Assessing process capability based on Bayesian approach with subsamples

Process capability indices (PCIs) have been widely used to measure the actual process information with respect to the manufacturing specifications, and become the common language for process quality between the customer and the supplier. Most of existing research works for capability testing are based on the traditional frequentist point of view and statistical properties of the estimated PCIs are derived based on the assumption of one single sample. In this paper, we consider the problem of estimating and testing process capability using Bayesian approach based on subsamples collected over time from an in-control process. The posterior probability and the credible interval for the most popular index _Cpk$C_{\mathit{pk}}$ under a non-informative prior are derived. The manufacturers can use the presented approach to perform capability testing and determine whether their processes are capable of reproducing product items satisfying customers’ stringent quality requirements when a daily-based or weekly-based production control plan is implemented for monitoring process stability.