Making decision to evaluate process capability index Cp with fuzzy numbers

The process capability index Cp has wide applications in the manufacturing industry. This paper extends those applications to a fuzzy environment, with a methodology for testing the index Cp 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 Ĉp, 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.