Lower bayesian confidence limits on the process capability index c_pm: A comparative study

The main focus of this paper is on a particular type of process capability indices, termed C _pm in the quality control community, enabling to consider proximity of the process center to the pre-specified target value as well as process inherent variability altogether whilst investigating process capability. In order to take the probabilistic properties of the point estimator used on C _pm into account, the key element of this study is to present a generalized Bayes-type approach that allows for the construction of a lower interval limit for the process measure C _pm. In comparison to the classical analogue for C _pm (built upon the traditional frequentist theory) entailing a non-central chi-square distribution that the practitioners are generally unfamiliar with, the Bayesian method relates simply to the integration of a gamma distribution. The lower Bayesian interval estimate on C _pm is also compared with the other three lower confidence bounds posed in the literature and then various experimental studies under a number of process parameter configurations assumed are conducted to illustrate practical guidance about the types of processes for which the Bayesian-based procedure might be advantageous. Directions of how to choose adequate lower confidence limits on C _pm for practical use are reported as well.