A Bayesian approach for assessing process precision based on multiple samples

Using process capability indices to quantify manufacturing process precision (consistency) and performance, is an essential part of implementing any quality improvement program. Most research works for testing the capability indices have focused on using the traditional distribution frequency approaches. Cheng and Spiring proposed a Bayesian procedure for assessing process capability index Cp based on one single sample. In practice, manufacturing information regarding product quality characteristic is often derived from multiple samples, particularly when a routine-based quality control plan is implemented for monitoring process stability. In this paper, we consider estimating and testing Cp with multiple samples using Bayesian approach, and propose accordingly a Bayesian procedure for capability testing. The posterior probability, p, for which the process under investigation is capable, is derived. The credible interval, a Bayesian analogue of the classical lower confidence interval, is obtained. The results obtained in this paper are generalizations of those obtained in Cheng and Spiring. Practitioners can use the proposed procedure determine whether their manufacturing processes are capable of reproducing products satisfying the preset precision requirement.