Measurement of process capability indices for lower and upper tolerance with fuzzy parameters

Abstract

When the target value (T) is located in the midpoint of the specification interval (m). Traditional process capability indices (PCIs) are often employed for a process with a symmetric tolerance (T = m). In case a process with asymmetric tolerance (T≠m) traditional PCIs can be misleading. Process capability indices (PCIs) with asymmetric tolerance have been designed and successfully used in a crisp form in process capability analysis (PCA). These PCIs with asymmetric tolerance can benefit from the use of fuzzy set theory to deal with ambiguity and to add greater flexibility and sensitivity to mean variance, and target value (T), and specification limits (SLs). In order to produce fuzzy SLs of PCIs with asymmetric tolerance fuzzy mean, fuzzy variance and the fuzzy target value have been used. Furthermore, these PCIs are graphically represented. It is concluded that the intermediate values of fuzzy SLs can be explored, which is not achievable with crisp SLs. Furthermore, it is recommended to utilize fuzzy SLs of PCIs with asymmetric tolerance to monitor goods that fall outside specification limits due to their flexibility and sensitivity in a fuzzy environment. The proposed FPCIs were illustrated with a real-life example using piston diameters that were produced in a factory.