On the confidence intervals of process capability index Cpm based on a progressive type-II censored sample

This paper is concerned with the process capability index in the case of the progressively type-II censored sample. In particular, the asymptotic distribution of maximum likelihood estimators of the process capability index is derived and it is used to construct the approximate confidence intervals with the delta rule. In addition, five parametric bootstrap confidence intervals for the (Formula presented.) index are discussed, in contrast to approximate confidence intervals, do not require second derivatives of the likelihood function. A Monte Carlo simulation study is performed to observe the coverage probabilities and the average width of these intervals. Simulation results indicate that the approximate confidence interval is better than the bootstrap based confidence intervals in terms of the coverage probabilities. Two practical examples are presented to illustrate the usability of the method discussed here.