A Bayesian approach for measuring process performance with asymmetric tolerances

Abstract

Process capability indices have been widely investigated as a means of summarising process performance relative to a set of specification limits. However, most research works in the literature were restricted to handle processes with symmetric tolerances. Recently, a generalised capability index has been proposed to measure process performance with asymmetric tolerances. Consequently, in this paper we consider the problem of estimating and testing the generalised index for processes with asymmetric tolerances based on Bayesian approach. The posterior probability p for which the process with an asymmetric tolerance under investigation is capable, is derived. The credibility interval, a Bayesian analogue of the classical lower confidence interval, can also be obtained. Practitioners can use the obtained results to perform capability testing and determine whether their manufacturing processes are capable of reproducing products satisfying the preset process capability requirement whenever the manufacturing tolerance is asymmetric or symmetric.