Fuzzy process capability indices with asymmetric tolerances

Abstract

Process performance can be analyzed by using process capability indices (PCIs), which are summary statistics to depict the process location and dispersion successfully. Traditional PCIs are generally used for a process which has a symmetric tolerance when the target value ( T) locates on the midpoint of the specification interval ( m). When this is not the case ( T ≠ m), there are serious disadvantages in the casual use and interpretation of traditional PCIs. To overcome these problems, PCIs with asymmetric tolerances have been developed and applied successfully. Although PCIs are very usable statistics, they have some limitations which prevent a deep and flexible analysis because of the crisp definitions for specification limits (SLs), mean, and variance. In this paper, the fuzzy set theory is used to add more information and flexibility to PCIs with asymmetric tolerances. For this aim, fuzzy process mean, μ ˜ and fuzzy variance, σ ˜ 2 , which are obtained by using the fuzzy extension principle, are used together with fuzzy specification limits (SLs) and target value ( T) to produce fuzzy PCIs with asymmetric tolerances. The fuzzy formulations of the indices C ∼ pk ″ , C ∼ pm ∗ , C ∼ pmk ″ , which are the most used PCIs with asymmetric tolerances, are developed. Then a real case application from an automotive company is given. The results show that fuzzy estimations of PCIs with asymmetric tolerances include more information and flexibility to evaluate the process performance when it is compared with the crisp case.