Classical and objective Bayesian inference of Cpy for first-failure progressively censored samples

This article takes into account the estimation of the process capability index (PCI), $C_{py}$ using first failure progressive censoring scheme (FFPCS). On the basis of FFPCS, $C_{py}$ is estimated for the inverse Nakagami distribution using maximum likelihood (ML), maximum product spacing (MPS) and Bayesian estimation methods. Bayes estimator of $C_{py}$ is obtained under squared error and linear exponential loss functions using objective prior. Besides, approximate confidence intervals (CIs) for the index $C_{py}$ using both classical methods are obtained and compared with the highest posterior density (HPD) credible intervals. Finally, a simulated study is performed to assess the finite sample performance of the proposed point estimates of $C_{py}$ based on mean squared errors (MSEs) and interval estimates are compared with their average length and coverage probabilities. In order to demonstrate the usefulness of the proposed index and estimation techniques, one real data set from the agricultural machine elevators is reanalyzed.