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1、 ELSEVIER Journal of Systems Engineering and Electronics Vol. 19, No. 6, 2008, pp.1165-1170 Available online at ScienceDirect Product design on the basis of fuzzy quality function deployment* Li Zhaoling1,2 7 Gao Qisheng1 & Zhang Donglin 1. Inst, of Complexity Science, Qingdao Univ., Qingdao 26607
2、1, P. R. China; 2. Coll, of Information Science & Technology, Qingdao Univ. of Science &c Technology, Qingdao 266061, P. R. China; 3. School of Economics, Qingdao Univ., Qingdao 266071, P. R. China (Received October 22, 2007) Abstract: In the implementation of quality function deployment (QFD), the
3、determination of the target values of engineering characteristics is a complex decision process with multiple variables and multiple objectives that should trade off, and optimize all kinds of conflicts and constraints. A fuzzy linear programming model (FLP) is proposed. On the basis of the inherent
4、 fuzziness of QFD system, triangular fuzzy numbers axe used to represent all the relationships and correlations, and then, the functional relationships between the customer needs and engineering characteristics and the functional correlations among the engineering characteristics are determined with
5、 the information in the house of quality (HoQ) fully used. The fuzzy linear programming (FLP) model aims to find the optimal target values of the engineering characteristics to maximize the customer satisfaction. Finally, the proposed method is illustrated by a numerical example. Keywords: quality f
6、unction deployment, house of quality, product design, fuzzy optimization, customer satisfaction. 1. Introduction Quality function deployment (QFD) is a customer- driven quality improvement method that aims to meet customer needs in a better way and enhance organizational capabilities1-2!. Typically,
7、 a QFD system can be broken down into four inter-linked phases to fully deploy the customer needs phase by phase, from customer needs into design requirements, which are also known as engineering characteristics and subsequently into parts characteristics, process plans, and production requirements.
8、 Each translation uses a chart called “house of quality”（ HoQ)【 3L Prom the view of system， QFD is a complex system with input, process and output, and thus, an important application of system engineering in product design. In the implementation of QFD, the determination of the target values of the
9、engineering characteristics is a complex problem with multiple variables and objectives that needs to tradeoff all kinds of conflicts and constraints, such as the conflicts among the engineering characteristics and the contradiction between the customer needs and design budget. So the construction o
10、f QFD planning model to optimize the target values is a very important activity. In QFD planning model, the key difficulty is how to determine the relationships between the customer needs and the engineering characteristics, and the correlations among the engineering characteristics. In traditional
11、QFD, crisp numerical data sequence is used to represent the relationships!4-5!, for example, 1, 3, 5, 7 and 9 are assigned to very weak, weak, moderate, strong, and very strong. However, in the early design stage, the information collected is vague and inaccurate. Many inputs are in the form of ling
12、uistic data, e.g., human perception, judgment, and evaluation. The information loss will inevitably occur with crisp numbers. Because of the inherent vagueness and imprecision of the functional relationships, fuzzy regression with the competitors, data sounds jastifiablel6-8. Kim et al.6 first sugge
13、sted using fuzzy regression to estimate functional relationships in the field of QFD. This project was supported by the National Natural Science Foundation of China (70571041). 1166 Li Zhaoling, Gao Qisheng k Zhang Dongling Then, Fung Richard Y K (2006) et alJ8 developed an asymmetric fuzzy linear r
14、egression approach to estimate the functional relationships for product planning on the basis of QFD. However, as we know, it would be very difficult to obtain sufficient data in many cases because of commercial secrets of competitors or high cost of data collection, such as the expensive conduction
15、 of engineering experiment to determine the target values of the engineering characteristics of main competitors. Furthermore, only a satisfactory solution, not an optimal one, will be reached with any method. QFD uses HoQ to plan product design. In the establishment of the first HoQ, the relationsh
16、ips between customer needs and engineering characteristics, and the correlations among the engineering characteristics are determined by aggregating the opinion of the design team and the experts, and so they are of good value for us to use. In this article, on the basis of inherent vagueness of QFD
17、, triangular fuzzy numbers are used to represent the relationships and fully use the information in HoQ to determine the functional relationships between the customer needs and engineering characteristics, and correlations among the engi- neering characteristics. Eventually, a product design model t
18、hat aims to maximize the customer satisfaction is established to optimize the target levels of engineering characteristics. 2. Optimization model of product design 2.1 Normalization of the engineering characteristics The engineering characteristics are incommensurable; in other words, they have no u
19、niform standards and measurement units, so they should be normalized at first. Three cases should be considered: larger-the- better characteristics, smallerthe-better characteris- tics, ajid nominal-the-best characteristics. They can be computed by the following equations, respectively. Xj ij - ifn
20、max _ mii X3 |Z0 - y where l is the target value of nominal-the-better characteristic. Hence, 0 Xj l and Xj is larger-the- better for j = 0,1,., n. 2.2 Fuzzy processing of the information in HoQ A typical HoQ contains some of the following elements: customers needs (WHATs), engineering characteristi
21、cs (HOWs), relationship matrix of WHATs vs. HOWs, correlation matrix of the HOWs, technical competitive assessment etcl9l. The components of HoQ are displayed in Fig. 1. Correlation Engineering characteristics Customer needs Relationship matrix Technical competitive assessment Fig. 1 House of qualit
22、y Among the elements of HoQ, the relationship matrix is a systematic method for identifying the levels of relationships between customer needs and en- gineering characteristics. Usually these relationships are measured by weak, moderate, and strong. In this article, instead of crisp number, each rel
23、ationship is represented by a triangular fuzzy number, and thus, relationship matrix can be represented by a matrix of triangular fuzzy number. At the same time, the correlation matrix is to help the producing company establish which engineering characteristics are correlated and determine the exten
24、t of these correlations, which can be obtained through engineering analysis and experience. Similarly， these correlations are measured by no, weak, moderate, and strong, and either negative or positive. In this article, they are also represented by triangular fuzzy numbers. 2.3 The determination of
25、the objective function Let Y = (yi,y2,-.,ym)T be the satisfactory extent vector of customer needs, where m is the number of customer needs. The objective is to maximize every customer need. It can be expressed as max Y (4) Pwduct design on the basis of fuzzy quality function deployment 1167 Assume t
26、hat K = WTRAt, v = (,02,.,), The multiple objective problem can be transformed into a single objective one by linear weighting method， so we can get max WtY (5) where W = (u； i， o； 2,， Wm)T is the weight vector of customer needs and o； iis the weight of the customer need i. Then, the objective can b
27、e given as m max (6) i=l Assume that R is the relationship matrix of customer needs and engineering characteristics, and the degree of customer satisfaction is a linear combination of the actual attainment levels of engineering characteristics, and the degree of customer satisfaction can be defined
28、as y = (7) where y = (x， . ， a4)T is the actual level vector of attainment of engineering characteristics and n is the number of ECs. Let be the level of relationship between the customer need i and the engineering characteristic and Eq. (7) is equivalent to Vi = fi22 ) inn i = 1， 2, ， m (8) Afterwa
29、rds, tradeoffs among the engineering characteristics are considered. LetA bethe correlation matrix, and the actual attainment degree of each engineering characteristic is a linear combination of all the planned attainment degrees of engineering characteristics， then ， the actual attainment degrees o
30、f engi- neering characteristics can be represented as Xf = ATX (9) where X = (xi, X2,. , xn)T is the vector of the target degrees of engineering characteristics without considering the correlation of the engineering characteristics. Let ajA： be the correlation extent between the engineering characte
31、ristic i and the engineering characteristic j) then, Eq. (9) is equivalent to A/ lj Substituting Eqs. (7) and (9) into Eq. (5), we have max WrRATX (11) and it is the weight vector of planned degrees of engineering characteristics, we have max VX (12) It is equivalent to max s = VjXj (13) i=i With th
32、e operational rule of fuzzy numbers, ij(j = 1 2,， n) can be determined by Vj = (wi rn tl； 2 f2l . 0 fml) jl (w 0 fi2 22 rm2) 0 Cbj2 切 282n 尸 mn) n (14) 2.4 FLP optimization model The objective of the FLP optimization model is to find the target values of the engineering characteristics to maximize t
33、he customer satisfaction. The considered optimization model is given as follows. n max s = VjXj Q Xj 1, j = 1,2,， n m C(x) = CjXj B )=i In this model, the first constraint is the result of the normalization of the engineering characteristics. The second constraint ensures that total cost of improvem
34、ents does not exceed the given budget limit if there are enough data about cost .Because (V” ， is a triangular fuzzy number, the optimization model is a fuzzy linear programming one whose objective coefficients are triangular fuzzy numbers. This problem is equivalent to solving the following crisp l
35、inear programming problem by using possibilistic linear programming!10! max f n 53 v Xj 八 j= s.t. - - - 彡 a, 2vj3Xj i=i i=i n n /i fh 1168 Li Zhaolingf Gao Qisheng & Zhang Dongling (x) C3 X 3 及， i=i 0 Xj 1, j = 1 , 2 , . . . , n Here, a is confidence level (usually 0.8). 3. Illustrated example and s
36、imulation results To clarify the performance of the model and solution approach, a simple example revised from the one in Kwong C K11! is introduced and some results are illustrated in this section. A corporation is developing a new type of digital camera. Figure 2 shows the HoQ of the digital camer
37、a design. The HoQ has six CNs which are “Photo quality” (CNi)， “Take distant image” (CN2)，“Low price”（ CN3) ， “Versatility”（ CN4)， “Easy to operate” （ CN5) ， and “Portability” （ CNe)_ These customer needs are translated into corresponding six engineering characteristics, namely 4Max. Resolution supp
38、ort” (ECi), “Optical zoom” (EC2)， “Aperture EC EC! EC2 EC3 EC4 EC, EC6 EC1 EC2 A EC3 A EC4 A A ECS EC6 A CN, 16.88 A CN2 9.5 CN3 8.95 A A CN4 23.74 CN5 25.02 A A A A CN8 15.9 A 參 unit Mp X - inch - g max 8 10 3 2.5 3 900 Min 2 1 0 1.5 1 100 Correlation: Relationship: #: Most Positive; Most Strong; :
39、 Positive; ; None; Moderate; : Negative; Weak; : Most Negative; Most Weak Fig. 2 House of quality for digital camera design exposure control” (EC3)， “LCD size” (EC4), “Storage media support”（ EC5) and “Weight”（ EC6). The relative importance of customer needs can be given by AHP12， 14】 and other meth
40、ods15j. In this example, the weight vector of customer needs has already been determined as W = (； l,2, = (16.88, 9.5, 8.95, 23.74,25.02,15.9)T For the sake of simplicity, triangular fuzzy numbers are used to represent the degrees of the relationships and correlations. The relationships between the
41、customer needs and engineering characteristics are linguistically judged as most weak, weak, moderate, strong, or very strong, which can be expressed by a predefined triangular fuzzy set 1，2，。 3，。 4，。 5， and U = (0,0,0.2), (0,0.25,0.5), C/3 = (0.3,0.5, 0.7) ， 仏 =(0.5,0_75 ， 1)， &5 = (0.7,1,1). These
42、 five triangular fuzzy membership functions are shown in Fig. 3. Similarly, the correlations between two engineering characteristics are linguistically judged as most negative, negative, none, positive ， most positive, and the correlation of itself, which can also be expressed by a pre-defined trian
43、gular fuzzy set HUH2,HHA)HHq, and Hr = (-l,-0.75, -0.5), H2 = (-0.5,-0.25,0), H3 = (-0.25,0,0.25), HA = (0,0.25,0.5), 5 = (0.5,0.75,1), H6 = (1,1,1). These triangular fuzzy membership functions are shown in Fig. 4. On the HoQ, the relationship matrix R and correlation matrix A are given as follows F
44、ig. 4 Membership function for the correlation Product design on the basis of fuzzy quality function deployment 1169 (0.5,0.75,1) (0.3,0.5,0.7) (0.7,1,1) (0,0,0.2) (0,0,0.2) (0,0,0.2) (0.5,0.75,1) (0.7,1,1) (0,0,0.2) (0.3,0.5,0.7) ( , , 0-2) ( , , 0-2) (0.5,0.75,1) (0.7,1,1) (0.7,1,1) (0.5,0.75,1) (0
45、,0.25,0.5) (0.5,0.75,1) (0.5,0.75,1) (0.5,0.75,1) (0.7,1,1) (0,0.25,0.5) (0.7,1,1) (0,0,0.2) (0,0.25,0.5) (0,0.25,0.5) (0,0.25,0.5) (0-7,1,1) (0,0.25,0.5) ( , , 0-2) ( , , 0.2) (0,0.25,0.5) (0.3,0.5,0.7) ( , , 0-2) ( , , 0.2) (0.7,1,1) (1,1,1) (0.5,0.75,1) (1，一 0,75, 一 0.5) (0,0.25,0.5) (1，一 0.75, 一
46、 0.5)(-l，一 0.75, 一 0.5) (0.5,0.75,1) (1,1,1) (-0.5, -0.25,0) (0,0.25,0.5) (-1,-0.75,-0.5) (0,0.25,0.5) (-l,-0.75,-0.5) (-0.5,-0.25,0) (1,1,1) (-0.25,0,0.25) (-1, -0.75, -0.5)(-l, -0.75, -0.5) (0,0.25,0.5) (0,0.25,0.5) (-0.25,0,0.25) (1,1,1) (-1， 一 0.75, 0.5) (0.5, -0.25,0) (1， -0.75, 0.5)(1， -0.75,
47、-0.5)(-l， 0.75, -0.5)(-1， -0.75, 0.5) (1,1,1) (-0.25,0,0.25) (-1, -0.75, -0.5) (0,0.25,0.5) (-1, -0.75, -0.5) (-0.5, -0.25,0) (-0.25,0,0.25) (1,1,1) _ With Eq. (14), the weights of planned degrees of engineering characteristics can be determined, and the results are as follows vi =(-1.197 1,0.133 9,
48、1-429 0), v2 = (-0.421 2,0.689 8,1.903 8), v3 - (-1.410 8, -0.290 1,0.589 9), vA = (-0.541 5,0.389 6,1.253 5), vb = (-2.706 7, -1.265 2, -0.027 0), v6 = (-1.679 4, -0.600 1,0.549 0). Using above data and the optimization model in Section 2.4, the following formulation is obtained max /i s.t. /i-0.392 9xi-0.932 6x2 + 0.114 lx3 -0.562 4a：4 + 1.017 6 工 5 + 0.370 3x6 ， /! - 1.4291.903 &r2-0.588 9x3 -1.253 5a： 4 + 0.027x5