Parametric estimation of PCI C * pm under doubly type II censored sampling scheme with application to electronics industry data

This study investigates the estimation of the process capability index Cpm∗ for the Chen distribution under Doubly Type II Censored Sampling (DTIICS) Scheme. Estimators of Cpm∗ are developed within both classical and Bayesian frameworks. In the classical domain, three estimation methods are employed: maximum likelihood, least squares, and Cramér-von Mises. The Bayesian estimators are derived under the squared error loss function and the asymmetric linear exponential loss function, assuming gamma priors for the model parameters. Beyond point estimation, approximate confidence intervals for Cpm∗ are obtained via classical technique and compared with highest posterior density credible intervals from the Bayesian approach. Using multiple optimality criteria, an optimal DTIICS design is also proposed. A comprehensive simulation study is carried out to assess the finite-sample performance of classical and Bayesian estimators. The evaluation focuses on mean squared error, as well as the properties of confidence intervals (CIs) and highest posterior density (HPD) intervals, including their average width and coverage probability. The findings reveal that, among classical approaches, the maximum likelihood estimator (MLE) consistently outperforms alternatives across different parameter settings, sample sizes, and censoring schemes. Moreover, Bayesian estimators demonstrate better performance compared to their classical counterparts. The practical applicability and robustness of the proposed methodology are further illustrated through an analysis of real data on electronic device failures.