Inference on the Chen Distribution Under Step-Stress Accelerated Life Testing with Hybrid Censoring

This paper develops classical and Bayesian inferential procedures for the Chen distribution under a simple step-stress accelerated life test with Type-I hybrid censoring. The cumulative exposure model links lifetime distributions across stress levels, while the censoring scheme limits the test duration and permits earlier termination once a prespecified number of failures is observed. Maximum likelihood and maximum product of spacings estimators are obtained numerically, and asymptotic confidence intervals are constructed using estimated information matrices. Bayesian estimates under squared-error loss and highest posterior density intervals are computed using a Metropolis–Hastings algorithm. A Monte Carlo simulation study assesses bias, mean squared error, interval lengths, and coverage probabilities across different sample sizes and censoring configurations. The simulation results indicate that larger sample sizes and lighter censoring generally reduce bias and mean squared error, while the relative performance of the estimation methods varies with the parameter values and experimental settings. Appropriately specified informative priors can further reduce the bias and mean squared error of Bayesian estimators and yield shorter credible intervals. Finally, a real-life data set is analyzed to demonstrate the practical applicability of the proposed inferential procedures.