Bayesian and classical estimation of PCI ℂ _<i>s</i> under multiple interval type-II censoring with log-logistic distribution

{Classical and Bayesian methods are employed to construct point and interval estimators of the process capability index C, with performance evaluated via Monte Carlo simulation under multiple interval type-II censoring} This paper investigates the estimation of the process capability index Cs for the log–logistic distribution under a newly proposed multiple interval type–II censoring scheme. Three estimation approaches are considered: maximum likelihood estimation, maximum product of spacings, and Bayesian inference. Within the Bayesian framework, both the likelihood and product of spacings functions are employed under two loss functions, namely the squared error loss and the linear exponential (LINEX) loss, assuming gamma prior distributions for the model parameters. In addition to point estimation, interval estimation is carried out by constructing approximate confidence intervals using classical methods and comparing them with highest posterior density credible intervals obtained from Bayesian procedures. Furthermore, percentile bootstrap confidence intervals based on both the likelihood function and the product of spacings function are also obtained. A comprehensive Monte Carlo simulation study is conducted to evaluate the finite-sample performance of the proposed estimators. Further, the optimal multiple interval type–II censoring plan is examined under different optimality criteria. Finally, the practical applicability of the proposed methods is demonstrated through the analysis of two real-life data sets.