Fuzzy confidence regions for the Taguchi capability index
Most of the traditional methods for assessing the capability of manufacturing processes are dealing with crisp quality. In quality control, such as other statistical problems, we may confront imprecise concepts. One case is a situation in which specification limits (SLs) are imprecise. In this situation, the fuzzy process capability indices (PCIs) (C) over tilde (p), (C) over tilde (pk) and (C) over tilde (pm) are necessary for measuring the fuzzy quality in an in-control process. These fuzzy capability indices are also helpful for comparing manufacturing processes with SLs. The fuzzy capability index (C) over tilde (pm) is used to provide an assessment of the ability of the fuzzy process to be clustered around the target value. The emphasis on the use of (C) over tilde (pm) over the other two fuzzy indices, (C) over tilde (p) and (C) over tilde (pk), is due to its definition that provides indications of both the process variability and deviation of process mean from a specified target. In this article, by using triangular fuzzy SLs, we present four approximate 100(1 - alpha)% fuzzy confidence regions for the fuzzy PCI (C) over tilde (pm). A numerical example is given to show the performance of the method.
confidence region triangular fuzzy numbers process capability index fuzzy statistics ranking function