Inference on exponentiated Rayleigh distribution with constant stress partially accelerated life tests under progressive type-II censoring

This study aims to explore the issues of evaluating the parameters and the accelerating factor based on constant stress for partially accelerating life tests when the potential failure times have an exponentiated Rayleigh distribution. Within the framework of progressive Type-II censoring schemes, we employ the Newton-Raphson algorithm as an iterative methodology to gain the maximum likelihood estimates, accompanied by proof of the existence of these point estimators. We also construct asymptotic confidence intervals for interested parameters and acceleration factors by utilizing the asymptotical characteristics of the maximum likelihood estimators. The Bayesian estimations of unknown parameters are derived by using the independent gamma priors and dependent Gamma-Dirichlet prior on the basis of square error and relatively smooth LINEX loss functions, respectively. Furthermore, we adopt the importance sampling method to compute Bayesian point estimates and the credible intervals with the highest posterior density. To validate the effectiveness of the suggested approaches, a series of simulated experiments are carried out. Lastly, we conduct analyzes on two actual datasets to show the applicability of the suggested techniques.