An integrated fuzzy QFD and grey decision-making approach for supply chain collaborative quality design of large complex products

Journal Pre-proofs An Integrated Fuzzy QFD and Grey Decision-making Approach for Supply Chain Collaborative Quality Design of Large Complex Products Huan Wang, Zhigeng Fang, Daao Wang, Sifeng Liu PII: DOI: Reference:

S0360-8352(19)30681-3 https://doi.org/10.1016/j.cie.2019.106212 CAIE 106212

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Computers & Industrial Engineering

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4 May 2019 20 October 2019 1 December 2019

Please cite this article as: Wang, H., Fang, Z., Wang, D., Liu, S., An Integrated Fuzzy QFD and Grey Decisionmaking Approach for Supply Chain Collaborative Quality Design of Large Complex Products, Computers & Industrial Engineering (2019), doi: https://doi.org/10.1016/j.cie.2019.106212

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Title An Integrated Fuzzy QFD and Grey Decision-making Approach for Supply Chain Collaborative Quality Design of Large Complex Products Author names and affiliations Huan Wang1, Zhigeng Fang1, Daao Wang2, Sifeng Liu1, 1 College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, China 2 School of Public Finance and Taxation, Nanjing University of Finance and Economics, Nanjing, China Corresponding author Huan Wang Email: [email protected] Mobile phone: +86-18551770890 Present address College of Economics and Management, Nanjing University of Aeronautics and Astronautics, 29 General Avenue, Jiangning District, Nanjing, Jiangsu, China Postal address: 211106

An Integrated Fuzzy QFD and Grey Decision-making Approach for Supply Chain Collaborative Quality Design of Large Complex Products

Abstract: Complex structure and high technical barriers make it difficult for manufacturers to design new products independently, hence supply chain collaborative design prevails. Supply chain collaborative design has been discussed in the literature and multiple effective methods have been proposed. Nevertheless, the systematic framework for collaboration has been scarcely addressed, and multi-objective decision-making with uncertain information and poor data is still a research difficulty. This paper proposes a novel collaborative quality design framework for large complex products supply chain by integrating the fuzzy QFD (quality function deployment) and the grey decision-making approach. The proposed method exerts QFD design deployment function to decompose design tasks to all participants in the supply chain systematically, from overall design to detailed design. The joint design team composed of supply chain participants, can effectively ensure that all design phases are aligned with the general design objective. In addition to market competitiveness and quality, multi-objective assessments are developed in the fuzzy QFD to make the design method more practical. Moreover, a weighted multi-attribute grey target decision-making method assists decision-makers to identify the optimal quality scheme with uncertain information and poor data. The proposed framework is applied to a new launch vehicle design in China to illustrate its effectiveness. Implications and suggestions for future research are discussed. Keywords: large complex product development; collaborative quality design; supply chain management; fuzzy QFD; grey decision-making; grey target decision

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1

Introduction

In order to rapidly respond to small batches and customized requirements in the market, manufacturers of large complex products, such as aircraft and rockets, have transformed their product development model. Traditional modular outsourcing gradually turns to collaborative development in the supply chain; thus, manufacturers can concentrate their superior resources on breaking through core technology. It has been proved that customers can provide requirements about the new product and suppliers can offer ideas and suggestions for modifications, which are key factors of new product development (Yoshimura, 2012; B¨ uy¨ uk¨ozkan and Arsenyan, 2012; Tang and Qian, 2008). Quality design is an important part of large complex product development. Collaborative quality design that takes customer needs and operability of production into account leads to a reasonable and feasible design scheme. The participation of customers and suppliers can assist to overcome design limitations caused by the complex structure and technical barriers. However, collaborative quality design is not without hinders. The process involves multiple subjects from multiple supply chain levels. Therefore, how to unify design goals, coordinate the design behavior of multiple subjects systematically, and form an optimal quality solution, is a challenge for manufacturers. Moreover, fully tapping customer requirements and choosing the most satisfactory solution among various quality schemes, are critical issues for the collaborative quality design of large complex products. In general, the difficulties for supply chain collaborative quality design are shown as following. (1) The complex structure and multi-subject involvement make the collaborative design process extremely complex and difficult to control. It cannot be executed orderly without a systematic framework. (2) Collaborative quality design with multi-agent participation often brings design conflicts, which makes quality schemes deviate from customer needs. It is difficult to mitigate design conflicts between upstream and downstream agents in the supply chain to assure design consistency. (3) It is hard to identify the optimal quality scheme among many alternatives with uncertain information and poor data under multi-objectives. It is shown from literature that collaborative product development has attracted researchers’ interest widely, and system structure and technical barriers make it difficult for manufacturers to complete quality design independently, based on which the following research questions will be addressed in this paper.

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(1) How to construct a systematic framework for collaborative quality design, by which manufacturers can decompose design tasks orderly. (2) How to extend the fuzzy QFD method to a multi-objective evaluation in quality design, so that more comprehensive factors can be considered in decision making. (3) How to identify the optimal quality scheme among alternatives with uncertain information and poor data under multi-objectives. To address the above issues of collaborative quality design, integrating fuzzy QFD and grey decision-making, this paper proposes a novel collaborative quality design framework for large complex products supply chain. Complex design tasks are decomposed from overall quality design to detailed design, which simplifies the supply chain systematically. First, in the overall quality design phase, a joint overall design team is constructed to identify quality requirements and core quality parameters, and collect quality schemes. The proposed method extends fuzzy QFD to a multi-objective evaluation, which can obtain more comprehensive evaluation results. The weighted multi-attribute grey target decision-making method is used to identify the optimal quality overall scheme with uncertain information and poor data under multi-objectives. Then, based on the optimal quality overall scheme, a hierarchical framework is built for large complex products quality detailed design. In this case, quality detailed design is carried out step by step to achieve the overall design scheme by utilizing the hierarchical deployment function of the fuzzy QDF analysis platform. Finally, the overall design team integrates all schemes into a master quality scheme and discusses with customers to ensure customer satisfaction. This study makes two contributions to the collaborative quality design of large complex products. First, this approach provides a systematic framework for collaborative quality design, links the supply chain subjects in an orderly way, and solves design inconsistency problems in collaboration. Additionally, this paper further explores uncertain analysis and decision-making problems. We extend the fuzzy QFD method to a multi-objective evaluation in quality design, so that more comprehensive factors can be considered, and the multi-objective decision-making problem with uncertain information and poor data has been addressed by integrating the grey decision-making approach into the fuzzy QFD approach. This approach has a comprehensive analysis function with the relatively simple decision-making process. It is rather practical and easy to popularize. The paper is organized as follows. Section 2 presents the literature review, Section 3 focuses on the proposed methodology, an illustrative example is presented in Section 4, where the results are also discussed. Finally, Section 5 presents the implications and suggestions for future research. 3

2

Literature review

In this section, we review studies related to the collaborative development of new products, fuzzy QFD (quality function deployment), and the grey decision-making approach.

2.1

Collaborative development of new products

Since the rapidly changing markets require higher quality and higher performing products at lower cost (B¨ uy¨ uk¨ ozkan and Arsenyan, 2012; Tang and Qian, 2008; Lv and Qi, 2019), collaborative development of new products have received increasing attention from researchers and practitioners, and valuable studies have emerged. Some of them focus on collaboration’s support system and platform design (Tang et al., 2010; Dou et al., 2016), framework and methodologies (Yoshimura, 2012; Lu et al., 2013), and resources integration (Kleinsmann et al., 2010; Du et al., 2012), etc. More scholars emphasize the involvement of customers and suppliers in collaboration. It is widely recognized that the involvement of customers and suppliers is a critical factor in the successful product development, because customers can provide requirements about the new product and suppliers can give suggestions for modifications (Wognum, 2002; Liu et al., 2011). Ma and Braiden (2001) established multi-disciplinary project teams to maximize the use of enabling technologies in new products development. Lee and Wang (2012) explored how different supplier and manufacturer relationship impacts on the workload and R&D-system equilibrium. Yoo et al. (2015) argued that an active and early supplier involvement program was beneficial for the new product development performance. Taking a social exchange theoretic perspective, Schoenherr and Wagner (2016) tried to enhance the degree of supplier involvement in the fuzzy front end of the new product development process. Most of the existing researches on collaborative product development are concerned about the involvement of suppliers and customers. However, rather few analytical researches address the collaborative quality design of large complex products. Moreover, few explicit processes and methodologies are available to guide customers and suppliers on how they participate in the quality design process of large complex products orderly.

2.2

Fuzzy QFD

Quality function deployment (QFD) was originally developed in 1972 at Mitsubishi. QFD has been especially valuable for product design (Sakao, 2010; Liu et al., 2011; Wu and Chung, 2015)due

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to the fact that it can translate customer requirements into engineering characteristics, process specifications, and production requirements (Yang et al., 2011). QFD not only shows great advantages in product development, but also has been applied in other research fields, such as supplier selection (Dursun and Karsak, 2013; Karsak and Dursun, 2014; Asadabadi, 2017; Babbar and Amin, 2018), decision making (Xingli and Huchang, 2018; Chowdhury et al., 2019), factor identification (Hsu et al., 2017), enhancing agility of companies (Eleonora Bottani, 2009), KPI(key performance indicator) management (Akkawuttiwanich and Yenradee, 2018), market analysis (Quoc et al., 2015), course design (Kamvysi et al., 2014), etc. In order to improve the practicability of QFD, scholars have integrated other theoretical methods into QFD and put forward valuable extensions, such as AHP (analytic hierarchy process), ANP (analytic network process), DEA (data envelopment analysis), grey system theory, multiple objective optimization, Kano model (Karsak and Dursun, 2014; Kamvysi et al., 2014; Ho et al., 2012; Demirel et al., 2014; Md. Maruf Hossan Chowdhury, 2015; Siu et al., 2015; Lina He, Wenyan Song, Zhenyong Wu, Zhitao Xu. Maokuan Zheng, 2017; Yazdani et al., 2019), etc. Among them, fuzzy set theory is one of the most widely adopted methods in QDF analysis. Since human decision is imprecise, vague and inconsistent in nature, people always expresses their opinions using linguistic judgement. Research has shown that fuzzy set theory can deal with vague and uncertainty of human thought. Siu et al. (2015) proposed a hybrid ANP-weighted fuzzy methodology to better rank technical characteristics of a product while implementing QFD. Wu and Chung (2015) used the fuzzy theory to reduce customers’ subjective judgment when studied green design in the product design process. Akkawuttiwanich and Yenradee (2018) proposed a new fuzzy QFD approach to manage the SCOR (supply chain operations reference) KPIs. Babbar and Amin (2018) used trapezoidal fuzzy numbers to eliminate the vagueness of human thoughts when evaluating suppliers considering environmental concerns. While there have been valuable research, there remain gaps because most of these studies fail to select the optimal scheme under uncertain information and poor data. Furthermore, traditional fuzzy QFD method only considers whether the technical parameters fully meet the needs of customers, which is far from enough, because factors such as cost, delivery date and risk in product design should also be considered in product design. This paper addresses these research gaps by introducing multi-objective evaluation to fuzzy QFD and utilizing weighted multi-attribute grey target decision for scheme selection.

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2.3

Grey decision-making approach

Grey decision-making approach utilizes the model containing grey elements or grey models combined with grey modules. Grey decision-making emphasizes on the study of choosing plans. The major advantage is that it can generate a satisfactory solution to the problem with incomplete and non-deterministic information. Because of its wide applicability grey decision making approach has been used in various fields such as product development investment decision making (Tai et al., 2011), supplier selection (Li et al., 2007; Golmohammadi and Mellat-parast, 2012), quality evaluation of introduced FDI (foreign direct investment) (Liu et al., 2011), coal-fired power plant decision making (Li et al., 2018b), barriers evaluation for reverse logistics implementation (Bouzon et al., 2018), and planning district heating system (Wang et al., 2018). Grey target decision-making model is a basic model of grey decision making approach, which embodies the non-uniqueness principle through the concept of grey targets. Under the condition without a standard model, the measurement set of the indicator set is transformed to get the unified dimension Euclidean space, which is the grey target. The benefits of the traditional grey target decision model have been highlighted by various researchers. For example, Chen et al. (2006) applied grey target theory in oil monitoring for wear mode recognition and proved the validity of the method. Chen et al. (2019) introduced a grey target decision model into the comprehensive performance evaluation of asphalt mixture to determine the suitable mixing ratio of raw materials. Ren et al. (2019) evaluated the reasonable location of electric vehicle charging stations by using this method. Some scholars optimized the grey target decision-making model and have enriched the theory (Zhu and Hipel, 2012; Luo and Wang, 2012; Li et al., 2018a). In the case of multi-objective, it is noteworthy that Liu (2015) proposed a weighted multi-attribute grey target decision model based on the traditional grey target. In his research uniform effect measure was first designed, which shows a remarkably physical meaning and applicability. However, the literature reviewed above seldom considered, or deeply discussed how to get the accurate effect value which is the raw data for the grey target decision-making model and has a decisive impact on the accuracy of decision-making results. This paper addresses this research gap by integrating the fuzzy QFD approach which has excellent analysis function, to provide a detailed and accurate basis for the weighted multi-attribute grey target decision.

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3

Research methodology

Before proposing the framework for large complex product quality collaborative design, we firstly present a research flowchart to explain the framework of the methodology (see Figure 1). Establish Fuzzy QFD Analysis Platform for quality overall design Evaluate schemes and build grey decision-making approach for optimization

Hierarchical framework for complex product quality detailed design

Reanalyze customer requirements

Integrate quality schemes and discuss with customer

Is customer satisfied? No Yes End

Figure 1: Framework of the proposed methodology Although the system structure is extremely complex, there are some core quality parameters, which have a decisive impact on large complex product’s quality, cost, risk, etc. The selection of core parameters is the key to a successful quality design. Therefore, we divide the quality design into overall design and detailed design. Specifically, the first stage is to establish a Fuzzy QFD Analysis Platform for quality overall design, select core quality parameters and collect quality plans based on full analysis of customer requirements. The second stage is to evaluate the various quality schemes under multiple objectives and build a weighted multi-attribute grey target decision-making model to select the optimal quality overall scheme among alternative options. In the third stage, we transform the optimal core quality parameter scheme, which are HOWs in the overall design, into WHATs of suppliers’ detailed

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design, and similarly apply the grey decision-making approach to identify the optimal detailed design scheme. Expanding quality design layer by layer can simplify onerous tasks, and ensure the consistency of the design objectives in the supply chain. The last stage is to summarize the quality schemes from various levels to the joint overall design team. The team consults with the customer to confirm whether the customer is satisfied with the scheme. If the customer is satisfied with the solution, the collaborative design ends. If not satisfied, customer requirements should be reanalyzed, and go to stage 1 until the customer is satisfied.

3.1

Fuzzy QFD Analysis Platform establishment for quality overall design

In this stage, a Fuzzy QFD Analysis Platform for large complex product quality overall design is established. Figure 2 presents the brief structure of the Fuzzy QFD Analysis Platform. This stage consists of the following steps.

Correlation (Cij ) HOWS(CPj)

WHATS W (i ) ( QRi)

R(ij )

RI Quality Scheme Set (B)

Figure 2: Fuzzy QFD Analysis Platform for quality overall design Step1. Form a joint team for the overall design Customer’s quality requirements and suppliers’ capability to meet these requirements are crucial to product quality design. Therefore, the manufacturer first organizes a joint design team composed of several experts from various departments of the customer, manufacturer, and core suppliers.

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They have multi-disciplinary expertise, a common understanding of customer requirements, costs, technologies, and market so that they can evaluate quality schemes objectively. The joint design team is responsible for top-level quality design. It aims at formulating an overall quality scheme and provides a basis for a detailed design. Step 2. Identify customer requirements (WHATs) and core quality parameters (HOWs) In the Fuzzy QFD Analysis Platform, customer’s quality requirements are referred to as WHATs, and HOWs are core quality parameters that can fulfill customer’s quality requirements. We collect information through interviews and questionnaires filled out by experts. As shown in Figure 2, row elements QRi represents customer’s quality requirements, and column elements CPj represents core quality parameters. Step 3. Calculate fundamental data in Fuzzy QFD Analysis Platform For customers, all quality requirements are not equally important, and the final quality scheme is hard to satisfy all quality requirements, so we first define Wi (see Figure 2) as quality requirements weights. Then, to explain the extent that each core quality parameter contributes to each quality requirement, it is necessary to build a relationship matrix Rij (see Figure 2) to present the relationship value between the ith WHAT and jth HOW. Next, RI in Figure 2 is the relative importance of the HOWs, which can be determined from “relative importance of WHATS” and the “relationships between the WHATS and HOWS”. Finally, the roof of the platform cij shows the correlation between HOWS. To sum up, in the Fuzzy QFD Analysis Platform, the following fundamental data are needed, (1) relative importance of WHATS (Wi ) (2) relationships between WHATS and HOWS (Rij ) (3) relative importance of HOWS (hj ) (4) correlation between HOWS (cij ) Human decision is imprecise, vague and inconsistent in nature. When dealing with the data in our method, experts always express their opinions using linguistic judgement. Fuzzy set theory is a suitable method to solve the uncertainty and fuzziness of human thought in QFD. As we have discussed in section 2, fuzzy QFD has been widely applied in research, and its effectiveness has been demonstrated by many researchers. Fuzzy set theory was originally proposed by Zadeh in 1965 (Zadeh, 1965). It is an effective means to represent imprecise and vague data in the real world. Membership function is used to 9

express a set and the value of a membership function lies between 0 and 1. In line with previous literature (Bevilacqua et al., 2006; Chowdhury et al., 2019), we use a triangular fuzzy membership function (see Figure 3) to quantify the linguistic data in our study, where a, b, c, refer to the smallest possible value, the most promising value, and the largest possible value. The fuzzy membership function is shown in (1). Let U = {V L, L, M, H, V H} be the linguistic sets that expresses opinions on a 5-point scale, where, V L = very low, L = low, M = medium, H = high, V H = very high. We can use this linguistic sets to express the relevance degree of a pair of indicators and evaluate the size of an indicator. µ(x) is quantified using triangular fuzzy numbers as shown in Figure 4, where V L = (0, 1, 2), L = (2, 3, 4), M = (4, 5, 6), H = (6, 7, 8), V H = (8, 9, 10).

  x 1

0

a

b

x

c

Figure 3: A triangular fuzzy number

µA¯ (x) =

            

x−a , b−a c−x , c−b 0,

a≤x≤b (1)

b≤x≤b otherwise.

  x VL

L

M

H

VH

1

0

2

4

6

8

10

Figure 4: Triangular fuzzy membership of the important rating

10

x

We’ll show the algorithms for calculating these fundamental data. (i) Relative importance of WHATS fik , we use (2) to calculate Assume that expert EMk rates the relative importance of Wi as W fi . Then W fi is defuzzied as W ∗ using (3), and W ∗ is the average relative importance rating W i i normalized as Wi using (4).   fi = 1 W fi1 + W fi2 + · · · + W fik W k

Wi∗ =

(2)

fi−lower + 2W fi−mostlikely + W fi−upper W 4

(3)

Wi∗ m P Wi∗

(4)

Wi =

i=1

(ii) Relationships between WHATS and HOWS (Rij ) Similarly, the extent that each core quality parameter contributes to each quality requirement is evaluated by experts. Suppose that expert EMk rates the relationship between the ith WHAT eijk , which follows triangular fuzzy numbers as shown in Figure 4. We can and the jth HOW as R eij using (5). R eij is defuzzied as Rij using (6). get the average relative importance rating R   eij = 1 R eij1 + R eij2 + · · · + R eijk R k

Rij =

eij−lower + 2R eij−mostlikely + R eij−upper R 4

(5)

(6)

(iii) Relative importance of HOWS (hj ) To find the relative importance (hj ) of core quality parameters, we first calculate the absolute importance (aj ) of core quality parameters, where (7)is used.

aj =

m X

Wi Rij ,

(7)

i=1

where i = 1, · · · , m and aj > 0. From (7), we find that when Rij = 0, ∀ i, i = 1, · · · , m, aj = 0. It means that the jth core quality parameter has no contributions to all the customer’s requirements. It can be inferred that

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jth parameter is not the core quality parameter of the large complex product. In this case, we stop the process and go back to step 2 to re-select core quality parameters. Then we obtain the relative importance (hj ) of core quality parameters using (8).

hj =

aj , n P aj

(8)

i=1

where

n P

aj > 0. From (8), we find that when aj = 0, ∀ j, j = 1, · · · , n,

i=1

n P

aj = 0. That

j=1

means that every core quality parameter has no contributions to all the customer’s requirements. We deduce all the j parameters are not the core quality parameter of the large complex product. Under this condition, we stop the process and go back to step 2 to re-select core quality parameters. (iv) Correlation between HOWS (cij ) Literature has demonstrated that the correlations between HOWS may influence system performance. For a large complex product, the correlation between quality parameters may also have an effect on the cost ang risk of the final product. We apply several symbols to indicate the correlation: ++, which means a strong positive correlation between HOWs, +, denoting a positive correlation, −, denoting a negative correlation and −− means a strong negative correlation, blank means no correlation. The specific impact will be evaluated according to specific circumstances. Step 4. Collect quality schemes According to the customer requirements and core quality parameters in the Fuzzy QFD Analysis Platform, the joint design team extensively collects quality schemes. It should be noted that collected schemes only need to have basic feasibility without any comparison and optimization. Finally, a Quality Scheme Set B is formed (see Figure 2).

3.2

Evaluate schemes and build grey decision-making approach for optimization

This stage aims to evaluate Quality Scheme Set and select the optimal quality scheme. One of the key points is the multi-objective evaluation of the Quality Scheme Set. Traditional QFD analysis method can obtain quality competitiveness and market competitiveness, but in today’s competitive market environment, it is far from enough to simply consider whether quality parameters meet customer needs. Other evaluation criteria, such as product cost, delivery date, development risk, should be concerned in the design phase. Therefore, this study extends fuzzy QFD to multiobjective evaluation to make a more comprehensive optimization.

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Moreover, uncertainty in the product design stage, such as conflicting evaluation criteria, few available data, also gives a challenge to decision-makers. Grey target decision approach has advantages in dealing with uncertain information and few data. According to grey decision-making theory and the follow-up research results (Liu, 2015), we adopt the weighted multi-attribute grey target decision model to select the optimal scheme. Figure 5 presents the structure of evaluation and optimization, and the detailed steps are as follows.

-

+ QR1 W1 QR2 W2 ...

...

...

QRi Wi AI RI B1 B Bm

CP1 R11 R21 ...

CP2 R12 R22 ...

Ri1 a1 h1 b11 ...

Ri2 a2 h2 b12 ...

bm1

bm2

++ ... ... ... ... ... ... ... ... ... ...

Grey Decision-making Approach

Fuzzy QFD Analysis Platform

-CPj R1j R2j ... Rij aj hj b1j ... bmm

B1 t11 t21 ... ti1 u111

... ... ... ... ... ...

Bm t1m t2m ...

Ranking

tim u1m1

Objective 1

u112 ...

u113 ...

u1m2

u1m3

Objective 2 Objective 3

... ... ... ...

u11k ... u1mk Objective k

Figure 5: Structure of the evaluation and optimization Step 5 Define the key elements of decision-making model Definition 3.1. Event set The totality of all events within a range of research is called event set which is denoted as A = {a1 , a2 , · · · , an }, where ai , i = 1, 2, · · · , n, stands for the ith event. In this study, we define the event set A = {a1 }, where a1 stands for the event (quality design). Definition 3.2. Countermeasure set The set of all possible countermeasures is called the countermeasure set. In this study, every quality scheme collected is a countermeasure for the event, so we define the Quality Scheme Set B as the countermeasure set B = {b1 , b2 , · · · , bm } where the jth quality scheme bj , j = 1, 2, · · · , m is the jth countermeasure. Definition 3.3. Situation set

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The Cartesian product A × B = {(ai , bj )|ai ∈A, bj ∈B}is called a situation set, written as S = A × B. Ordered pair (ai , bj ) is called a situation, denoted Sij . Definition 3.4. Effect (k)

Sij = {(ai , bj )|ai ∈A, bj ∈B} is the situation set, assuming that uij is the effect value of situation Sij with respect to objective k. Step 6 Determine decision objectives and their weights Considering the requirements of customers and characteristics of similar products in the market, the joint design team should first formulate k decision objectives. Objectives may be included but not limited to market competitiveness, quality competitiveness, cost level, progress capability and development risk, etc. Since these objectives are not equally important, as the same way as we obtain relative importance of WHATS (Wi ) in step 3, we adopt fuzzy set approach to measure their weight η1 , η2 , · · · , ηk . Due to space constraints, the process will not be presented here. Step 7 Evaluate schemes and measure effect Based on the Fuzzy QFD Analysis Platform, experts evaluate each scheme in the quality scheme set under objective k. The resulting effect values form an observed effect matrix U k under objective k. Definition 3.5. Observed effect matrix (k)

Assume that Sij = {(ai , bj )|ai ∈A, bj ∈B} is the situation set, uij is the effect value of situation Sij under objective k, and U k is the observed effect matrix of situation S under objective k(k = 1, 2, · · · , n). 

···

u1m

(k)



 (k) (k) h i   u21 u22 · · · (k) k  U = uij =  . .. ..  .. . .  (k) (k) un1 un2 · · ·

(k) u2m

      

(k)

(k)

u11

u12

.. . (k)

(9)

unm

In the Fuzzy QFD Analysis Platform, we can obtain the effect value under objective 1 (Market competitiveness), objective 2 (Quality) using (10)-(11).

u11m =

i X

Wi tim

(10)

i=1

u21m =

j X i=1

14

hj tij

(11)

The effect value under other objectives can be evaluated by experts, and experts use triangular fuzzy numbers to rate the effect using a 5-point scale as shown in Figure 4. We obtain the crisp effect value as the same way as Rij in step 3. Due to space constraints, the process will not be presented here. Step 8 Set threshold effect value and transform to uniform effect measure matrix Considering the different attributes of different decision objectives, we divide them into three types, namely, a benefit type objective, a cost type objective, a moderate-value objective. For a benefit type objective, we pursue a larger effect value, which can bring more benefits. For a cost type objective, we pursue a lower effect value, which can bring more benefits. For a moderate-value objective, we pursue effect value close to a specific value. Because different objective effect values have different meanings, dimensions, and properties, it is necessary to set a threshold effect value for each objective in order to obtain comparability, and then measure the comprehensive effect of the situation. Then, transform the effect value into the uniform effect measure, and transform the observed effect matrix into the uniform effect measure matrix. Definition 3.6. Uniform effect measure (j)

(i) Let j be a benefit type objective, and the threshold effect value of the objective is uk0 n0 , the  n o (j) (j) (j) decision grey target of objective j is ukn ∈ uk0 n0 , max max ukn ,then n

k

(j)

(j)

rkn =

(j)

ukn − uk0 n0 n o , (j) (j) max max ukn − uk0 n0 k

(12)

n

is referred to as the effect measure of a benefit-type objective. (j)

(ii) Let j be a cost type objective, and the threshold effect value of the objective is uk0 n0 , the   n o (j) (j) (j) decision grey target of objective j is ukn ∈ min min ukn , uk0 n0 ,then k

n

(j)

(j) rkn

=

(j)

uk0 n0

(j)

uk0 n0 − ukn n o, (j) − min min ukn k

(13)

n

is referred to as the effect measure of a cost-type objective. (iii) Let j be moderate-value objective, under this objective, we pursue effect value close to h i ¯ the decision grey target of objective j is u(j) ∈ A¯ − u(j) , A¯ + u(j) , where a specific value A, kn k0 n0 k0 n0

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(j) (j) A¯ − uk0 n0 , A¯ + uk0 n0 are lower threshold effect value and upper threshold effect value, respectively.

Then h i (j) (j) When ukn ∈ A¯ − uk0 n0 , A¯ , (j) rkn

=

(j) (j) ukn − A¯ + uk0 n0 (j)

,

(14)

uk0 n0

is referred to as the lower threshold effect value of moderate-value objective. h i (j) ¯ A¯ + u(j) , When u ∈ A, kn

k0 n0

(j)

rkn =

(j) (j) A¯ + ukn − uk0 n0 (j)

,

(15)

uk0 n0

is referred to as the upper threshold effect value of moderate-value objective. We define benefit type uniform effect measure, cost type uniform effect measure, lower moderate value uniform effect measure, and upper uniform moderate value effect measure as uniform effect measure. Definition 3.7. Uniform effect measure matrix Then we can transform the uniform effect measure matrix Rk from the observed effect matrix U k using the three transfer approach analyzed above. 

(k)

(k)

r11

r12

···

(k)



(k)

      

r1m

 (k) (k) h i   r21 r22 · · · (k) k  R = rij =  . .. ..  .. . .  (k) (k) rn1 rn2 · · ·

r2m .. . (k)

(16)

rnm

Step 9 Calculate the weighted synthetic effect measure m P Assume ηk , k = 1, 2, · · · , m is the weight of objective k, = 1. Uniform effect measure matrix k=1

under objective k is Rk , as shown in (16). Then, weighted synthetic effect measure matrix is     R = [rij ] =    

where rij =

S P k=1

r11

r12

···

r1m

r21 .. .

r22 .. .

··· .. .

r2m .. .

rn1 rn2 · · ·

rnm

(k)

ηk · rij . 16

    ,   

(17)

Step 10 Determine the optimal situation For the case of weighted synthetic effect measures, rij ≤ 0 represents that the situation Sij misses the target, that is to say, quality scheme j is not a satisfying scheme for quality overall design. When rij ≥ 0, the situation Sij hit the target, that is to say, quality scheme j is a satisfying scheme for quality overall design. We can also rank the quality schemes and select the optimal scheme by comparing their weighted synthetic effect measures.

3.3

Hierarchical framework for large complex product quality detailed design

In the collaborative design of the supply chain, we emphasize that the downstream participants are the customers of the upstream participants. Therefore, after the joint design team has completed a quality overall design scheme that is able to satisfy customer’s quality requirements, the suppliers should also set up joint design teams at their levels to a conduct detailed quality scheme design to meet the overall design plan. According to the approach proposed in the preceding two subsections, the joint team has completed the overall quality design using the weighted multi-attribute grey target decision based fuzzy QFD approach and obtained the optimal core quality design scheme. Next, the hierarchical deployment function of the fuzzy QDF analysis platform is brought into, and the quality detailed design is carried out step by step to achieve the overall design scheme. Grey target decision making models are established according to different decision-making problems and applied to the process of detailed design scheme selection in a similar way. The hierarchical framework for large complex product quality detailed design is shown in Figure 6.

17

Figure 6: Hierarchical framework for large complex product quality detailed design

3.4

Integrate quality schemes and iterative optimization

After all the participants in the supply chain have completed the detailed quality design, they submitted their schemes to upstream participants step by step, and finally to the overall design team which is responsible to integrate the schemes into a master quality scheme. Then the overall joint design team will communicate with the customer. If the customer is satisfied, the whole supply chain will carry out the follow-up development work based on the master quality scheme, supply chain collaborative quality design process ends at this point. If there are issues needing to be improved, the procedure is repeated by reanalyzing the customer’s quality requirement and revising the core quality parameters continuously until a satisfactory scheme is generated. Similarly, this iteration process can also be applied to the optimization process of detailed schemes for upstream participants.

18

4

An illustrative example

To show how the proposed approach works in practice, the collaborative quality design of a new launch vehicle for institute A in China is illustrated as a numerical example. We select three subjects from three successive levels in the supply chain, namely manufacturer A, system supplier B, and subsystem supplier C. Manufacturer A is an institute and plans to develop a new launch vehicle according to customer needs. System supplier B is responsible for power system design, and subsystem supplier C is responsible for the fuel filling system, which is a subsystem of the power system. We interviewed them and applied the proposed approach to their collaboration.

4.1

Overall design

Manufacturer A formed a joint design team composed of 10 experts, including 2 from the customer, 2 from institute A, 2 from system supplier B, 2 from arrow structure supplier, and 2 from control system supplier. Firstly, they established the Fuzzy QFD Analysis Platform for the quality overall design, analyzed customer’s quality requirements (Table 1) and core quality parameters (Table 2). Table 1: Customer’s quality requirements Customer’s quality requirements QR1 QR2 QR3 QR4 QR5 QR6

GTO load LEO load Orbit injection accuracy Reliability Multitask adaptability Environmental performance

Table 2: Core quality parameters Core quality parameters CP1 CP2 CP3 CP4 CP5 CP6 CP7 CP8

Structural coefficient of core stage Takeoff thrust Takeoff weight Propellant properties Fuel Control accuracy Core manufacturing capability Stability of electronic equipment

Then, as shown in Figure 7, fundamental data, relative importance of WHATS (Wi ), relation19

ships between WHATS and HOWS (Rij ), relative importance of HOWS (hj ), correlation between HOWS (cij ), were calculated. Furthermore, the team collected 6 quality schemes forming the Quality Scheme Set BA . Then we applied the weighted multi-attribute grey target decision model for quality scheme optimization. The joint team determined the 5 decision objectives and evaluated their weight (Table 3). First, the effect value under Market Competitiveness and Quality are calculated and then effect value under the other three objectives are evaluated, and the result is listed in Figure 7.

-

++ +

-

+ + ++ CP1 CP2

-

+

+

++

+ +

CP3

CP4

CP5

CP6

CP7

CP8

BA1

BA2

BA3

BA4

BA5

BA6

QR1 0.215 5.8

7.4

7

7.6

6.6

5.6

4.6

5.4

6.8

3.8

8

6.6

4.8

7.2

QR2 0.209 5.0

7.2

7.2

7.4

6.8

6.0

6.6

5.6

4.8

4.2

7.6

7.2

6.0

6.4

QR3 0.174 6.0

6.6

6.4

8.2

3.2

7.8

5.2

7.4

5.0

6.0

5.4

8

5.4

6.4

QR4 0.163 4.2

4.6

5

3.2

3.6

8.4

7.0

7.2

3.0

5.6

5

6.4

7.2

7.0

QR5 0.134 6.2

7.2

6.8

3.4

3.4

3.4

5.8

3.8

8.2

5.2

3.8

7.4

6.4

8

0.105 6.6

4.8

4.2

3.2

4.0

3.2

4.0

3.8

6.2

3.4

6.2

6.8

5.8

5.8

5.6

4.7

6.2

7.1

5.9

6.8

QR6

BA

AI

5.544 6.463 6.291 5.921 4.859 5.976 5.611 5.701

RI

0.119 0.139 0.136 0.128 0.105 0.129 0.121 0.123

Market Competitiveness

BA1

4.6

7.2

8.0

6.6

3.2

7.0

5.8

8.0

6.4

7.2

5.0

6.6

BA2

5.6

6.8

5.6

2.8

5.2

6.6

6.0

7.4

5.8

6.4

8.2

7.0

BA3

7.0

6.0

7.0

7.2

6.8

6.4

5.0

3.4

6.1

3.0

6.4

3.8

BA4

3.4

7.0

6.4

5.6

3.2

5.6

7.2

6.4

5.7

4.3

5.6

4.6

BA5

8.0

7.4

6.6

7.8

7.4

5.4

6.8

6.2

6.9

8.0

7.0

5.0

BA6

6.0

4.8

4.2

3.2

3.0

2.8

6.6

5.8

4.6

5.2

4.8

5.4

Quality

Cost Delivery Risk

Figure 7: Fuzzy QFD Analysis Platform of overall design

20

Table 3: Decision objectives of manufacturer A

1 2 3 4 5

Objective

Weight

Threshold effect value

Market Competitiveness Quality Cost Delivery Risk

0.171 0.302 0.274 0.131 0.120

6 6 7 5±1.5 5

The observed effect matrix U k is followed. U 1 = [5.6, 4.7, 6.2, 7.1, 5.9, 6.8] U 2 = [6.4, 5.8, 6.1, 5.7, 6.9, 4.6] U 3 = [7.2, 6.4, 3.0, 4.3, 8.0, 5.2] U 4 = [5.0, 8.2, 6.4, 5.6, 7.0, 4.8] U 5 = [6.6, 7.0, 3.8, 4.6, 5.0, 5.4] Set the threshold effect value (Table 3) and the Uniform effect measure matrix Rk is followed. R1 = [−0.364, − 1.444, 0.182, 1.222, − 0.091, 0.727] R2 = [0.444, − 0.220, 0.111, −0.330, 1, − 1.560] R3 = [−0.050, 0.150, 1, 0.690, − 0.250, 0.450] R4 = [0.280, − 0.320, 0.040, 0.200, − 0.080, 0.26] R5 = [−1.330, − 1.670, 1, 0.333, 0, − 0.330] The weighted synthetic effect measure matrix is R = [−0.064, − 0.516, 1, 0.464, 0.364, 0.207−0.228], and Ba3 is the optimal overall quality scheme.

4.2

Detailed design

After the quality overall design scheme is selected, system supplier B adopted its design activities based on the overall design scheme BA3 . They formed their own joint design team, established the Fuzzy QFD analysis platform to analyze how to design the detailed system parameters to meet the overall design scheme BA3 . The detailed system parameters are shown in Table 4. Objectives are listed in Table 5. Fuzzy QFD Analysis Platform for the detailed design of supplier B is shown in Fig. 8.

21

Table 4: Detailed system parameters Detailed system parameters SP1 SP2 SP3 SP4 SP5

Fuel filling system Pressure control system Power control and testing system On-board Power System Connector

Table 5: Decision objectives of supplier B

1 2 3 4 5

Objective

Weight

Threshold effect value

Market Competitiveness Quality Cost Delivery Risk

0.154 0.432 0.179 0.091 0.144

6 7 6.5 5±1.3 6

+ + +

++

BA3

+

SP1 SP2

SP3

SP4

SP5

BB1

BB2

BB3

BB4

CP1 0.119

8.2

4.4

5.2

8.6

8.2

5.8

4.6

7.6

6.0

CP2 0.139

6.4

7.8

5.8

7.8

6.0

7.0

5.2

6.0

5.2

CP3 0.136

6.0

7.6

5.6

8.0

5.6

7.2

6.4

4.8

7.2

CP4 0.128

4.6

5.0

3.6

7.2

3.6

3.0

6.0

5.4

6.8

CP5 0.105

8.8

3.0

3.2

6.8

3.2

5.4

7.0

2.0

7.2

CP6 0.129

3.2

6.4

8.4

6.6

7.6

3.8

6.8

3.6

6.4

CP7 0.121

3.4

2.8

7.4

7.0

6.4

4.4

6.2

7.4

6.8

CP8 0.123

5.8

4.6

7.0

6.4

3.8

6.8

5.8

6.2

4.6

5.5

6.0

5.4

6.3

BB

AI

5.732 5.327 5.823 7.317 5.590

RI

0.192 0.179 0.195 0.246 0.188

Market Competitiveness

BB1

5.6

6.6

5.8

6.8

4.2

5.9

4.8

5.8

6.8

BB2

7.8

6.8

6.4

7.6

6.2

7.0

5.2

6.4

6.0

BB3

6.6

3.6

6.2

8.0

6.0

6.2

6.6

6.0

5.6

BB4

3.8

3.6

4.4

6.4

7.4

5.2

7.0

6.0

7.0

Quality Cost Delivery Risk

Figure 8: Fuzzy QFD Analysis Platform of supplier B

22

They selected an optimal detailed scheme using the weighted multi-attribute grey target decision model and the detailed calculation process is as follows. The observed effect matrix U k is followed. U 1 = [5.5, 6.0, 5.4, 6.3] U 2 = [5.9, 7.0, 6.2, 5.2] U 3 = [4.8, 5.2, 6.6, 7.0] U 4 = [5.8, 6.4, 6.0, 6.0] U 5 = [6.8, 6.0, 5.6, 7.0] Set threshold effect value (Table 3) and the Uniform effect measure matrix Rk is followed. R1 = [0, 0.625, − 0.125, 1] R2 = [−0.571, 1, −0.143, −1.571] R3 = [1, 0.765, −0.059, −0.294] R4 = [0.385, − 0.0773, 0.231, 0.231] R5 = [−2, 0, 1, − 2.5] The weighted synthetic effect measure matrix is R = [−0.321, 0.658, 0.0735, − 0.917], and BB2 is the optimal detailed quality scheme. Then, subsystem supplier C formed a joint design team and established the Fuzzy QFD analysis platform to analyze the detailed system parameters meeting scheme BB2 . The detailed subsystem parameters are shown in Table 6. Objectives are listed in Table 7. Fuzzy QFD Analysis Platform for the detailed design of supplier C is shown in Figure 9. Table 6: Detailed subsystem parameters Detailed subsystem parameters U P1 U P2 U P3 U P4

Filling model Parallel pump technology Filling control Flow metering device

23

Table 7: Decision objectives of supplier B

1 2 3 4 5

Objective

Weight

Threshold effect value

Market Competitiveness Quality Cost Delivery Risk

0.193 0.256 0.262 0.190 0.099

5.8 5.9 6.8 6±1.5 5.8

+

++

+

BB2

UP1 UP2

UP3

UP4

BC1

BC2

BC3

BC4

BC5

SP1 0.192

8.8

7.4

8.2

5.8

4.4

8.2

6.0

3.4

4.2

SP2 0.179

6.4

7.0

6.6

6.2

6.6

8.0

5.8

4.8

5.8

SP3 0.195

7.2

6.4

7.2

6.8

7.4

5.6

5.8

5.4

6.0

SP4 0.246

5.6

4.0

5.6

3.2

7.8

3.4

7.2

5.6

6.8

SP5 0.188

3.6

3.8

4.4

3.6

5.6

5.0

4.4

3.4

6.8

6.4

5.9

5.9

4.6

6.0

BC

AI

6.294 5.620 6.365 5.013

RI

0.270 0.241 0.273 0.215

Market Competitiveness

BC1

3.8

8.0

7.2

5.8

6.2

6.8

7.4

5.6

BC2

5.4

5.8

6.2

6.0

5.8

4.4

7.0

7.8

BC3

5.0

6.2

5.4

6.4

5.7

5.8

4.2

4.8

BC4

6.4

4.4

6.0

7.0

5.9

7.2

3.8

5.2

BC5

7.2

2.0

5.4

4.6

4.9

6.6

6.8

6.0

Quality Cost Delivery Risk Figure 9: Fuzzy QFD Analysis Platform of supplier C They selected the optimal detailed scheme using the weighted multi-attribute grey target decision model and the detailed calculation process is as follows. The observed effect matrix U K is followed. U 1 = [6.4, 5.9, 5.9, 4.6,6.0] U 2 = [6.2, 5.8, 5.7, 5.9, 4.9] U 3 = [6.8, 4.4, 5.8, 7.2, 6.6] U 4 = [7.4, 7.0, 4.2, 3.8, 6.8] U 5 = [5.6, 7.8, 4.8, 5.2, 6.0] 24

Set threshold effect value (Table 3) and the Uniform effect measure matrix Rk is followed. R1 = [1, 0.167, 0.167, − 2, 0.333] R2 = [1, − 0.333, − 0.667, 0, − 3.333] R3 = [0, 1, 0.417, − 0.167, 0.083] R4 = [0.067, 0.333, − 0.2, −0.467, 0.467] R5 = [0.2, −2,1.064, 0.6, − 0.2] The weighted synthetic effect measure matrix is R = [0.482, 0.074, 0.038, −0.459−0.698] , and BC1 is the optimal detailed quality scheme.

4.3

Scheme integration

Finally, core supplier B and subsystem supplier C submitted their detailed schemes to the joint overall design team, and the team integrated them into a master quality scheme and discussed it with the customer. The customer is satisfied with the master quality scheme and the design process ends. Above all, the application of the proposed approach is illustrated through a three-level collaboration example. The three subjects are satisfied with the efficient framework and obtain a satisfactory quality solution for large complex products supply chain. The feasibility and practicability of the proposed approach have been confirmed as well.

5

Conclusions

This paper develops a novel quality collaborative design framework for large complex products. Integrating the fuzzy QFD and grey decision-making approach, the primary objective of the proposed approach is to help manufacturers organize the quality collaborative design systematically, analyze customer expectations and select the optimal scheme to meet their requirements.

5.1

Theoretical implications

Integrating the fuzzy QFD approach and the grey decision-making, this study proposes a novel collaborative design framework for large complex product supply chain, which has made a unique contribution to large complex product collaborative design literature. Additionally, this research contributes to large complex product collaborative design by

25

(1) developing a novel collaborative design framework by integrating the fuzzy QFD approach and the grey decision-making approach. (2) based on customer requirements analysis, complex design tasks can be simplified from the overall design to the detailed design and from manufacturer to suppliers by using the proposed approach. (3) extending fuzzy QFD with multi-objective evaluation, the design decision-making can consider more comprehensive objective factors, and the extended fuzzy QFD is more practical.

5.2

Managerial implications

The proposed collaborative design approach will assist large complex product manufacturers systematically organize customers’ and suppliers’ participation in the product design. The joint design team has matrix management characteristics, which can reduce communication costs and improve the accuracy and feasibility of design schemes. The deployment of QFD effectively prevents the deviation of supplier design. This framework can also be adapted in other industries with a complicated collaborative design issues. Grey target decision-making approach can effectively handle decision problems with uncertain information and few data. When there is no optimal alternative, a relatively satisfactory alternative can be quickly selected. Furthermore, the model is convenient to use with strong practicability.

5.3

Limitations

This study has some limitations which should be addressed in further research. First, a fruitful area for future research would be to discover more about how to obtain rich and detailed data to enhance the accuracy of the method, and how to eliminate the impact of subjective evaluation. As we have shown in section 4, the quantitative case study is conducted with part of large complex product design and a complete practical application should be developed to further verify the feasibility of the method. Our immediate future research intends to address some of these issues.

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Acknowledgements This work was supported by PhD short-term visiting scholar project (No.190408DF09), Postgraduate Research & Practice Innovation Program (No. SJKY19_0161), the National Natural Science Foundation of China (Nos.71801127, 71673119), and Special Funds from China Postdoctoral Science Foundation (No. 2019TQ0150).

Highlights A systematic collaborative quality design framework for large complex products is developed. Design inconsistency problem in collaboration is solved. Extend fuzzy QFD to multi-objective evaluation, which is more practical. Optimal quality scheme is identified under uncertain information and poor data.