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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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 ( NH)) distribution.Under this setup,we obtain the maximum likelihood

estimates and the Bayes Estimators of of the unknown parameters using MCMC

method under various loss functions. Also, The confidence intervals are derived by

using the asymptotic distributions of the the maximum likelihood estimates and we

obtained the highest posterior density (HPD) 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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