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New Approach for Quality Function Deployment Using Linguistic Z-Numbers and EDAS Method

Abstract

Quality function deployment (QFD) is an effective product development and management tool, which has been broadly applied in various industries to develop and improve products or services. Nonetheless, when used in real situations, the traditional QFD method shows some important weaknesses, especially in describing experts’ opinions, weighting customer requirements, and ranking engineering characteristics. In this study, a new QFD approach integrating linguistic Z-numbers and evaluation based on distance from average solution (EDAS) method is proposed to determine the prioritization of engineering characteristics. Specially, linguistic Z-numbers are adopted to deal with the vague evaluation information provided by experts on the relationships among customer requirements and engineering characteristics. Then, the EDAS method is extended to estimate the final priority ratings of engineering characteristics. Additionally, stepwise weight assessment ratio analysis (SWARA) method is employed to derive the relative weights of customer requirements. Finally, a practical case of Panda shared car design is introduced and a comparison is conducted to verify the feasibility and effectiveness of the proposed QFD approach. The results show that the proposed linguistic Z-EDAS method can not only represent experts’ interrelation evaluation information flexibly, but also produce a more reasonable and reliable prioritization of engineering characteristics in QFD.

1Introduction

Quality function deployment (QFD) was first introduced by Akao (1972) for designing new products systematically, which can translate customer requirements (CRs) into engineering characteristics (ECs) for maximum customer satisfaction (Bevilacqua et al.2006). Nowadays, the QFD has become a powerful tool for designing and developing products or services (Huang et al.2019). It can not only improve customer satisfaction, but also reduce cycle-time of product development, cut down production cost and enhance the performance of manufacturing process. Due to its effectiveness and benefits, the QFD method has been applied for product design and quality improvement in various areas, such as construction (Fargnoli et al.2020; Lapinskienė and Motuzienė, 2021), manufacturing (Neramballi et al.2020; Shi and Peng, 2020) and service (Lee et al.2020; Park et al.2021) industries.

When implementing QFD, house of quality (HOQ) occupies a central position, which assists designers in translating CRs into ECs through explicit assessment matrix of users and products. In this way, the QFD method serves as a valuable tool for managers or designers to develop products. However, when used in real situations, the traditional QFD method has some inherent deficiencies (Huang et al.2019; Jia et al.2016; Ping et al.2020; Wu et al.2020). On the one hand, crisp values are utilized to deal with the relationships between CRs and ECs in the traditional QFD. However, in the real world, it is often hard for experts to give accurate numerical values on the relationships between CRs and ECs due to the uncertainty and fuzziness of human perception (Aliev and Huseynov, 2014; Lorkowski et al.2014). Instead, they prefer to use linguistic terms to express their opinions (Liu et al.2019; Tian et al.2019; Liu et al.2021). Based on linguistic term sets (Zadeh, 1975) and Z-numbers (Zadeh, 2011), the concept of linguistic Z-numbers was introduced by Wang et al. (2017) to express both vagueness and randomness of uncertain linguistic information. For a linguistic Z-number, the two components (i.e. restriction and reliability measure) are represented with linguistic terms. Compared to other linguistic computing methods, the linguistic Z-numbers can not only describe decision-making information more flexibly, but also avoid the distortion and loss of original information effectively (Peng and Wang, 2017; Wang et al.2017). Hence, it is promising to employ the linguistic Z-numbers to represent experts’ uncertain and vague evaluation information on the relationships between CRs and ECs in QFD.

On the other hand, the ranking of ECs in QFD can be considered as a multiple criteria decision making (MCDM) problem because it involves multiple and conflicting CRs (Ping et al.2020). Accordingly, many MCDM methods have been adopted to improve the performance of QFD in previous researches (Mistarihi et al.2020; Ocampo et al.2020; Yazdani et al.2016). As an effective MCDM method, the evaluation based on distance from average solution (EDAS) was put forward by Ghorabaee et al. (2015) to address MCDM problems. The EDAS includes two measures, i.e. positive distance from average (PDA) and negative distance from average (NDA), for dealing with the desirability of alternatives (Keshavarz-Ghorabaee et al.2018; Keshavarz Ghorabaee et al.2017). It has simple logic and is especially useful for decision making problems with conflicting criteria (Darko and Liang, 2020). Since its introduction, the EDAS method has been broadly adopted to solve MCDM problems in many areas, which include supplier selection (Ghorabaee et al.2016), manufacturer selection (Stević et al.2018), health-care waste disposal technology selection (Ju et al.2020), typhoon disaster assessment (Tan and Zhang, 2021), car selection (Yanmaz et al.2020) and logistics centre location (Özmen and Aydoğan, 2020). Therefore, it is of vital importance to adopt the EDAS method to determine the ranking of ECs in QFD analysis.

Based on the aforementioned discussions, an approach combining linguistic Z-numbers with EDAS method is presented in the study to improve the effectiveness of QFD. Specifically, the linguistic Z-numbers are used to cope with the vague and uncertain assessments provided by experts on the relationships among CRs and ECs, and the EDAS method is utilized to acquire the priority orders of ECs in the process of product development. Moreover, the weights of CRs are obtained by the use of stepwise weight assessment ratio analysis (SWARA) method. Finally, a practical case of product design for Panda shared cars is introduced to testify the effectiveness and efficiency of the proposed QFD approach.

The remainder of the article is organized as follows: Section 2 briefly reviews research progress of the QFD method. The preliminaries of linguistic Z-numbers are presented in Section 3. Then the new integrated QFD approach combining linguistic Z-numbers and EDAS method is developed in Section 4. In Section 5, a practical example is given to demonstrate the proposed QFD framework. Lastly, conclusions of this study and outlines for future research are discussed in Section 6.

2Literature Review

In the past decade, an increasing number of improved QFD methods have been developed to eliminate the deficiencies and enhance the performance of the traditional QFD. For instance, Li et al. (2014) introduced analytical network process (ANP) into QFD for deciding the importance of CRs and evaluating corresponding characteristics of software quality. Jia et al. (2016) proposed an integrated QFD method combining fuzzy evidence reasoning theory with fuzzy discrete Choquet integral to determine the importance value of design characteristics. Integrating QFD and decision-making trial and evaluation laboratory (DEMATEL) technique, Ramezankhani et al. (2018) designed a hybrid model and applied it to supply chain performance measurement. Liu et al. (2019) proposed a QFD approach by using partitioned Bonferroni mean operator and interval type-2 fuzzy sets to select a better solution from various green suppliers. Vats and Vaish (2019) employed QFD in combination with vlseKriterijumska optimisacija I kompromisno resenje (VIKOR) approach to select smart materials for thermal energy efficient architecture. Based on cloud model and grey relational analysis, Wang et al. (2020) put forward an integrated QFD model to control the quality of the rotor used in air compressor. Via integrating interval type-2 fuzzy sets and DEMATEL, Yazdani et al. (2020) designed a QFD approach to evaluate and rank sustainable supply chain drivers.

Recently, it has become a trend to integrate the advantages of different MCDM approaches for the improvement of traditional QFD. For example, by using DEMATEL and VIKOR, Wu et al. (2016) developed a QFD model for the product development of electric vehicle. Combining fuzzy BWM, fuzzy maximizing deviation method and fuzzy multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA), Tian et al. (2018) established a hybrid QFD model to assess the performance of a smart bike-sharing program. Huang et al. (2019) constructed a QFD technique to design manufacture system, in which the relationships between CRs and ECs were expressed by hesitant fuzzy linguistic term sets, the weights of CRs were derived by the best-worst method (BWM) and the ranking order of ECs were determined by the prospect theory. Lu et al. (2019) presented a QFD model by combining fuzzy analytic hierarchy process (AHP) with fuzzy ANP for the design of brand revitalization. A QFD model integrating TOPSIS and EDAS method was proposed by Ping et al. (2020) for a product-service system design.

As reviewed previously, many studies handled the uncertainty and vagueness of experts’ assessments in QFD using fuzzy sets, interval type-2 fuzzy sets and hesitant fuzzy linguistic term sets. However, the reliability of experts’ assessment information cannot be reflected in the processes of QFD. Besides, although different types of MCDM methods have been proposed to obtain the EC prioritization in QFD, they are extremely complex or not considering the conflict of CRs. To overcome these issues, in this paper, we develop a novel QFD approach integrating linguistic Z-numbers and an extended EDAS method to determine the priorities of ECs. Our proposed QFD model can not only represent experts’ evaluation information flexibly, but also provide engineers more practical and reliable solutions for identifying critical ECs to improve product or service.

3Preliminaries

In this section, some basic concepts of linguistic term sets and linguistic Z-numbers are introduced to aid in understanding the proposed QFD model.

Definition 1

Definition 1(Duan et al. 2019).

Let S={s0,s1,,s2t} be a finite and ordered linguistic term set with odd cardinality, where si is the possible value for a linguistic variable and t is a nonnegative integer. In this linguistic term set S, si and sj are required to satisfy the following characteristics:

  • (1) The set is ordered: si>sj, if and only if i>j;

  • (2) Negation operator: neg(si)=sj, if i+j=2t.

Definition 2

Definition 2(Peng and Wang 2017).

Let S={s0,s1,,s2t} be a linguistic term set. If θi[0,1] is a numerical value, then the linguistic scale function is a mapping from si to θi (i=0,1,,2t), and it is defined as:

(1)
F:siθi(i=0,1,,2t),
in which 0θ0θ1θ2t1.

A linguistic scale function is a monotonic increasing function. The following functions are two commonly used in the literature (Liu and Liu, 2017; Wang et al.2016).

(2)
F1(θi)=θi=i2t,(0i2t),
(3)
F2(θi)=θi=atati2at2,(0it),at+ait22at2,(t+1i2t),
where the variable a is a special value obtained from experiments or subjective methods.

Definition 3

Definition 3(Wang et al. 2017).

Let X be a universe of discourse, S1={s0,s1,,s2l}, S2={s0,s1,,s2k} are two finite and totally ordered uncontinuous linguistic term sets, with nonnegative integers l and k. Furthermore, let Aϕ(x)S1 and Bφ(x)S2. A linguistic Z-number set Z in X can be denoted in the following form:

(4)
Z={(x,Aϕ(x),Bφ(x))|xX},
where Aϕ(x) is a fuzzy restriction on the values that uncertain variable x is allowed to take, and Bφ(x) is a measure of reliability of Aϕ(x).

When X has only one element, the linguistic Z-number set Z is reduced to (Aϕ(α),Bφ(α)). For convenience, zα=(Aϕ(α),Bφ(α)) is called a linguistic Z-number.

Definition 4

Definition 4(Wang et al. 2017).

Let zi=(Aϕ(i),Bφ(i)) and zj=(Aϕ(j),Bφ(j)) be two linguistic Z-numbers; let f and g be the different linguistic scale functions and their inverse functions are f1 and g1. Then, the basic operational rules of linguistic Z-numbers are defined as follows:

  • (1) zizj=(f1(f(Aϕ(i))+f(Aϕ(j))),g1(f(Aϕ(i))×g(Bφ(i))+f(Aϕ(j))×g(Bφ(i))f(Aϕ(i))+f(Aϕ(j))));

  • (2) λzi=(f1(λf(Aϕ(i))),Bφ(i)), where λ0;

  • (3) zizj=(f1(f(Aϕ(i))f(Aϕ(j))),g1(g(Bφ(i))g(Bφ(j))));

  • (4) ziλ=(f1(f(Aϕ(i))f(Aϕ(j))),g1(g(Bφ(i))λ)), where λ0.

Definition 5

Definition 5(Wang et al.2017).

Let zi=(Aϕ(i),Bφ(i)) be linguistic Z-numbers. Then, the score function S(zi) of zi is defined as:

(5)
S(zi)=f(Aϕ(i))×g(Bφ(i)),
and the accuracy function A(zi) of zi is defined as:
(6)
A(zi)=f(Aϕ(i))×(1g(Bφ(i))).

Definition 6

Definition 6(Wang et al.2017).

Let zi=(Aϕ(i),Bφ(i)) and zj=(Aϕ(j),Bφ(j)) be two linguistic Z-numbers. Then the comparison rules of the two linguistic Z-numbers are listed below:

  • (1) If Aϕ(i)>Aϕ(j) and Bφ(i)>Bφ(j), then zi is strictly greater than zj, denoted by zi>zj;

  • (2) If S(zi)S(zj) and A(zi)>A(zj), then zi is greater than zj, denoted by zizj;

  • (3) If S(zi)=S(zj) and A(zi)=A(zj), then zi equals zj, denoted by zizj;

  • (4) If S(zi)=S(zj) and A(zi)<A(zj) or S(zi)<S(zj), then zi is less than zj, denoted by zizj.

Definition 7

Definition 7(Wang et al.2017).

For any two linguistic Z-numbers zi=(Aϕ(i),Bφ(i)) and zj=(Aϕ(j),Bφ(j)). The distance between zi and zj is calculated by:

(7)
d(zi,zj)=12(|f(Aϕ(i))×g(Bφ(i))f(Aϕ(j))×g(Bφ(j))|+max{|f(Aϕ(i))f(Aϕ(j))|,|g(Bφ(i))g(Bφ(j))|}).

Definition 8

Definition 8(Duan et al.2019).

Let zi=(Aϕ(i),Bφ(i)), (i=1,2,,n) be a collection of linguistic Z-numbers. Then the linguistic Z-numbers weighted average (LZWA) operator is defined as:

(8)
LZWA(zi)=i=1nwizi=(f1(i=1nwif(Aϕ(i))),g1(i=1nwif(Aϕ(i))g(Bφ(i))i=1nwif(Aϕ(i)))),
where w=(w1,w2,,wn)T is the weight vector of zi (i=1,2,,n), satisfying wi0 and i=1nwi=1.

4The Proposed QFD Approach

In this section, a new comprehensive QFD model combining linguistic Z-numbers and EDAS method is devised to acquire the ranking of ECs. Specially, linguistic Z-numbers are utilized to evaluate the relationships between CRs and ECs, the relative weights of CRs are computed by the SWARA method, and an extended EDAS method is employed to estimate the final priority ratings of ECs. Flowchart for the developed QFD model consisting of three phases is depicted in Fig. 1.

Fig. 1

Framework of the proposed QFD model.

Framework of the proposed QFD model.

For a QFD analysis problem, suppose that there are m engineering characteristics ECi (i=1,2,,m) and n customer requirements CRj (j=1,2,,n). Meanwhile, l experts Ek (k=1,2,,l) are invited to provide their assessments for the relationships between CRs and ECs, and each expert is assigned a weight λk satisfying λk>0 and k=1lλk=1 to describe his/her relative importance in the QFD analysis. Let Zk=[zijk]m×n be the linguistic assessment matrix of Ek, where zijk=(Aϕ(ijk),Bφ(ijk)) is the linguistic Z-number evaluation ECi with respect to CRj provided by Ek. Based on the above assumptions, the proposed QFD model is described as follows:

Stage 1. Evaluate the relationships between ECs and CRs using linguistic Z-numbers.

Step 1: Establish the collective linguistic evaluation matrix Z.

By using the LZWA operator, the individual linguistic evaluation matrices Zk (k=1,2,,l) can be aggregated to obtain the collective linguistic evaluation matrix Z=(zij)m×n, in which

(9)
zij=LZWA(zij1,zij2,,zijl)=(f1(k=1lλkf(Aϕ(ijk))),g1(k=1lλkf(Aϕ(ijk))g(Bφ(ijk))k=1lλkf(Aϕ(ijk)))).

Stage 2. Acquire the weights of CRs by the SWARA method.

The SWARA method proposed by Keršuliene et al. (2010) is a powerful weighting method in solving MCDM problems. The superiority of the SWARA is that it is uncomplicated, straightforward and involves less comparisons compared with other weighing methods (Hashemkhani Zolfani et al.2013; Karabasevic et al.2016; Ruzgys et al.2014; Stanujkic et al.2017). Given its strength, it has been used to find the relative weights of evaluation criteria in many researches (Duan et al.2019; Liu et al.2020; Naeini et al.2020). Therefore, the SWARA method is introduced to acquire the weights of CRs in this study. The detailed steps are listed as follows:

Step 2: Sort CRs in a descending order.

The n customer requirements CRj (j=1,2,,n) are sorted in a descending order according to their expected importance. Then, newly ranked CRs are denoted as CRj (j=1,2,,n).

Step 3: Determine the comparative importance of CRs.

Starting from the second CR, experts are invited to assess the relative importance of CRj to CRj1 (j=2,3,,n). Then the comparative importance of CRs ρj is obtained.

Step 4: Calculate the CR coefficient kj by

(10)
kj=1,j=1,ρj+1,j>1.

Step 5: Compute the recalculated CR weights qj by

(11)
qj=1,j=1,qj1kj,j>1.

Step 6: Determine the final weight of each CR wj by

(12)
wj=qjk=1nqj.

Finally, the weight vector of the n customer requirement CRj (j=1,2,,n), i.e. w=(w1,w2,,wn), can be derived by rearranging the weights wj (j=1,2,,n).

Stage 3. Rank the ECs through EDAS method.

In this part, we extend the EDAS method with linguistic Z-numbers, and adopt the linguistic Z-EDAS to obtain the ranking of ECs. The detail steps for ranking ECs are as follows.

Step 7: Determine the linguistic average EC.

The linguistic average engineering characteristics EC is defined as zA=(zA1,zA2,,zAn), which can be derived by

(13)
zAj=1mi=1mzij.

Step 8: Compute the matrices of PDA and NDA.

The PDA matrix D+=[dij+]m×n and the NDA matrix D=[dij]m×n are, respectively, computed by

(14)
dij+=max{0,(s(zij)s(zAj))}s(zAj),ifzij>zAj,0,ifzijzAj,
(15)
dij=max{0,(s(zij)s(zAj))}s(zAj),ifzij<zAj,0,ifzijzAj.

Step 9: Calculate the weighted sum of PDA and NDA for each EC.

Considering the weight of each customer requirement w, the weighted sums of PDA and NDA for each EC are calculated by

(16)
SPi=j=1nwjdij+,i=1,2,,m,
(17)
SNi=j=1nwjdij,i=1,2,,m.

Step 10: Normalize the weighted sums of PDA and NDA for each EC.

The normalized values of SPi and SNi for each EC can be derived by

(18)
SPi=SPimaxiSPi,i=1,2,,m,
(19)
SNi=1SNimaxiSNi,i=1,2,,m.

Step 11. Compute the important score for all ECs.

The importance scores for the m ECs can be computed by

(20)
ISi=12(SPi+SNi),i=1,2,,m.

In the process of QFD analysis, the larger the important score ISi, the higher the importance of the engineering characteristics ECi is. Therefore, the priority of all the ECs can be obtained according to the descending order of the values of ISi (i=1,2,,m).

5Case Study

In this section, the designing process of Panda shared cars (Wu and Liao, 2018) is provided to illustrate the feasibility and applicability of our proposed QFD approach.

5.1Implementation and Results

In the past several years, “shared economy” has profoundly influenced people’s daily life, and has been strongly advocated at the national level. Recently, as a most representative form of “shared economy”, “shared cars” began to appear in Chinese market to improve the efficiency of transport and solve the problem of scarcity of transportation resources. The “Panda” is a travel platform of shared new energy cars, which focuses on the form of “internetwork + vehicle networking + energy economy + auto service”. Due to its unique mode of electric vehicles and excellent smart travel experience, “Panda” has become the fastest time sharing leasing business and the largest shared project of new energy vehicles in a single city in China. Nowadays, more and more shared car brands are appearing in the market, therefore the expansion of the market and success in the competition of the “shared cars” market is a big challenge. Thus, it is urgent for “Panda” to design new products that satisfy people’s travel needs at low prices.

Through interviews and surveys of users and specialists, five CRs (CRj, j=1,2,,5) and six ECs (ECi, i=1,2,,6) are identified for the product design of “Panda”, as shown in Table 1. For the QFD problem, five experts (Ek, k=1,2,,5) are organized to express their evaluations on the interrelations between the ECs and CRs. The weights of experts are assumed the same in this study. The evaluations are conducted by using the following linguistic term sets:

S=s0=None,s1=Extremely weak,s2=Weak,s3=Medium,s4=Strong,s5=Extremely strong,s6=Perfect,S=s0=Uncertain,s1=Slightly uncertain,s2=Medium,s3=Slightly sure,s4=Sure.

As a result, the evaluation results of the five experts toward the relationships between ECs and CRs are obtained, and shown in Table 2.

Table 1

CRs and ECs identified in the case.

CRsCustomer requirementsECsEngineering characteristics
CR1PriceEC1Cost
CR2ComfortabilityEC2Car body material
CR3SafetyEC3Seat material
CR4ConvenienceEC4Car internal decoration
CR5SpaceEC5On-board system
EC6Air-conditioning system

In what follows, the steps of the proposed QFD model were implemented to determine the ranking orders of ECs for the given case study.

Step 1: By using Eq. (9), the individual evaluation matrices Zk (k=1,2,,5) are aggregated to obtain the collective linguistic evaluation matrix Z=(zij)6×5, as shown below

Z=(s5.40,s4.00)(s1.00,s1.00)(s5.40,s3.22)(s2.00,s3.00)(s0.20,s2.00)(s2.00,s4.00)(s0.00,s1.00)(s5.20,s3.19)(s0.00,s3.20)(s0.60,s2.00)(s3.00,s3.80)(s3.00,s3.80)(s1.00,s2.00)(s0.00,s3.20)(s0.20,s1.00)(s0.00,s3.00)(s3.00,s2.20)(s0.00,s3.80)(s0.00,s3.20)(s0.00,s3.20)(s2.00,s3.00)(s0.00,s3.20)(s0.00,s3.80)(s0.80,s3.25)(s0.20,s1.00)(s3.00,s3.80)(s4.00,s0.80)(s0.80,s3.00)(s0.00,s3.20)(s0.00,s1.60).

Table 2

Evaluation results provided by the five experts.

ExpertsCRsEC1EC2EC3EC4EC5EC6
E1CR1(s5,s4)(s2,s4)(s3,s3)(s0,s3)(s2,s3)(s3,s4)
CR2(s1,s1)(s0,s1)(s4,s1)(s3,s2)(s4,s2)(s4,s1)
CR3(s5,s3)(s5,s3)(s1,s2)(s0,s3)(s0,s3)(s0,s3)
CR4(s2,s3)(s0,s3)(s0,s3)(s0,s3)(s0,s3)(s0,s3)
CR5(s0,s1)(s0,s1)(s0,s1)(s3,s1)(s0,s1)(s0,s1)
E2CR1(s6,s4)(s2,s4)(s3,s4)(s0,s3)(s2,s3)(s3,s4)
CR2(s1,s1)(s0,s1)(s4,s1)(s3,s2)(s4,s2)(s4,s1)
CR3(s5,s3)(s5,s3)(s1,s2)(s0,s4)(s0,s4)(s1,s3)
CR4(s2,s3)(s0,s3)(s0,s3)(s0,s3)(s1,s3)(s0,s3)
CR5(s0,s2)(s1,s2)(s0,s1)(s3,s1)(s0,s1)(s0,s2)
E3CR1(s5,s4)(s2,s4)(s3,s4)(s0,s3)(s2,s3)(s3,s4)
CR2(s1,s1)(s0,s1)(s4,s1)(s3,s2)(s4,s2)(s4,s1)
CR3(s5,s3)(s5,s3)(s1,s2)(s0,s4)(s0,s4)(s1,s3)
CR4(s2,s3)(s0,s3)(s0,s3)(s0,s3)(s1,s3)(s0,s3)
CR5(s0,s0)(s0,s0)(s0,s1)(s3,s2)(s0,s2)(s0,s1)
E4CR1(s5,s4)(s2,s4)(s3,s4)(s0,s3)(s2,s3)(s3,s3)
CR2(s1,s1)(s0,s1)(s4,s0)(s3,s3)(s4,s2)(s4,s1)
CR3(s6,s3)(s6,s3)(s1,s2)(s0,s4)(s0,s4)(s1,s3)
CR4(s2,s3)(s0,s3)(s0,s3)(s0,s3)(s1,s3)(s0,s3)
CR5(s0,s2)(s1,s2)(s0,s3)(s3,s3)(s0,s1)(s0,s2)
E5CR1(s6,s4)(s2,s4)(s3,s4)(s0,s3)(s2,s3)(s3,s4)
CR2(s1,s1)(s0,s1)(s4,s1)(s3,s2)(s4,s2)(s4,s0)
CR3(s6,s4)(s5,s4)(s1,s2)(s0,s4)(s0,s4)(s1,s3)
CR4(s2,s3)(s0,s4)(s0,s4)(s0,s4)(s1,s4)(s0,s4)
CR5(s1,s2)(s1,s2)(s1,s1)(s3,s1)(s1,s0)(s0,s2)

Step 2: According to the opinions of experts, the five customer requirements are sorted in a descending order. As a result, we can determine the newly ranked customer requirements as: CR1=CR1, CR2=CR3, CR3=CR4, CR4=CR2, CR5=CR5.

Step 3: Starting from the second customer requirement, experts are invited to assess the relative importance of the customer requirement CRj with respect to the previous customer requirement CRj1. Then the comparative importance ρj of CRs is derived as shown in Table 3.

Steps 4–6: Via Eqs. (10)–(12), the CR coefficient kj (j=1,2,,5), the recalculated CR weights qj (j=1,2,,5) and the final weights of CRs wj (j=1,2,,5) are calculated, respectively. The results are listed in Table 3.

Table 3

Computation results of the SWARA method.

CRsρjkjqjwj
CR11.001.000.47
CR20.901.900.530.25
CR30.801.800.290.14
CR40.501.500.190.09
CR50.901.900.100.05

Finally, the weight vector of the five CRs CRj (j=1,2,,5) is determined as:

w=(0.47,0.09,0.25,0.14,0.05).

Step 7: Through Eq. (13), the linguistic average EC (ECA) is computed as:

ZA={(s2.57,s3.79),(s2.67,s1.23),(s2.07,s3.10),(s0.47,s3.07),(s0.70,s1.57)}.

Step 8: Utilizing Eqs. (14) and (15) the PDA matrix D+=[dij+]6×5 and the NDA matrix D=[dij]6×5 are required as:

D+=1.220.001.723.190.000.000.001.590.000.090.170.000.000.000.000.001.020.000.003.360.000.710.000.810.000.170.000.000.000.00,D=0.002.270.000.000.701.733.270.001.430.000.000.074.401.430.909.730.006.401.430.003.730.006.400.000.900.000.074.001.431.10.

Step 9: Based on Eqs. (16) and (17) the weighted sum of PDA and NDA for each EC SPi (i=1,2,,6) and SNi (i=1,2,,6) are derived as presented in Table 4.

Step 10: The normalized values of SPi (i=1,2,,6) and SNi (i=1,2,,6) for each EC are calculated by Eqs. (18) and (19) The results are displayed in Table 4.

Step 11: Applying Eq. (20) the importance scores for the ECs ISi (i=1,2,,6) are obtained as shown in Table 4.

Table 4

The calculate results using the linguistic Z-EDAS method.

ECsSPiSNiSPiSNiISi
EC11.450.571.000.690.85
EC20.401.040.280.430.36
EC30.080.700.060.620.34
EC40.261.840.180.000.09
EC50.181.230.120.330.23
EC60.080.650.060.650.35

According to the descending order of the important scores, the ranking of the considered six ECs is determined as: EC1EC2EC6EC3EC5EC4. Therefore, the design engineer should pay more attention to EC1, which is the most important EC for reducing costs and improving customer satisfaction.

5.2Sensitivity Analysis

In this section, to explore the influence of CRs weights on the obtained results, a sensitivity analysis is conducted by assigning different weight values to CRs. Four cases, as listed in Table 5, are considered in the sensitivity analysis. Case 0 describes the original weights of CRs derived by the SWARA method, and other three cases are different sets of CRs weights in a possible range of value. By using the proposed QFD method, the ranking results for the six ECs in four cases are obtained, as presented in Table 5.

As can be seen from Table 5, the ranking results of the ECs vary with the change of CRs weights. Except for EC1, the remaining ECs have inconsistent ranking orders in the four cases. In case 0, EC2 is ranked the second when the weight of CR1 is the highest and the weight of CR5 is the lowest. In Case 2, EC4 is at the second position when the weight of CR1 is the lowest whereas the weight of CR5 is the highest. In contrast, EC6 is the second important engineering characteristic in Case 3. The sensitivity analysis shows that the weights of CRs have a great impact on the final priorities of ECs. Therefore, it is of vital importance to determine suitable CR weights for the ranking of ECs in the practical situations.

Table 5

Sensitivity analysis with different weight values to CRs.

ECsCase 0Case 1Case 2Case 3
wj=(0.47,0.09,0.25,0.14,0.05)wj=(0.2,0.2,0.2,0.2,0.2)wj=(0.1,0.35,0.1,0.1,0.35)wj=(0.35,0.35,0.1,0.1,0.1)
EC11111
EC22243
EC34554
EC46326
EC55665
EC63432

5.3Comparative Analysis

To verify the effectiveness of our developed QFD model, a comparative analysis is performed with the probabilistic linguistic ORESTE (PL-ORESTE) method (Wu and Liao, 2018), the hesitant fuzzy VIKOR (HF-VIKOR) method (Wu et al.2016) and the classical EDAS method (Ghorabaee et al.2015). The ranking results of the six ECs derived by the considered methods are exhibited in Fig. 2. It can be observed from Fig. 2 that the most vital EC for the considered problem remains the same (i.e. EC1) for the proposed method and the other three methods. Thus, the proposed QFD model is validated.

Fig. 2

The EC ranking results of comparative analysis.

The EC ranking results of comparative analysis.

There are some differences between the ranking results derived by the proposed method and the PL-ORESTE method. Apart from EC1 and EC4, the ranking orders for the other ECs obtained by the proposed method are different from those by the PL-ORESTE method. The big difference happens in EC6, which ranks the third, in the proposed model. Nevertheless, based on the PL-ORESTE, EC6 ranks in the fifth position. This difference can be attributed to the fact that the PL-ORESTE does not consider the reliability of the evaluation information provided by experts, which results in the distortion of initial information. Moreover, EC5 is the second critical EC with the PL-ORESTE method, while by using the proposed QFD, it ranks in the fifth position. Giving the fifth position to EC5 can also be validated by the HF-VIKOR and the classical EDAS methods.

The ranking orders of EC3 and EC6 determined by the HF-VIKOR are different from those yielded by the proposed method. More specifically, EC6 is ranked behind EC3 according to the HF-VIKOR method. However, in the reality, the former is more important, because it has a higher comfortability. Thus, the result of the proposed model is more reasonable, which suggests that EC6 has a higher priority in comparison with EC3.

In comparison to the classical EDAS method, the proposed method gives different ranking orders for EC2, EC3, EC4 and EC6. These differences can be explained by the different evaluation and prioritization mechanisms of the two methods. First, crisp values are utilized by experts to evaluate the relationships between ECs and CRs. It is not efficient to express the uncertain and fuzzy evaluation information provided by experts. Second, the classical EDAS method determines the ranking orders of ECs based on the EDAS algorithm, while the proposed model obtains the prioritization of ECs based on the linguistic Z-EDAS method.

5.4Managerial Implications

Considering the findings related to this study, the proposed QFD model has some practical implications for engineers to design new products for reducing costs and improving customer satisfaction. First, the proposed model is performed in the uncertain linguistic environment where experts can flexibly and conveniently evaluate ECs by using linguistic rating. In this way, the proposed model can offer a convenient and flexible technique to obtain more comprehensive and reliable evaluation information about ECs in real-world application. Second, the SWARA method, a powerful weighting method, is adopted to derive the weights of CRs in the proposed QFD. Via this method, the proposed model is able to obtain a more reasonable weights of CRs easily, since expert’s opinions about the importance ratios of CRs are taken into account. Finally, an extended EDAS method is employed to determine the ranking orders of ECs in QFD. Hence, the proposed approach can derive a more credible and reasonable ranking of ECs with a straightforward computational procedure, and help product engineers get a final solution efficiently.

6Conclusions

In this paper, we presented a novel systematic QFD method based on linguistic Z-numbers and EDAS method to improve the performance of QFD. First, linguistic Z-numbers were used by experts to assess the relationships between ECs and CRs. Second, an extended EDAS method was proposed to determine the prioritization of ECs. Besides, the SWARA method was adopted to derive the weights of CRs. Finally, the effectiveness and reliability of the proposed method were testified by a shared cars’ product design case. The results indicate that the proposed QFD model can not only represent experts’ interrelation evaluation information flexibly, but also produce a more reasonable and reliable prioritization of ECs in QFD.

Future studies will focus on the following aspects. First, the relationships among ECs are not considered in the proposed QFD model. Thus, in future research, effort can be devoted to incorporate the correlations among ECs into the proposed QFD. Second, in practice, there are some situations in which the weight information of CRs is completely unknown. Hence, the extension of the proposed model can be developed to solve the QFD problems with unknown CR weights. Lastly, an intelligent information system can be constructed to help product managers and designers to reduce the task of QFD analysis in real-life applications.

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