Classical and Bayesian reliability inference for the chen distribution under a block-adaptive progressive hybrid censoring plan

This study investigates statistical inference for lifetime data that are terminated by a block-adaptive progressive hybrid censoring scheme, a design that splits test units across several groups so that experiments finish earlier without losing information. Assuming lifetimes follow the two-parameter Chen distribution, point and interval estimators are obtained for the model parameters, and some key reliability measures are evaluated using both classical and Bayesian frameworks. Bayesian inference is carried out through a Markov chain Monte Carlo procedure that combines Gibbs sampling with Metropolis-Hastings updates for non-standard conditional distributions. The effect of heterogeneity between test blocks on reliability performance is examined. Furthermore, a comprehensive simulation study evaluates the competing estimation methods in terms of bias, mean squared error, average width of the confidence intervals, and coverage probability. The results indicate that the Bayesian estimators achieve the highest accuracy and yield the narrowest interval estimates while maintaining nominal coverage. Two real data applications, from cancer patient survival and electrical breakdown experiments, illustrate the practical advantages of the proposed methodology in reducing test time while preserving essential reliability information.