Inference for a Simple Step-Stress Model for The Extension of Exponential Distribution Under Progressive Type-II Censored Competing Risks Data.

Document Type : Original Article

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1 Department of Statistics and Insurance, Faculty of Commerce, Zagazig University,Egypt

2 Department of Statistics and Insurance, Faculty of Commerce, Zagazig University, Egypt

Abstract

In a special class of accelerated life tests known as step stress tests, the stress levels increase discretely at pre-fixed time points, and this allows the experimenter to obtain information on the parameters of the lifetime distributions more quickly than under normal operating conditions. In this paper, we consider the simple step-stress model with competing risks under progressive Type-II censoring. The cumulative exposure model is assumed when the lifetime of test units follows an extension of the exponential Nadarajah-Haghighi distribution. Under this setup, we obtain the maximum likelihood estimates and the Bayes Estimators of the unknown parameters using the Markov chain Monte Carlo method under various loss functions. Also, the confidence intervals are derived by using the asymptotic distributions of the maximum likelihood estimates, and we obtained the highest posterior density credible intervals based on different prior distributions. Their performance is assessed through Monte Carlo simulations, and finally, we illustrate the methods of inference discussed here with an example.

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