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This article considers the problem of estimating the unknown parameters of the compound Rayleigh distribution with progressive first-failure censoring scheme during step-stress partially accelerated life tests (ALT). Progressive first-failure censoring and accelerated life testing are performed to decrease the duration of testing and to lower test expenses. The maximum likelihood estimators (MLEs) and Bayes estimates (BEs) for the distribution parameters and acceleration factor are obtained. The optimal time for stress change is determined. Furthermore, the approximate, bootstrap and credible confidence intervals (CIs) of the parameters are derived. Methods of Markov chain Monte Carlo (MCMC) are used to obtain the Bayes estimates. Finally, the accuracy of the MLEs and BEs for the model parameters is investigated through simulation studies.

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