Classical and Bayesian Reliability Inference for Step‐Stress Accelerated Life Tests Under Progressive Type‐II Censoring Using the Exponential Power Lifetimes

ABSTRACT Step‐stress partially accelerated life tests (SSPALTs) have received considerable attention in both industrial and academic settings as effective tools for inducing early failures and generating informative data for reliability analysis. In this article, we develop statistical inference procedures and examine the optimal censoring design for SSPALTs under a progressive Type‐II censoring scheme (PTII‐CS), assuming that the lifetimes of test units follow a two‐parameter exponential power distribution. The proposed censoring scheme offers a practical and flexible rule for terminating the experiment based on a pre‐specified number of observed failures. Both maximum likelihood and Bayesian approaches are employed to estimate the unknown model parameters, including the acceleration factor. Under normal operating conditions, estimators of the reliability function, hazard rate function, and mean time to failure are derived using both methods. To assess estimation uncertainty, approximate confidence intervals (CIs) are constructed along with two bootstrap‐based procedures, namely the percentile bootstrap (Bootstrap‐p) and the studentized bootstrap (Bootstrap‐t). Within the Bayesian framework, two loss functions—covering both symmetric and asymmetric forms—are considered. Independent piecewise gamma prior distributions are assumed for the model parameters, and highest posterior density (HPD) credible intervals are obtained for the parameters as well as for the associated reliability characteristics. A comprehensive Monte Carlo simulation study is conducted under various sample sizes and censoring schemes to evaluate and compare the performance of the proposed estimation methods. Furthermore, the optimal design of the PTII‐CS is systematically investigated using multiple optimality criteria to ensure efficient and reliable parameter estimation. Finally, two real data examples are presented to illustrate the practical applicability and effectiveness of the proposed inferential procedures and optimal design strategy.