Bayesian sequential estimation and evaluation of process capability indices with multiple subsamples

Process capability analysis is designed to estimate the proportion of parts that do not meet engineering requirements in a stable production process. Using process capability indices to quantify manufacturing process precision and performance is essential part of implementing any quality improvement program. In this paper, we proposed a Bayesian sequential approach to estimate and evaluate the process capability based on multiple subsamples. Its advantage is that the parameters¿ posterior distribution in the current states is considered to be their prior distribution in the next state, thus reducing the variance of the estimators through the use of the information about the past production manufacturing process. According to the parameters¿ sequential posteriors, we establish the point estimation and the one-sided confidence interval for the process capability. Finally, we give an example to illustrate application of the proposed approach.