described byρ (ai, ak) = <αij, βij> = <1 – d1 (ai, ak) – d3 (ai, ak), d2 (ai, ak)>:(13)D=ρijn×n=ρ11ρ12…ρ1jρ21ρ22…ρ2j⋮⋮…⋮ρi1ρi2…ρnn.Step 3: convert the intuitionistic fuzzy similarity matrix into a real matrix:(14)F=fijn×n=αij+η1−αij−βij,whereη is the satisfaction threshold, η ∈ [0, 1], such that(15)F=fijn×n=f11f12…f1jf21f22…f2j⋮⋮…⋮fi1fi2…fnn.Step 4: use the demand units as the nodes, the correlations of the demand units as the edges in the weighted network, and the similarities of the demand units as the weights of the edges to establish an undirected weighted network model of customer demands.Step 5: calculate the connectivity, weighted degree, weighted aggregation, clustering coefficient, and weighted network comprehensive eigenvalues of the nodes, respectively:(16)Di=vi,vj:vi,vj∈E,vi,vj∈V,whereDi represents the connectivity of node i;(17)WDi=∑vi,vj∈Ewij,where WDi represents the weighted degree of node i;(18)WKi=∑vj,vk∈Rwjk,where WKi represents the weighted aggregation degree of node i, with R = {(vj, vk) : (vi, vj) ∈ E, (vi, vk) ∈ E, (vi, vk) ∈ E, vi, vj, vk ∈ V};(19)WCi=2WKiWDiWDi−1,where WCi represents the aggregation coefficient of node i; and(20)WFi=βWCi+1−ηWDin,where WFi represents the weighted network’s comprehensive eigenvalue of node i, with β taking the value range of [0, 1] and n as the total number of nodes in the weighted network. Finally, by normalizing the integrated eigenvalues of the weighted network of nodes, the initial P of each demand is determined.Step 6: update the attraction and attribution values utilizing equations (4) to (8) until the stop condition is satisfied.


## 2.2. Cluster Analysis of Customer Demands for a Control Service System

To analyze customer demands, the example of a control service system for an iPSS for a water heater tank capping press is used. The capping press is for an enamel water tank liner of an air energy water heater, and it automatically presses the inner barrel and top cover in different diameters and lengths. The process flow diagram is depicted in Figure3. The equipment uses a programmable logic controller (PLC) as the control core, an ABB robot as the top cover automatic feeding device, and a touch screen as the human-computer interaction interface.Figure 3
The capping press process.
(a)(b)The determination of customer demands can be divided into two stages. The first is the interview stage. When the water heater manufacturer purchases equipment, the designer obtains the customer’s product and technical service demands by communicating with the customer group responsible for the purchase. After the interview, the questionnaire stage will be conducted. Use questionnaires to further obtain the use demands of maintenance personnel and operators.Finally, the customers’ demands for a control service system are categories into 35 types, as shown in Table2.Table 2
Customer demands for a control service system.
NumberNameNumberNameCr1Information storageCr19Reset promptCr2Parameter settingsCr20Operation monitoringCr3Boot operationCr21Information queryCr4Error alarmCr22Maintenance costCr5Accident detailsCr23Graphical button sizeCr6Workpiece informationCr24Picture colorCr7EconomicalCr25Failure machine stopCr8Button layoutCr26Line labelCr9Selection error promptCr27System upgradeCr10Part stabilityCr28Program structureCr11Part speciesCr29Program modificationCr12Full featuresCr30Part replacementCr13Login authenticationCr31Consistency checkCr14Three levels of login authorityCr32Clear interface markingCr15OperabilityCr33Equipment parameter queryCr16IntensityCr34Operation feedbackCr17Model switchingCr35Error resetCr18Error self-diagnosis——Furthermore, these customer demands can be clustered into subject categories. The design teams evaluate the similarity and dissimilarity of the demand units, and the evaluation results can be averaged, as shown in Table3.Table 3
Customer demands: evaluation results.
Cr1Cr2Cr3…Cr33Cr34Cr35Cr1(1, 0)(0.23, 0.72)(0.12, 0.76)…(0.32, 058)(0.16, 0.67)(0.10, 0.82)Cr2(0.23, 0.72)(1, 0)(0.71, 0.16)…(0.26, 0.60)(0.18, 0.69)(0.75, 0.12)Cr3(0.12, 0.76)(0.71, 0.16)(1, 0)…(0.12, 0.69)(0.34, 0.58)(0.67, 0.18)Cr4(0.08, 0.82)(0.23, 0.59)(0.12, 0.80)…(0.12, 0.72)(0.69, 0.23)(0.40, 0.48)……………………Cr32(0.18, 0.67)(0.32, 0.59)(0.24, 0.71)…(0.19, 0.68)(0.28, 0.64)(0.22, 0.58)Cr33(0.32, 058)(0.26, 0.60)(0.12, 0.69)…(1, 0)(0.09, 0.72)(0.15, 0.69)Cr34(0.16, 0.67)(0.18, 0.69)(0.34, 0.58)…(0.09, 0.72)(1, 0)(0.31, 0.64)Cr35(0.10, 0.82)(0.75, 0.12)(0.67, 0.18)…(0.22, 0.58)(0.31, 0.64)(1, 0)According to equations (10) to (14), the intuitionistic fuzzy similarity matrix D can be calculated as follows:(21)D=10.2430.1020.097…0.2030.3120.1340.1140.24310.7410.183…0.3020.2410.1770.7150.1020.74110.162…0.2260.1720.3050.6970.0970.1830.1621…0.1520.1810.6290.4070.2030.3020.2260.152…10.1890.2750.2230.3120.2410.1720.181…0.18910.0960.164⋮⋮⋮⋮…⋮⋮⋮⋮0.1340.1770.3050.629…0.2750.09610.3040.1140.7150.6970.407…0.2230.1640.3041.In the weighted network, the demand units are represented by the nodes, the correlations of the demand units are represented by the edges, and the similarities of the demand units are represented by the weights of the edges. An undirected weighted network model of customer demand can be built by selecting the Force Atlas layout in the Gephi software, as shown in Figure4.Figure 4
Undirected weighted network model of customer demands.In the undirected weighted network model of customer demand, the parameterβ is 0.5 according to equations (16) to (20). The calculation of the network attribute value of every node is shown in Table 4.Table 4
Eigenvalues of the weighted network nodes.
NodeDegreeWeighted degree WDWeighted aggregationAggregation coefficient WCWeighted network’s comprehensive eigenvaluesCr1356.3132.27.924.05Cr2358.9129.83.691.97Cr3358.1130.44.532.38Cr4357.4131.15.542.87Cr5358.0130.54.662.44Cr6358.5130.04.082.16Cr7355.5133.010.755.45Cr8358.2130.34.412.18Cr9357.0131.56.263.23Cr10357.8130.74.932.57Cr11358.4130.14.192.21Cr12357.3131.25.712.96Cr13356.8131.76.683.44Cr14356.2132.38.214.19Cr15359.9128.62.921.60Cr16359.8128.72.981.63Cr17359.7128.83.051.66Cr18358.1130.44.532.38Cr19358.2130.34.412.32Cr20358.8129.73.782.01Cr21359.6128.93.121.69Cr22356.3132.27.924.05Cr23357.3131.25.712.96Cr24357.9130.64.792.51Cr25357.2131.35.883.04Cr26357.2131.35.883.04Cr27358.7129.83.882.06Cr28356.7131.86.903.54Cr29356.5132.07.383.78Cr303510.2128.32.731.51Cr31356.4132.17.643.91Cr32359.2129.33.431.84Cr33357.1131.46.073.13Cr34358.7129.83.882.06Cr35359.2129.33.431.84Since the range of the initialP value in the AP clustering algorithm is [0, 1], the initial P value of the customer requirements Cr1, Cr2, …, Cr35 can be assumed to be p1,p2,…,p35. By adopting the normalization method to process the weighted network’s comprehensive feature value of each node, the initial P value of every customer demand can be obtained, as shown in Table 5.Table 5
InitialP value of every customer demand.
p1p2p3p4p5p6p7p8p9p10p11p120.890.170.310.480.330.2410.240.610.380.250.52p13p14p15p16p17p18p19p20p21p22p23p240.680.950.040.050.060.310.290.180.070.90.520.36p25p26p27p28p29p30p31p32p33p34p35—0.540.540.20.720.8000.850.130.580.20.13—To facilitate calculation and programming, 35 random coordinate points are set to correspond to customer demands Cr1, Cr2, …, Cr35. The values of the initial deviation parameters for every demand are shown in Table 5, where the maximum number of iterations is set to 500 and the number of consecutive iterations of the cluster center without a change is set to 50. The value of λ is set to 0.5 in Matlab R2014b. Figure 5 shows the results.Figure 5
Clustering of customer demands.
(a)(b)In Figure5, when λ = 0.5, after 40 iterations, the fitness value becomes stable at 22.20, indicating that the clustering center no longer changes and the value of λ is reasonable. There are nine clusters, where the dots represent demand items, demands in the same category are connected by straight lines, and different categories are displayed in various colors. According to the coordinate points corresponding to each demand, the customer demands displayed in Table 1 can be grouped into nine categories, {(Cr1, Cr13, Cr14), (Cr2, Cr3, Cr15, Cr16, Cr17, Cr35), (Cr4, Cr18, Cr19, Cr34), (Cr5, Cr6, Cr20, Cr21, Cr33), (Cr7, Cr22), (Cr8, Cr23, Cr24, Cr32), (Cr9, Cr25, Cr31), (Cr27, Cr10, Cr11, Cr26, Cr30), (Cr12, Cr28, Cr29)}. The customer demands for the control service system can then be divided into nine different subject categories, as shown in Table 6.Table 6
Architecture of customer demands.
Primary customer demandsSecondary customer demandsTertiary customer demandsCustomer demands for a control service systemInformation security,CR1Cr1, Cr13, Cr14Operability,CR2Cr2, Cr3, Cr15, Cr16, Cr17, Cr35Alarm prompt,CR3Cr4, Cr18, Cr19, Cr34Information query,CR4Cr5, Cr6, Cr20, Cr21, Cr33User-friendly interface,CR5Cr8, Cr23, Cr24, Cr32System program,CR6Cr12, Cr28, Cr29Error-proof design,CR7Cr9, Cr25, Cr31Maintainability,CR8Cr1, Cr10, Cr11, Cr26, Cr30Economy,CR9Cr7, Cr22


## 3. Function Domain Determination for a Control Service System

### 3.1. Overview of QFD

QFD, a typical customer-driven design method, was first proposed by Mizuno and Akao [51]. The basic display tool of QFD is the house of quality, an intuitive matrix framework for the conversion of customer demands [52]. As a customer-driven product development method, it is a simple and logical demand conversion tool. At present, the QFD configuration process can be broken down into four stages: the product planning quality house, the parts’ development quality house, the process planning quality house, and the production planning quality house (see Figure 6). These four stages use various expansion tables to transform the important parts of the demands downward, step by step, to ensure that the product design process does not deviation from the customer’s requirements.Figure 6
Four stages of QFD configuration.In QFD, the correlation matrix is used to express the complex relation between every demand item and every technical feature of the product [53]. After determining the correlations between a customer’s demands and the product’s technical characteristics, the importance of the latter can be further determined. As shown in Table 7, a set of symbols is generally used to indicate the degree of correlation.Table 7
Evaluation and decision table for the correlations between the demand and technical characteristics.
SymbolValueMeaning5Strong correlation between the demand and technical characteristics3Medium correlation between the demand and technical characteristics1Weak correlation between the demand and technical characteristics0No correlation with technical characteristicsFurthermore, the product’s technical features can be calculated by the equations(22)TIRj=∑i=1nCIRi×Rij,i=1,2,…,n;j=1,2,…,m,TIRj′=TIRj∑TIRj,j=1,2,…,m,where n represents the number of customer demands, m represents the number of the product’s technical features, CIRi is the weight of the ith customer demand item, Rij is the value of the correlation symbol between the ith customer demand item and the jth product technical feature item, TIRj is the weight of the jth product technical feature item, and TIRj′ is the relative weight of the jth product technical feature item.


### 3.2. Function Planning for a Control Service System

After the customer demands have been standardized, a mapping analysis between the demand domain and the function domain is carried out. The system’s functional characteristics are the customer’s requirements, described in engineering and technical language. The control service system usually takes into consideration the process requirements, performance requirements, working environment, industry standards, and so on, as well as functional characteristics. For example, the equipment must be able to process multiple products. Therefore, the system should be compatible with multiple models. The customer demands include the real-time display of workpiece information. Therefore, system function monitoring is required. The customer demands also involve low labor intensity and the ability to convert quickly between different models of products. Therefore, the system must have the capability of automatically switching models. Table8 shows the functional characteristics of the system, following the analysis.Table 8
Functional characteristics of the control service system.
NameFR1FR2FR3FR4FR5ParaphraseCompatible with multiple modelsAutomatic switching modelUser loginAlarm functionDevice drivenNameFR6FR7FR8FR9—ParaphraseAutomatic feedingMultiple working modesMonitoring functionHumanized design—In addition, some requirements in the customer demand domain have constraints on other functional features, although they might not individually correspond to specific functional features. For example, economic requirements hold throughout the entire design process because cost factors must be considered for every function. Therefore, a HoQ of system functions should be built to analyze the correlations between customer demands and system functional characteristics and clarify the system design’s focus (see Figure7).Figure 7
HoQ of the functional planning for the control service system.Following the functional planning output of the HoQ, the designer can clarify major and minor points in the design process, focus on the main points, and avoid deviating from the customer’s directions due to personal experience and cognitive limitations. The control service system requires nine functions: FR1, compatibility with multiple models, FR2, automatic model switching, FR3, a user login, FR4, an alarm function, FR5, being device driven, FR6, automatic feeding, FR7, multiple working modes, FR8, a monitoring function, and FR9, humanized design. The relative importance levels of each functional characteristic are shown in Table 9.Table 9
Relative importance of system functional characteristics.
FeaturesFR1FR2FR3FR4FR5FR6FR7FR8FR9Relative weightμ10.2587μ20.1114μ30.0661μ40.0905μ50.0169μ60.0689μ70.0954μ80.0486μ90.0907


## 3.1. Overview of QFD

QFD, a typical customer-driven design method, was first proposed by Mizuno and Akao [51]. The basic display tool of QFD is the house of quality, an intuitive matrix framework for the conversion of customer demands [52]. As a customer-driven product development method, it is a simple and logical demand conversion tool. At present, the QFD configuration process can be broken down into four stages: the product planning quality house, the parts’ development quality house, the process planning quality house, and the production planning quality house (see Figure 6). These four stages use various expansion tables to transform the important parts of the demands downward, step by step, to ensure that the product design process does not deviation from the customer’s requirements.Figure 6
Four stages of QFD configuration.In QFD, the correlation matrix is used to express the complex relation between every demand item and every technical feature of the product [53]. After determining the correlations between a customer’s demands and the product’s technical characteristics, the importance of the latter can be further determined. As shown in Table 7, a set of symbols is generally used to indicate the degree of correlation.Table 7
Evaluation and decision table for the correlations between the demand and technical characteristics.
SymbolValueMeaning5Strong correlation between the demand and technical characteristics3Medium correlation between the demand and technical characteristics1Weak correlation between the demand and technical characteristics0No correlation with technical characteristicsFurthermore, the product’s technical features can be calculated by the equations(22)TIRj=∑i=1nCIRi×Rij,i=1,2,…,n;j=1,2,…,m,TIRj′=TIRj∑TIRj,j=1,2,…,m,where n represents the number of customer demands, m represents the number of the product’s technical features, CIRi is the weight of the ith customer demand item, Rij is the value of the correlation symbol between the ith customer demand item and the jth product technical feature item, TIRj is the weight of the jth product technical feature item, and TIRj′ is the relative weight of the jth product technical feature item.


## 3.2. Function Planning for a Control Service System

After the customer demands have been standardized, a mapping analysis between the demand domain and the function domain is carried out. The system’s functional characteristics are the customer’s requirements, described in engineering and technical language. The control service system usually takes into consideration the process requirements, performance requirements, working environment, industry standards, and so on, as well as functional characteristics. For example, the equipment must be able to process multiple products. Therefore, the system should be compatible with multiple models. The customer demands include the real-time display of workpiece information. Therefore, system function monitoring is required. The customer demands also involve low labor intensity and the ability to convert quickly between different models of products. Therefore, the system must have the capability of automatically switching models. Table8 shows the functional characteristics of the system, following the analysis.Table 8
Functional characteristics of the control service system.
NameFR1FR2FR3FR4FR5ParaphraseCompatible with multiple modelsAutomatic switching modelUser loginAlarm functionDevice drivenNameFR6FR7FR8FR9—ParaphraseAutomatic feedingMultiple working modesMonitoring functionHumanized design—In addition, some requirements in the customer demand domain have constraints on other functional features, although they might not individually correspond to specific functional features. For example, economic requirements hold throughout the entire design process because cost factors must be considered for every function. Therefore, a HoQ of system functions should be built to analyze the correlations between customer demands and system functional characteristics and clarify the system design’s focus (see Figure7).Figure 7
HoQ of the functional planning for the control service system.Following the functional planning output of the HoQ, the designer can clarify major and minor points in the design process, focus on the main points, and avoid deviating from the customer’s directions due to personal experience and cognitive limitations. The control service system requires nine functions: FR1, compatibility with multiple models, FR2, automatic model switching, FR3, a user login, FR4, an alarm function, FR5, being device driven, FR6, automatic feeding, FR7, multiple working modes, FR8, a monitoring function, and FR9, humanized design. The relative importance levels of each functional characteristic are shown in Table 9.Table 9
Relative importance of system functional characteristics.
FeaturesFR1FR2FR3FR4FR5FR6FR7FR8FR9Relative weightμ10.2587μ20.1114μ30.0661μ40.0905μ50.0169μ60.0689μ70.0954μ80.0486μ90.0907


## 4. Structure Domain Determination for the Control Service System

### 4.1. Overview of AD

The core of AD is the domain. According to Suh, the domain is the boundary of four design activities with different types and different modes in the product design phase [54]. The domains in axiomatic theory are the customer domain, the function domain, the structure domain, and the process domain. Between two adjacent design domains, the left domain represents the “what,” that is, the purpose, and the right domain represents the “how,” that is, the method that satisfies the left domain. The hierarchical structure and zigzag mapping are the core methods of the AD design process [55]. As depicted in Figure 8, the hierarchical structure describes the relation of various elements within the domain, and the zigzag mapping represents the mapping of the domains.Figure 8
(a) Hierarchy and (b) zigzag mapping of AD.
(a)(b)Figure8(a) illustrates the hierarchical structure of collection self-decomposition in the domain. A group of subsystems can be composed of elements in the domain according to certain rules. Here, a top-down method is used to decompose the abstract total function into subfunctions, layer by layer, until the final design is produced. The correlations of the functional, structural, and process domains are described according to the zigzag mapping in Figure 8(b). The zigzag mapping is a top-down approach in the form of a Z, and it repeats the mapping of the same and different levels in every domain until the previous domain can no longer be decomposed.To judge the reasonability of the design process, AD theory proposes a design axiom. While mapping the function domain to the structure domain, the designer can judge the appropriateness of the mapping according to the design axioms. The entire mapping can be described as(23)FRm×1=Am×nDPn×1,where {FR}m×1 represents the FRs, {DP}n × 1 represents the DPs, and Am×n represents the design matrix, which can be expressed as(24)Am×n=A11A12…A1nA21A22…A2n⋮⋮…⋮Am1Am2…Amn,where the matrix elements are determined by Aij = (∂FRi)/(∂DPj) (i = 1, 2, …, m; j = 1, 2, …, n).In an actual design, the numbers of FRs and DPs will not be the same. As shown in Table10, given the relation between the numbers of FRs and the number of DPs, the design can be split into an ideal design, a redundant design, and a coupling design.Table 10
Ideal, redundant, and coupling designs.
Design nameConditionDesign matrixIdeal designNumber of FRs = number of DPsDiagonal matrixRedundant designNumber of FRs < number of DPsTriangular matrixCoupling designNumber of FRs > number of DPsNontriangular matrix and nondiagonal matrix


### 4.2. House of Quality for Risk Prediction

Once the basic structure of a control service system is described, high-risk modules in the structure domain can be predicted and analyzed to determine potential failure modes and analyze the possible consequences. These measures can be taken in advance. Because the importance of the elements in the domain cannot be evaluated in AD, this paper introduces a risk prediction HoQ model. This model transmits the decomposition and mapping results of the AD functional and structural domains to the HoQ, builds a risk prediction HoQ, and proposes the ERPN to measure every structural module and clarify the key points of the process.The concept of ERPN is based on risk probability number. Taking into account the importance of the system functions, the system structure can be optimized to determine measures to reduce the chance of potential failure. The formula for the ERPN is(25)ERPN=μj⋅Ik⋅S⋅O⋅D,where μj is the relative weight of the jth system function characteristic in the HoQ, Ik is the weight of the kth subfunction characteristic in the risk prediction HoQ, and S is the severity (see Table 11).Table 11
Severity (S) scoring criteria.
HarmAssessment criteria: severity of the impact on the systemSeverity levelNo warning hazardNo alarm is issued when the equipment is faulty and the control system is completely out of order10Warning hazardAlarm when the equipment is faulty and the control system fails9Very seriousHas a serious impact on the control system and the system is difficult to repair8SeriousHas a serious impact on the control system, but the system can be partially repaired7MediumHas a certain impact on the control system, but the system can be repaired6LowHas a certain impact on the control system, but the system can be repaired completely5Very lowHas less impact on the control system and the system can be repaired more quickly4SlightThe impact on the control system is small, and the system can be repaired quickly3VeryThe impact on the control system is very slight, and the system can be easily repaired2NothingNo impact on the control system, and the system can work normally1Table12 shows the scoring criteria for the frequency O.Table 12
Frequency (O) scoring criteria.
Possibility of failureEvaluation criteria: frequency of occurrenceFrequencyVery highGreater than 1/210About 1/39HighAbout 1/88About 1/207ModerateAbout 1/806About 1/4005About 1/20004LowAbout 1/15,0003About 1/150,0002Very lowLess than 1/150,0001Table13 shows the scoring criteria for the degree of detection D.Table 13
Scoring criteria for the degree of detectionD.
Detectability levelEvaluation criteria: the possibility of detecting the cause of system failures in the prior artLevelInfinitesimalThe prior art cannot detect the cause of the failure of the control system10Very tinyExisting technology has difficulty detecting the cause of the failure of the control system9TinyExisting technology has more difficult detecting the cause of the failure of the control system8Very lowNeed a control system designer to investigate the cause of the fault7LowA technician can discover the cause of the failure6MediumThe control system has alarm tips, but does not display fault information5HigherThe control system has alarm tips and displays fault information4HighThe cause of the fault can be determined by a simple test instrument3Very highThe cause of the failure can be visually identified2Almost certainlyThe cause of the fault can be detected almost certainly1


### 4.3. Structure Domain Solution of the Control Service System

The system’s functional characteristics are only a visual description of the control system and do not correspond directly to the basic composition of the system. Therefore, a practical system design is impossible. According to the principle of functional decomposition mapping in AD, the basic structure of the water heater liner top press control system can be determined through the zigzag mapping. Functions can then be transformed from the conceptual to the specific, and an overall system structure can be built. Finally, when all the basic components of the system are worked out, the structure can be optimized by establishing a HoQ for risk prediction.In the example of the decomposition map of the automatic switching model function, FR2, the corresponding basic structure module and risk prediction of the basic structure in question are proposed. The water heater tank capping press has an inner liner press and an inner liner top cover automatic feeding device. The automatic model switching function, FR2, requires that the automatic feeding device of the top cover recognize different workpiece types and automatically feed different types of top covers. According to the equipment’s execution sequence, FR2 can be decomposed into two subfunctions, such as sending the workpiece model, FR21, and receiving the workpiece model, FR22. The corresponding mapping structures are the model identification module of the PLC system, DP21, and the model identification module of the ABB robot control system, DP22. The design equation of the mapping is thus(26)FR21FR22=1011DP21DP22.The subfunctions of the sent workpiece model, FR21, can be decomposed into the model selection carrier, FR211, and the workpiece model selection item, FR212, recognizes the selected workpiece model of the PLC system, FR213, and transmits the workpiece model information, FR214. The working principle involves receiving the input signal of the workpiece model, generating a control signal after the program is run, and then issuing a control command. The corresponding mapping structures are the selection screen, DP211, the workpiece selection list, DP212, the PLC model judgment program, DP213, and PLC workpiece model information output point, DP214. The design equation of the mapping is(27)FR211FR212FR213FR214=1000010000100001DP211DP212DP213DP214.The subfunctions of the received workpiece model, FR22, can be decomposed into the ABB robot input workpiece information, FR221, whereas the ABB robot can judge the workpiece model, FR222, and executes the loading action, FR223. The working principle of model, FR22, is to receive input signals, generate control signals after the program is run, and then issue control commands. The function sequence relations are FR221 > FR222 > FR223. The mapping structure is the ABB robot signal input point, DP221, the ABB robot model program, DP222, and feeding control program, DP223. The design equation of the mapping is then(28)FR221FR222FR223=100010001DP221DP222DP223.The zigzag mapping of the functional structure of FR2 is presented in Figure 9.Figure 9
The zigzag mapping of FR2.To reasonably evaluate the importance of each basic structure of DP2 and clarify the design focus of the system, the risk prediction HoQ can be illustrated according to the decomposed mapping and the zigzag mapping matrix of FR2. Furthermore, the ERPN of DP2 can be obtained, as shown in Figure 10.Figure 10
The risk prediction house of quality of DP2.As shown in Figure10, the modules of DP21, DP223, and DP22 have higher risk sequence numbers. Thus, the designers should focus on analyzing possible failures and incorporate preventive measures during the design process. Similarly, other system functions, such as FR1 and FR3 to FR9 can be decomposed via mapping and solved to obtain all the basic structural modules.


## 4.1. Overview of AD

The core of AD is the domain. According to Suh, the domain is the boundary of four design activities with different types and different modes in the product design phase [54]. The domains in axiomatic theory are the customer domain, the function domain, the structure domain, and the process domain. Between two adjacent design domains, the left domain represents the “what,” that is, the purpose, and the right domain represents the “how,” that is, the method that satisfies the left domain. The hierarchical structure and zigzag mapping are the core methods of the AD design process [55]. As depicted in Figure 8, the hierarchical structure describes the relation of various elements within the domain, and the zigzag mapping represents the mapping of the domains.Figure 8
(a) Hierarchy and (b) zigzag mapping of AD.
(a)(b)Figure8(a) illustrates the hierarchical structure of collection self-decomposition in the domain. A group of subsystems can be composed of elements in the domain according to certain rules. Here, a top-down method is used to decompose the abstract total function into subfunctions, layer by layer, until the final design is produced. The correlations of the functional, structural, and process domains are described according to the zigzag mapping in Figure 8(b). The zigzag mapping is a top-down approach in the form of a Z, and it repeats the mapping of the same and different levels in every domain until the previous domain can no longer be decomposed.To judge the reasonability of the design process, AD theory proposes a design axiom. While mapping the function domain to the structure domain, the designer can judge the appropriateness of the mapping according to the design axioms. The entire mapping can be described as(23)FRm×1=Am×nDPn×1,where {FR}m×1 represents the FRs, {DP}n × 1 represents the DPs, and Am×n represents the design matrix, which can be expressed as(24)Am×n=A11A12…A1nA21A22…A2n⋮⋮…⋮Am1Am2…Amn,where the matrix elements are determined by Aij = (∂FRi)/(∂DPj) (i = 1, 2, …, m; j = 1, 2, …, n).In an actual design, the numbers of FRs and DPs will not be the same. As shown in Table10, given the relation between the numbers of FRs and the number of DPs, the design can be split into an ideal design, a redundant design, and a coupling design.Table 10
Ideal, redundant, and coupling designs.
Design nameConditionDesign matrixIdeal designNumber of FRs = number of DPsDiagonal matrixRedundant designNumber of FRs < number of DPsTriangular matrixCoupling designNumber of FRs > number of DPsNontriangular matrix and nondiagonal matrix


## 4.2. House of Quality for Risk Prediction

Once the basic structure of a control service system is described, high-risk modules in the structure domain can be predicted and analyzed to determine potential failure modes and analyze the possible consequences. These measures can be taken in advance. Because the importance of the elements in the domain cannot be evaluated in AD, this paper introduces a risk prediction HoQ model. This model transmits the decomposition and mapping results of the AD functional and structural domains to the HoQ, builds a risk prediction HoQ, and proposes the ERPN to measure every structural module and clarify the key points of the process.The concept of ERPN is based on risk probability number. Taking into account the importance of the system functions, the system structure can be optimized to determine measures to reduce the chance of potential failure. The formula for the ERPN is(25)ERPN=μj⋅Ik⋅S⋅O⋅D,where μj is the relative weight of the jth system function characteristic in the HoQ, Ik is the weight of the kth subfunction characteristic in the risk prediction HoQ, and S is the severity (see Table 11).Table 11
Severity (S) scoring criteria.
HarmAssessment criteria: severity of the impact on the systemSeverity levelNo warning hazardNo alarm is issued when the equipment is faulty and the control system is completely out of order10Warning hazardAlarm when the equipment is faulty and the control system fails9Very seriousHas a serious impact on the control system and the system is difficult to repair8SeriousHas a serious impact on the control system, but the system can be partially repaired7MediumHas a certain impact on the control system, but the system can be repaired6LowHas a certain impact on the control system, but the system can be repaired completely5Very lowHas less impact on the control system and the system can be repaired more quickly4SlightThe impact on the control system is small, and the system can be repaired quickly3VeryThe impact on the control system is very slight, and the system can be easily repaired2NothingNo impact on the control system, and the system can work normally1Table12 shows the scoring criteria for the frequency O.Table 12
Frequency (O) scoring criteria.
Possibility of failureEvaluation criteria: frequency of occurrenceFrequencyVery highGreater than 1/210About 1/39HighAbout 1/88About 1/207ModerateAbout 1/806About 1/4005About 1/20004LowAbout 1/15,0003About 1/150,0002Very lowLess than 1/150,0001Table13 shows the scoring criteria for the degree of detection D.Table 13
Scoring criteria for the degree of detectionD.
Detectability levelEvaluation criteria: the possibility of detecting the cause of system failures in the prior artLevelInfinitesimalThe prior art cannot detect the cause of the failure of the control system10Very tinyExisting technology has difficulty detecting the cause of the failure of the control system9TinyExisting technology has more difficult detecting the cause of the failure of the control system8Very lowNeed a control system designer to investigate the cause of the fault7LowA technician can discover the cause of the failure6MediumThe control system has alarm tips, but does not display fault information5HigherThe control system has alarm tips and displays fault information4HighThe cause of the fault can be determined by a simple test instrument3Very highThe cause of the failure can be visually identified2Almost certainlyThe cause of the fault can be detected almost certainly1


## 4.3. Structure Domain Solution of the Control Service System

The system’s functional characteristics are only a visual description of the control system and do not correspond directly to the basic composition of the system. Therefore, a practical system design is impossible. According to the principle of functional decomposition mapping in AD, the basic structure of the water heater liner top press control system can be determined through the zigzag mapping. Functions can then be transformed from the conceptual to the specific, and an overall system structure can be built. Finally, when all the basic components of the system are worked out, the structure can be optimized by establishing a HoQ for risk prediction.In the example of the decomposition map of the automatic switching model function, FR2, the corresponding basic structure module and risk prediction of the basic structure in question are proposed. The water heater tank capping press has an inner liner press and an inner liner top cover automatic feeding device. The automatic model switching function, FR2, requires that the automatic feeding device of the top cover recognize different workpiece types and automatically feed different types of top covers. According to the equipment’s execution sequence, FR2 can be decomposed into two subfunctions, such as sending the workpiece model, FR21, and receiving the workpiece model, FR22. The corresponding mapping structures are the model identification module of the PLC system, DP21, and the model identification module of the ABB robot control system, DP22. The design equation of the mapping is thus(26)FR21FR22=1011DP21DP22.The subfunctions of the sent workpiece model, FR21, can be decomposed into the model selection carrier, FR211, and the workpiece model selection item, FR212, recognizes the selected workpiece model of the PLC system, FR213, and transmits the workpiece model information, FR214. The working principle involves receiving the input signal of the workpiece model, generating a control signal after the program is run, and then issuing a control command. The corresponding mapping structures are the selection screen, DP211, the workpiece selection list, DP212, the PLC model judgment program, DP213, and PLC workpiece model information output point, DP214. The design equation of the mapping is(27)FR211FR212FR213FR214=1000010000100001DP211DP212DP213DP214.The subfunctions of the received workpiece model, FR22, can be decomposed into the ABB robot input workpiece information, FR221, whereas the ABB robot can judge the workpiece model, FR222, and executes the loading action, FR223. The working principle of model, FR22, is to receive input signals, generate control signals after the program is run, and then issue control commands. The function sequence relations are FR221 > FR222 > FR223. The mapping structure is the ABB robot signal input point, DP221, the ABB robot model program, DP222, and feeding control program, DP223. The design equation of the mapping is then(28)FR221FR222FR223=100010001DP221DP222DP223.The zigzag mapping of the functional structure of FR2 is presented in Figure 9.Figure 9
The zigzag mapping of FR2.To reasonably evaluate the importance of each basic structure of DP2 and clarify the design focus of the system, the risk prediction HoQ can be illustrated according to the decomposed mapping and the zigzag mapping matrix of FR2. Furthermore, the ERPN of DP2 can be obtained, as shown in Figure 10.Figure 10
The risk prediction house of quality of DP2.As shown in Figure10, the modules of DP21, DP223, and DP22 have higher risk sequence numbers. Thus, the designers should focus on analyzing possible failures and incorporate preventive measures during the design process. Similarly, other system functions, such as FR1 and FR3 to FR9 can be decomposed via mapping and solved to obtain all the basic structural modules.


## 5. Construction of the Control Service System

According to the solution for the functional structure of the control service system, the resulting basic structure can be split into a hardware system, a system program, and a human-computer interaction interface. According to the results of the risk prediction house of quality for each structural module, the structural modules are found to have a higher risk order in the hardware system, system program, or human-computer interaction interface, respectively. During the design stage, designers adopt targeted measures to resolve these potential risks and to reduce their impact on later system debugging. Figure11 shows the hardware structural scheme of the control service system for the water tank liner top cover press system. Figure 12 shows the system’s program structural scheme.Figure 11
Hardware structure of the control service system.Figure 12
Control service system’s program structure scheme.The basic structural schemes related to the human-computer interaction interface are screened to determine those related to the human-machine interaction interface. The basic structural schemes of the human-computer interaction interface should then be combined according to the designer’s knowledge of industrial human-computer interaction interfaces. Figure13 shows the structural design of the human-computer interaction interface of the control service system.Figure 13
The human-machine interface of the control service system.After the hardware system’s structure scheme, the system’s program structure scheme, and the control service system’s human-computer interaction interface structure scheme are combined, the structural modules with higher risk order numbers in every scheme must be determined (see Table14). An analysis of these modules can determine potential failure modes and the possible consequences, and, on that basis, provide corresponding preventive measures. Potential risks can thus be resolved during the design stage.Table 14
Analysis of the potential failure risk of the control service system.
SystemModuleStructureRisk orderFault descriptionMeasuresHardwareSolenoid valveDP5597.69Solenoid valve does not work when energizedSelect an excellent solenoid valve, with timely detection and replacementSignal input deviceDP1493.13Unstable signal detectionChoose appropriate signal detection components and avoid vibrationDP5181.41Servo motorDP55167.84Servo drive alarmThe installation and cable routing of the servo drive adhere to strict anti-interference measures; the servo drive is separately equipped with a 24 V DC power supply to ensure the stability of the current in the servo systemDP55267.84DP55367.84DP55467.84DP1366.23Signal input elementDP5261.06An abnormal or unstable input signalSelect a distributed PLC, paying attention to whether the power supply voltage of the I/O terminal is normalDP12154.33Signal output elementDP5456.98An abnormal or unstable output signalSelect a ground wire of sufficient diameter and add an equipotential shielding plateDP12337.25ProgramAutomatic programDP532432.56Production cycle lengthBecome familiar with the process flow and plan the system action flow.Manual programDP532330.53Misoperation or wrong actionSet delayed action and add error-proof designAlarm programDP4126.87Alarm is not timelyCreate different alarm outputs for the different fault typesReclaiming programDP6224.80Poor movementRefine the action; the span between each action command is easily insufficiently large, so set the appropriate speed and turning radiusUnloading programDP5324.80Incorrect feeding positionSet a low speed when discharging, produce a linear motion, and prevent shakingHMIAction commandDP93113.06Incorrect operationSet button delay action and error proof the designOperation feedbackDP939.79Operation result unknownAdd operation process indicator and position indicatorNavigation barDP928.17Cannot quickly switch between interfacesSet a reasonable interface display areaElement layoutDP9426.53Cannot quickly find the operation buttonReasonably arrange the buttons and add notes


## 6. Conclusion

According to the structure scheme of the control system of the water heater tank capping press, the detailed design of each structural module is carried out. In TIAPortal, the CPU1511 of S7-1500, HMI panel, and 4 servo drives form a configuration network, and Profinet industrial Ethernet is used to communicate among each part, as shown in Figure14.Figure 14
The equipment configuration network diagram of the control system of the water heater tank capping press.Then, according to the program structure scheme, the PLC program of the control system of the water heater tank capping press is divided into automatic program module, initialization program module, manual program module, return to the origin program module, alarm program module, and servo motor program module. Part of the manual program module is shown in Figure15. The touch screen interface design of the control system mainly includes parameter interface, monitoring screen, selection screen, alarm screen, automatic screen, manual screen, and I/O port screen. The manual screen is shown in Figure 16. The main body of the water heater tank capping press is shown in Figure 17.Figure 15
Part of the manual program of the water heater tank top press system.Figure 16
Manual operation interface of water heater tank top press system. (a) Operation feedback indication. (b) In-place instructions. (c) Operation button. (d) Servo motor monitoring. (e) Servo motor power up. (f) Servo motor inching control. (g) Step operation. (h) Navigation bar.Figure 17
The water heater tank capping press.
(a)(b)After the design of the control system is completed, the water heater tank capping press is produced and operated in the actual working environment. The water heater tank capping press works stably and satisfies the production demands well. It is verified that the upper design method can effectively guide the design process of the control system.The design method preferred in this paper is based on the analysis of customer demands to ensure the accurate input of the demand domain and to complete the mapping between the demand domain and the function domain and between the function domain and the structure domain. This approach makes up for the lack of a single design method, to a certain extent. It also has the advantages of accuracy, clarity, and being a complete system. It can guide the designers to make better design decisions and evaluations during the design process more quickly and improve the design efficiency and quality of the control project. This method improves the cluster analysis of customer demands and proposes a weighted network AP clustering algorithm to determine the characteristics of customers’ demands, compensating for the lack of regularization of customers’ requirements in traditional QFD and AD designs. On the contrary, the method takes full advantage of QFD and AD design methods, combining the empirical design and AD, not only benefiting from the designer’s experience but also avoiding subjective influence. Finally, the effectiveness and feasibility of the proposed method are demonstrated by using the example of the design and production of the control service system for a water heater liner top cover press.



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*Source: 8897539-2021-03-20.xml*