Markov chain Monte Carlo in Bayesian models for testing gamma and lognormal S-type process qualities

Abstract

The process capability index Cpu is widely used to measure S-type process quality. Many researchers have presented adaptive techniques for assessing the true Cpu assuming normality. However, the quality characteristic is often abnormal, and the derived techniques based on the normality assumption could mislead the manager into making uninformed decisions. Therefore, this study provides an alternative method for assessing Cpu of non-normal processes. The Markov chain Monte Carlo, an emerging popular statistical tool, is integrated into Bayesian models to seek the empirical posterior distributions of specific gamma and lognormal parameters. Afterwards, the lower credible interval bound of Cpu can be derived for testing the non-normal process quality. Simulations show that the proposed method is adaptive and has good performance in terms of coverage probability.

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