Bayesian testing for process capability indices

Abstract

Process capability indices have been widely used in the manufacturing industry. They measure the ability of a manufacturing process to produce items that meet certain specifications. A capability index relates the voice of the customer (specification limits) to the voice of the process. There is a need to understand and interpret process capability indices. Most of the existing work in this area has been devoted to classical frequentist large sample theory. An alternative approach to the problem of making inference about capability indices is the Bayesian approach. In this paper a Bayesian version of Tukey’s method is used for constructing simultaneous credibility intervals for all pairwise differences. A Bayesian procedure for testing all possible contrasts is also given. The problem of selecting the best supplier(s) has received considerable attention in the literature, but mainly from a classical frequentist point of view. A Bayesian simulation procedure is also illustrated to find the best supplier or group of suppliers.
This method seems much easier to perform than the Monte Carlo integration method given in Wu, Shiau, Pearn and Hung (2016). In section 10, a sensitivity analysis regarding the prior choice is considered and in the last section, t-distributed data are analysed.