A casting may be defined as a metal object obtained by allowing molten metal to solidify in a mould, the shape of the object being determined by the shape of the mould cavity. Defective castings, even at advanced foundries, account for 2 to 5% and sometimes from 10 to 25% of the number of produced castings. This leads to heavy loss to the foundries. Hence in this paper, a methodology to reduce defects in casting process has been proposed. The product considered for the study is car brake drum. Quality Function Deployment (QFD) is a customer-oriented tool for new or existing product development to maximize customer satisfaction. Identification of fulfillment levels of design requirements (DRs) and parts characteristics (PCs) is an important task in QFD activity process of new product development. The relationships between customer requirements (CRs) and design requirements (DRs) as well as among DRs are implemented using a relation matrix, also called a House of Quality (HOQ). Using traditional QFD process for relating the CRs and DRs as well as among DRs has been criticized by various authors. In this paper, fuzzy linear programming models have been used to determine the fulfillment levels of parts characteristics (PCs) of a casting product. The degree of importance of each customer requirements (CRs) is identified using Fuzzy Analytic Hierarchy Process (FAHP) approach. Based on the results from fuzzy QFD process, the fulfillment levels of design requirements (DRs) and parts characteristics (PCs) are determined.
Keywords-Brake drum casting, Fuzzy QFD, Fuzzy AHP, Fuzzy linear programming
[...] The steps of Chang's extent analysis can be given as in the following: Step:1 The value of fuzzy synthetic extent with respect to the ith object is defined as ª n m jº Si = M M gi j=1 1 j 1 m j gi To obtain Mjgi the fuzzy addition operation of m extent analysis values for a particular matrix are performed such as m m m l j , mj , u j j 1 j1 i 1 n j Mgi j 1 m V(M M1,M2, Mk) = V M1) and M2) and . [...]
[...] However, most studies concentrates on the priority of DRs or achievement levels of DRs in phase 1. In this paper, both the phase 1 and 2 are considered. Based on the mathematical programming for phase 1 using the fuzzy logic, this paper considers the close link between the two phases to build up a fuzzy linear programming model for phase 2 in determining the fulfillment levels of PCs. For reducing the design risk, risk analysis of DRs, namely a fuzzy FMEA is taken into account in the phase 2 model. [...]
[...] Based on the above steps the degree of importance weights of each customer requirements are calculated as Shown in Table II Table II The degree of importance weights for each customer requirements Customer The degree of importance weights requirements of each customer requirements C1 C2 C3 C4 C5 C ª n m jº and obtain M gi , perform the fuzzy addition 1 j 1 operation of M gi values is performed such as: j i 1 n j M gi j 1 m n n n li , mi , ui i 1 i1 and then compute the inverse of the vector above such as ª n 1 º j Mgi j 1 m n , n , n u i mi li i 1 i 1 Step: 2 As M1= (l1,m1,u1) and M2=(l2, m2, u2) are two triangular fuzzy numbers, the degree of possibility of M2= m2, u2) M1= m1, u1) is defined as V(M2 M1) = V FUZZY LINEAR PROGRAMMING APPROACH TO QFD For implementing QFD processes, a relation matrix, also called a House of Quality is usually used for each phase to construct the input-output relationships in determining the achievement priority or level of output variables. [...]
[...] proposed a methodology of determining aggregated importance of engineering characteristics in QFD which involves the consideration of conventional meaning of importance of engineering characteristics (ECs) as well as the impacts of an EC on other ECs. In this methodology, fuzzy relation measures between CRs and ECs as well as fuzzy correlation measures among ECs are determined based on fuzzy expert systems approach. These two measures are then used to determine the aggregated importance of ECs. Ertugrul Karsak proposed a fuzzy multiple objective programming framework to prioritize design requirements in quality function deployment to incorporate imprecise and subjective information inherent in the QFD planning process to determine the level of fulfillment of design requirements. [...]
[...] The proposed model is illustrated with a numerical example (casting defects of car Table VI The lower and upper bounds of fuzzy importance ratings of PCs in various levels WL WU WL WU WL WU WL WU WL WU WL WU Table VII The fuzzy risk ratings of PCs in various RiL RiU RiL RiU RiL RiU RiL RiU RiL RiU RiL RiU Table VIII The cost and technical ability for each PC Fulfillment level x2,1 x2,2 x2,3 x2,4 x2,5 x2,6 C2,k ( ) ( ) ( ) ( ) ( ) ( ) - cut [ 0.2 + - 0.1 ] [ 0.4 + - 0.1 ] [ 0.4 + - 0.1 ] [ 0.3 + - 0.1 ] [ 0.3 + - 0.1 ] [ 0.0 + - 0.1 ] 2,k Table IX The ranges for the fulfillment levels of x2,k in the second stage QFD process xL xU xL xU xL xU xL xU xL xU xL xU brake drum) to demonstrate the applicability in practice. [...]
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