Process capability analyses with fuzzy parameters

Process capability indices (PCIs) can be viewed as the effective and excellent means of measuring product quality and process performance. They are very useful statistical analysis tools to summarize process dispersion and location by using process capability analysis (PCA). However, there are some limitations which prevent a deep and flexible analysis because of the crisp definition of PCA’s parameters. In this paper, the fuzzy set theory is used to add more information and flexibility to PCA. For this aim, fuzzy process mean, μ ˜ and fuzzy variance, σ ˜ 2 , which are obtained by using the fuzzy extension principle, are used. Then fuzzy specification limits (SLs) are used together with μ ˜ and σ ˜ 2 to produce fuzzy PCIs (FPCIs). The fuzzy formulations of the indices Cp, Cpk, Ca, Cpm, and Cpmk which are the most used traditional PCIs, are developed and a numerical example for each from an automotive company is given. The results show that fuzzy estimations of PCIs have much more treasure to evaluate the process performance when it is compared with the crisp case.