Objective Bayesian and classical inference methods for power Rayleigh distributed lifetimes in constant-stress partially accelerated life tests under progressive type-II censoring

This paper proposes comprehensive estimation procedures for the parameters and acceleration factor of the Power Rayleigh distribution under constant-stress partially accelerated life tests (CSPALT) with progressive Type-II censoring. Three estimation approaches are developed maximum likelihood estimation (MLE), maximum product of spacing (MPS), and Bayesian inference. Within the Bayesian framework, both the model parameters and the acceleration factor are estimated using likelihood-based and product-spacing-based formulations. Bayesian estimation is carried out under two loss functions: the squared error loss function (SELF) and the linear exponential (LINEX) loss function, assuming objective prior for the model parameters. In addition to point estimation, approximate confidence intervals (CIs) for the parameters and acceleration factor are constructed using classical methods and compared with the highest posterior density (HPD) credible intervals obtained through Bayesian analysis. The Bayesian computations are implemented via Markov Chain Monte Carlo (MCMC) techniques, combining the Gibbs sampler with the Metropolis–Hastings algorithm. The performance of the proposed estimators is thoroughly assessed through extensive Monte Carlo simulations, evaluating key metrics such as bias, mean squared error (MSE), average interval width, and coverage probability. Moreover, the optimal design of the progressive Type-II censoring scheme (PT-IICS) is determined using multiple optimality criteria. Finally, the practical relevance and robustness of the proposed methodologies are demonstrated through two real-life datasets.