Statistical Inference on Process Capability Index Cpyk for Inverse Rayleigh Distribution under Progressive Censoring

In quality engineering, process capability indexes are used to determine the capability of a process. The well-known of the process capability indexes are Cp, Cpk, Cpm, and Cpmk. These indexes assume the normality of the product lifetime. \citet{maiti2010generalizing} suggested a Cpyk as a generalized process capability index without distributional assumption. In this paper, the maximum likelihood and Bayesian inference on the Cpyk are studied under progressive censoring when the underlying distribution is inverse Rayleigh distribution. Furthermore, Bayesian credible and highest posterior density intervals are discussed with the MCMC procedure. Several types of bootsrap confidence intervals are also considered. A Monte Carlo simulation is conducted in terms of the coverage probabilities and mean lengths of the proposed intervals. An illustrative example is presented to close the paper.