Making decision to evaluate process capability index C _p with fuzzy numbers

Abstract

The process capability index C _p has wide applications in the manufacturing industry. This paper extends those applications to a fuzzy environment, with a methodology for testing the index C _p of fuzzy numbers. A pair of nonlinear functions is formulated to find the α-cut of index $\widetilde{C}_{p}$. From various values of α, the membership function of index $\widetilde{C}_{p}$ is constructed, and the probability of rejecting the null hypothesis is calculated based on this membership function. Different from classical tests, the statistical decision proposed in this paper shows a grade of acceptability of the null hypothesis and the alternative hypothesis, respectively. With crisp values, the developed approach not only can boil down to the classical formula for calculating Ĉ _p , but also lead to a binary decision: to reject or to accept the null hypothesis. An example is used to illustrate the performance of the proposed approach.