Statistical Inference of the Reliability for Generalized Exponential Distribution Under Progressive Type-II Censoring Schemes

This paper discusses the estimation of R = P (Y <; X) when X and Y are independent generalized exponential random variables with different scale parameters and the same shape parameter based on progressive type-II censoring samples. The maximum likelihood estimator (MLE) of the parameter R is obtained. The approximate MLE (AMLE) of R by the Taylor series expansion is proposed. The asymptotic distribution of R is derived to construct the asymptotic MLE and AMLE confidence intervals. Also, the bootstrap-p and bootstrap-t confidence intervals are constructed. In addition, using the Metropolis-Hasting procedure, we derive the Bayes estimate and the corresponding credible interval. Finally, a Monte Carlo simulation and an analysis of two real datasets are presented to evaluate the various proposed methods.