Bayesian and classical inference of the process capability index under progressive type-II censoring scheme

This article uses the maximum likelihood technique, the bootstrap method, and the Markov chain Monte Carlo method to estimate the process capability index (C py ) for the generalised inverted exponential distribution. These methods are all based on the progressive Type-II censoring scheme. In reliability analysis, the generalised inverted exponential distribution is a frequently used distribution, and the C py is a critical tool in statistical process control. The manuscript proposes a comparative study of the three methods for estimating C py , and their performance is evaluated using simulation studies. Furthermore, three examples of real data is examined to show all the estimation approaches. The results demonstrate that all three methods can provide accurate estimates of C py , with the Markov chain Monte Carlo method having an advantage in providing more information on the uncertainty of the estimates. The manuscript concludes that the proposed methods can be useful in practice for estimating C py for the generalised inverted exponential distribution based on progressive Type-II censoring scheme, providing an objective measure of process performance and helping organizations to optimize their production processes.