The identification of key quality characteristics based on FAHP

Transcription

1 Iteratioal Joural of Research i Egieerig ad Sciece (IJRES ISSN (Olie: , ISSN (Prit: Volume 3 Issue 6 ǁ Jue 2015 ǁ PP The idetificatio of ey quality characteristics based o FAHP Che Dejia,Mao Jia College of Mechaical Egieerig, Shaghai Uiversity of Egieerig Sciece, 333 Log Teg Road, Shaghai , Chia Correspodece should be addressed to Jia Mao; jmao@sues.edu.c Abstract: Aimig at the complexity of importace sortig for multiple quality characteristics of mechaical product, the fuzzy comprehesive method based o Fuzzy Aalytical Hierarchy Process (FAHP is put forward. Therefore, the problems existig i the computatioal process of covetioal methods is solved effectively. Fuzzy theory ad FAHP are itroduced to establish the importace sortig model for multiple quality characteristics. The, the weights are computed by the method of fuzzy compariso which is expressed by the triagular fuzzy umber. The ratioality ad feasibility of this method is illustrated by a practical example. Keywords: mechaical product; quality characteristics; sortig; fuzzy aalytical hierarchy process; I. Itroductio The quality of the product eed to use multiple quality characteristics to describe, ad each quality characteristic must meet their specificatios, the product quality is the result of these comprehesive features [1]. The complex mechaical products, such as high precisio machie tool, the quality characteristics have diversity i differet subsystems ad differet levels. The quality characteristic of the mechaical products have characteristic of multidiscipliary ad multi-field itersectig i the field of characteristic; O the performace characteristics, it has the character of precisio, reliability ad availability; O the structural characteristics, it has multiple compoets ad structure features. Quality characteristic of importace are also differet, it geerally divided ito the ey quality characteristic, the importat quality characteristic ad the geeral quality characteristic, the ey ad importat quality characteristic eed to be ey-poit cotrol. Therefore, how to determie the importace degree of quality characteristic of mechaical product? This becomes the primary tas of product developmet process. I recet years, scholars at home ad abroad has carried o the related research for the quality characteristic of mechaical product. Zhag gebao et al. [2] through the statistics methods of Artificial Neural Networs (ANNs, the relative importace of techical specificatios of VOC ad the reflectig weights of each level are obtaied. A model of the ey quality characteristics of complicated mechaical products based o ANNs techology is formulated. Zhag gebao et al. [3] aimed at the complexity of importace sortig for multiple quality characteristics of mechaical product, the fuzzy comprehesive method based o Fuzzy Aalytical Hierarchy Process ad iformatio etropy was preseted. Therefore, the subjective ad ambiguous problems existig i the computatioal process of covetioal methods was solved effectively. Ya wei et al. [4] proposed the improved iformatio gai (IG algorithm to process such high-dimesio imbalace data. By this method, it reduces the ifluece of imbalace data o the performace such that the idetificatio of critical-to-quality characteristics (CTQ is sigificatly improved. Wag ig et al. [5] put forward a idetificatio method for ey quality characteristics i multi-stage maufacturig process by combiig the Partial Least Squares Regressio method 1 Page

2 The idetificatio of ey quality characteristics based o FAHP with the state space model to improve the existig methods of idetifyig the ey quality characteristics i multistage maufacturig process. He Yihai et al. [6] grasped the defiitio of the quality characteristics(qcs, the three-layer model ad techical cootatio of quality characteristics are preseted, the evolutio process model of ey quality characteristics(kqcs is created, ad the ey activities of KQCs evolutio are discussed i the cotext of desig for quality(dfq. Yu Hogji [7] established a model of the multi-stage productio process quality characteristic. Though this model describes the differet productio process quality characteristics trasitive relatio, ad ultimately this method ca idetify the ey quality characteristics of the multi-stage productio process. Tag Weibi et al. [8] proposed a systematic top dow decompositio approach for the idetificatio of ey characteristics. The methodology of the idetificatio ad decompositio of ey characteristics ca be divided ito two steps: first is the costructio of cadidate characteristics, ad secod is the idetificatio of ey characteristics. Ji Fuyi [9] based the simplified model of evolutio chai to machiig process, usig QFD ad eural etwor techiques, the extractio techology of ey quality characteristics is put forward i the product machiig process. From the above research situatio at home ad abroad, we ca be see that it has made great achievemets about the complexity of importace sortig for multiple quality characteristics of mechaical product ow. Fuzzy Aalytic Hierarchy Process fully cosidered the fuzziess of thiig, ad esured reliability ad the scietificess of the sortig for the multiple quality characteristics. I this paper, the comprehesive sortig method based o FAHP is put forward, this method accordig to the properties of the products to build aalysis model of multiple quality characteristics, ad the use FAHP goig to sort for multiple quality characteristics. Therefore, the reasoable ad accurate sortig result is obtaied. II. The idetificatio of ey quality characteristics FAHP is a id of multi-objective decisio method to solve the problem of multi-layered structure, it combie qualitative ad quatitative decisio reasoably, accordig to the law of thiig, psychological to hierarchical decisio-maig process ad quatificatio. I view of the quality characteristics of multilayered, diversity ad complexity, this article first aalyzes the ucertaity of importace sortig for multiple quality characteristics, applyig triagle fuzzy umbers of the FAHP, usig the method of pairwise compariso to judge the weight of multiple quality characteristics idex. The sortig method that based o multivariate quality characteristics of FAHP maily icludes the followig steps. 2.1 Calculatio of membership Usig triagular fuzzy umber to express the fuzzy set M = (l, m, r, the M's membership fuctios as follows: u x = x l /(m l, x [l, m; x r /(m r, x [m, r; 0, else (1 0 l m r, l ad r is M upper ad lower bouds respectively i this formula. The membership fuctio of triagular fuzzy umber [10] is show i figure 1. 2 Page

3 The idetificatio of ey quality characteristics based o FAHP u(x 1 0 l m r x follows: Fig.1. The triagular fuzzy umber Settig M= (l 1, m 1, r 1, N= (l 2, m 2, r 2 as the two triagular fuzzy Numbers, the calculatio of fuzzy math as the possibility of N M l 1 r 2 (m 2 r 2 (m 1 l 1, l L N M = 1 r 2 0, else 2.2 The structure of the judgmet matrix for triagular fuzzy Accordig to the defiitio of AHP s relative importace, usig the method of pairwise compariso to compare the various idex of the layer, so that usig triagular fuzzy umber to express it. Usig triagular fuzzy Numbers to go quatitative represetatio, so that get fuzzy judgmet matrix A=R ij. Fuzzy matrix is still positive ad egative iverse matrix, the calculatig formula as follows R ij 1 = R ij = ( The calculatio of comprehesive value The defiitio of fuzzy umber 1,, 1 r ij m ij (2 l ij (3 j =1 M ij = l ij j =1, m ij, r ij j =1 j =1, (4 M ij = 1 3 M ij j =1 i, j = 1,2,, (5 So composite triagular fuzzy degrees of the layer as follows: 1 Y i = M ij M ij j =1 i=1 j =1 (6 2.4 Hierarchical sigle sortig L Y i Y j = mi [L Y i Y 1,, L Y i Y j,, L Y i Y ] (7 Settig D A i = L Y i Y j, the A i is the i factor for the layer, the weight vector as follows: W = (D A 1, D A 2,, D A T (8 2.5 The ormalized The layer of all the elemets mae the total target about the sythesis of sortig as follows 3 Page

4 The idetificatio of ey quality characteristics based o FAHP W = (D A 1 D A i, D A 2 D A i, D A D A i T i=1 i=1 i=1 Accordig to the size of the weight W go to sort, the larger the value, to the top. (9 III. Numerical example This is a trasmissio actuator as show i figure 2, it is cosist of the belt wheel, rig flage, ey, base ad trasmissio shaft. The base is a importat part i the trasmissio actuator, its desig as show i figure 3, we first aalyze ad list all the quality characteristics of the base the maufacturig process, ad the build a hierarchical structure tree, as show i figure 4. Fig.2. The explosio figure of the trasmissio actuator Fig.3. Desig drawig of the base 4 Page

5 The idetificatio of ey quality characteristics based o FAHP The multivariate quality characteristics of base A Surface quality B 1 Dimesioal tolerace B 2 Form ad positio error B 3 Fudametal dimesios B 4 Roughess a1 Roughess a2 Roughess a3 Roughess a4 Roughess a5 Dimesio d6 Dimesio d5 Dimesio d4 Dimesio d3 Dimesio d2 Dimesio d1 Cocetricity c2 Cocetricity c1 Dimesio b5 Dimesio b4 Dimesio b3 Dimesio b2 Dimesio b1 Fig.4. The quality characteristics tree of the base Settig three experts have the equal weight coefficiet, maig score for the surface quality, dimesioal tolerace, form ad positio error, ad fudametal dimesio (expressed i B1 ~ B4, gettig the triagular fuzzy compariso matrix, as show i table 1. Table 1 The compariso matrix of Triagular fuzzy umber A B 1 B 2 B 3 B 4 B 1 2/3 3 3/2 2/5 2 2/3 2/ /3 4 3/2 1/3 2 5/2 2/3 3 3/2 2/7 5 2/5 2/3 3 1/2 2/5 5 2/3 B 2 2/3 1/3 3/2 3/2 1/2 5/2 2/5 1/5 3/2 5/2 3 7/2 3/2 2 5/2 5/2 3 7/2 1 1/2 3/2 2 2/5 3/2 2 2/3 5/2 B 3 2/3 1/4 3/2 2/5 1/2 2 2/3 1/3 3/2 2/7 1/3 2/5 2/5 1/2 2/3 2/7 1/3 2/5 2/5 2 1/2 1/2 1 2/3 2/5 2 1/3 B 4 5/2 1/5 7/2 2 1/3 5/2 3/2 1/5 5/2 2/ /3 1/2 5/2 2/5 1/2 3/2 2 1/2 5/2 3/ /2 5/2 By the formula (4 ad formula (5 calculate the triagular fuzzy umber, the result as show i table 2. Table 2 Comprehesive triagular fuzzy umber A B 1 B 2 B 3 B 4 B 1 (1.000, 1.000, (0.578,3.333,1.556 (0.611,3.000,1.833 (0.451,4.333, B 2 (0.856,0.344,1.833 (1.000, (2.167,2.667,3.167 (0.522,1.667, ,1.000 B 3 (0.578,0.361,1.667 (0.324,0.389,0.489 (1.000, 1.000, (0.433,1.667, B 4 (2.000,0.244,2.500 (0.578,0.667,2.000 (2.167,0.667,2.333 (1.000, 1.000, Page

6 The idetificatio of ey quality characteristics based o FAHP By the formula (6 calculate the comprehesive triagular fuzzy degree as follows: Y 1 = 2.640,11.667, , , = (0.109,0.499,0.321 Y 2 = 4.454,5.678, , , = (0.188,0.243,0.513 Y 3 = 2.335,3.417, , , = (0.096,0.146,0.240 Y 4 = 5.744,2.578, , , = (0.237,0.110,0.513 By the formula (2 ad formula (7 calculate the weight of each idicator as follows: L Y 1 Y 2 = 1, L Y 1 Y 3 = 1, L Y 1 Y 4 = 1; L Y 2 Y 1 = 0.611, L Y 2 Y 3 = 1, L Y 2 Y 4 = 1; L Y 3 Y 1 = 0.270, L Y 3 Y 2 = 0.349, L Y 3 Y 4 = 1; L Y 4 Y 1 = 0.509, L Y 4 Y 2 = 0.710, L Y 4 Y 3 = D B 1 = L Y 1 Y 2, Y 3, Y 4 = mi 1,1,1 = 1; D B 2 = L Y 2 Y 1, Y 3, Y 4 = mi 0.612,1,1 = 0.611; D B 3 = L Y 3 Y 1, Y 2, Y 4 = mi 0.270,0.349,1 = 0.270; D B 4 = L Y 4 Y 1, Y 2, Y 3 = mi 0.509,0.710,0.920 = By the formula (8 calculate the weight vector as follows: W = (1.000,0.611,0.270,0.509 By the formula (9 get the sort of weight as follows: W A = (0.418,0.256,0.113,0.213 Usig the same method to calculate the layer 2 idex, gettig the correspodig weights of sortig as follows: W B1 = 0.374,0.131,0.126,0.104,0.265, W B2 = 0.295,0.184,0.132,0.218,0.171, W B3 = 0.723,0.177, W B4 = (0.190,0.150,0.146,0.252,0.135,0.127 Accordig to the idicators of layer 1 ad layer 2, gettig the fial results: W=(0.156,0.055,0.053,0.043,0.111,0.076,0.046,0.034,0.056,0.044,0.082,0.031,0.040,0.032,0.031,0.0 54,0.029,0.027 The quality characteristics have a total of 18 i this istace, accordig to the 2/8 priciple, we ca choose 4 as the ey quality characteristics, amely roughess a1, roughess a5, dimesio b1 ad cocetricity c1. IV. Coclusio The sortig for multiple quality characteristics of mechaical product is a complex problem. I this paper, aimig at the complexity of the sortig for multivariate quality characteristics, The comprehesive method based o triagular fuzzy umber of FAHP is used, the ambiguous problems existig i the computatioal process of covetioal methods is solved effectively, the the accuracy ad ratioality for sortig is improved. Form this example, we ca be see that the method is more reasoable ad practical, ad provides a ew trai of thought for the sortig of multiple quality characteristics. V. Acowledgemets We would lie to acowledge the support of the Natioal Natural Sciece Foudatio of the People s Republic of Chia (No Referece [1] Tia Xiao. The quality ispectio of mechaical product [M]. Beijig: Chia metrology press, 2006 [2] Zhag Gebao, Ji Yifu, Re Xiali, Ge Hogyu, Zhag Shuhui. Key quality characteristics extractio model of complicated mechaical ad electrical products [J]. Joural of Chog qig Uiversity, 2010, 2(33:8-14 [3] Zhag Gebao, Pag Jihog, Re Xiali, Che Guohua. Importace sortig method for multiple quality characteristics of 6 Page

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