Inference on inverted exponentiated Rayleigh data from accelerated life testing with hybrid censoring

This paper addresses the problem of estimating unknown parameters of the inverted exponentiated Rayleigh distribution within the context of accelerated life testing. We consider lifetime data observed through step-stress and type-I hybrid censoring, and incorporate the cumulative exposure model assumptions to establish connections between the distribution at various stress levels. We then write the associated likelihood function based on the observed data and derive maximum likelihood estimators for the distribution's unknown parameters. Furthermore, employing a Bayesian approach, we initially adopt gamma priors and compute posterior distributions for the parameters. These posterior distributions are then utilized to calculate Bayesian estimates using the squared error loss function. To assess the performance of maximum likelihood and Bayesian estimates, we conduct a simulation study under various scenarios, considering both non-informative and informative priors. We also evaluate interval estimates and coverage percentages under both classical and Bayesian approaches. Finally, for illustrative purposes, we analyze two real data sets, demonstrating the practical application of our proposed methodology.