Classical and non-informative bayesian inference of Spmk for Nakagami distribution based on first-failure progressively censored samples

This study uses the Progressive First Failure Type-II Censoring Scheme (PFFT2CS) to estimate the Process Capability Index (PCI), Spmk, for the Nakagami Distribution (ND). Using maximum likelihood, maximum product spacing, and Bayesian estimation techniques, Spmk is calculated on the basis of PFFT2CS. Using noninformative prior, the Bayes estimator of Spmk is produced for the linear exponential (LINEX) loss function, the squared error loss function, and the generalised entropy loss function. Additionally, the approximate confidence intervals (CIs) for the index Spmk that were derived using both traditional approaches and the highest posterior density (HPD) credible intervals are compared. The performance of the classical and Bayes estimates of Spmk with respect to their mean squared errors is evaluated in a simulation exercise, and the average width and coverage probabilities of the CIs and HPDs intervals are compared. Two actual data sets are reanalyzed in order to illustrate the efficacy of the suggested index and estimation approaches.