Fuzzy process capability analysis and applications

Process capability indices (PCIs) are very useful statistical analysis tools to summarize process' dispersion and location through process capability analysis (PCA). PCIs are mainly used in industry to measure the capability of a process to produce products meeting specifications. Traditionally, the specifications are defined as crisp numbers. Sometimes, the specification limits (SLs) can be expressed in linguistic terms. Traditional PCIs cannot be applied for this kind of data. There are also some limitations which prevent a deep and flexible analysis because of the crisp definition of SLs. In this chapter, the fuzzy set theory is used to add more sensitiveness to PCA including more information and flexibility. The fuzzy PCA is developed when the specifications limits are represented by triangular or trapezoidal fuzzy numbers. Crisp SLs with fuzzy normal distribution are used to calculate the fuzzy percentages of conforming (FCIs) and nonconforming (FNCIs) items by taking into account fuzzy process mean, μ̃ and fuzzy variance, σ̃². Then fuzzy SLs are used together with μ̃ and σ̃² to produce fuzzy PCIs (FPCIs). FPCIs are analyzed under the existence of correlation and thus fuzzy robust process capability indices are obtained. Then FPCIs are improved for six sigma approach. And additionally, process accuracy index is analyzed under fuzzy environment. The results show that fuzzy estimations of PCIs have much more treasure to evaluate the process when it is compared with the crisp case.