Empirical Bayesian estimation of parameters in step-stress accelerated life testing under exponential distribution with constant censoring

Abstract

This study explores the Parametric Empirical Bayesian (PEB) estimation of average lifetime and acceleration factor parameters under the framework of exponential distribution with constant censoring, specifically when the hyperparameters of the prior distribution are completely unknown. Employing a weighted squared loss function, the performance of PEB estimations is compared against that of Maximum Likelihood Estimations (MLE) through numerical simulations. The results demonstrate the superiority of PEB estimations over MLE, particularly notable in scenarios involving small sample sizes, where it exhibits robust estimation capabilities. This paper extends the existing methodology by providing a comprehensive examination of the advantages and potential applications of empirical Bayesian approaches in the context of step-stress accelerated life testing, thereby offering valuable insights for researchers and practitioners in the field of reliability engineering.