We consider a simple step-stress model under the Gompertz distribution (GD) when the available data are type-II progressive censored. The cumulative exposure model is assumed when the lifetime of test units follows a Gompertz distribution. Maximum likelihood estimates and Bayes estimates are derived, utilizing the Markov Chain Monte Carlo (MCMC) method for computing Bayes estimates (BEs) and credible intervals. BEs of the parameters were obtained based on squared error (SE) and linear exponential (LINEX) loss functions under the assumptions of independent gamma priors. Finally, to illustrate these concepts, simulation studies and real-data examples are included.

Keywords: Step-stress accelerated life testing, Progressive type-II censoring, Maximum likelihood estimation, .Bayes estimation, Gompertz distribution, Cumulative exposure model, Markov Chain Monte Carlo

Keywords: Step-stress accelerated life testing, Progressive type-II censoring, Maximum likelihood estimation, Bayes estimation, Gompertz distribution, Cumulative exposure model, Markov Chain Monte Carlo.

Keywords: Step-stress accelerated life testing, Progressive type-II censoring, Maximum likelihood estimation, Bayes estimation, Gompertz distribution, Cumulative exposure model, Markov Chain Monte Carlo.