Measuring Loss-Based Process Capability Index Le and Its Generation Le with Fuzzy Numbers

Abstract

Loss-based process capability indices are appropriate and realistic tools in order to measure the process capability. Among them, index Le and its generation Le are well-known loss-based process capability indices, whose concepts are based on the worth (the opposite concept of loss). Sometimes, in order to calculate Le and Le there are some uncertainties in observations, so fuzzy logic can be employed to manage the uncertainties. This paper investigates fuzzification of process capability index Le and its generation Le. In order to find the membership function of process capability indices Le and Le, the α-cuts of fuzzy observation were employed. Then with an example of fuzzy process capability index, Le and Le were calculated and compared. Results showed that fuzzy Le was more sensitive compared with Le and was increased while the target departs (asymmetric tolerance). This example also showed that, with departure from the target, variation of fuzzy Le and consequently its fuzziness were increased.