Abstract

In this paper, we deal with the estimation of the reliability $R=P(Y<X)$ where $X$, a unit strength, and $Y$, a unit stress, are independent exponentiated Weibull random variables. The maximum likelihood and Bayesian methods are used to make inference about $R$. We obtain the Baysian estimator using Lindely's procedure under squared error loss and LINEX loss functions with gamma prior for the unknown model parameters. The asymptotic and bootstrap confidence intervals are obtained as well as the credible interval for R is constructed in view of the empirical Bayesian procedure. For illustrative purposes, analysis of real data sets is presented. Mont Carlo simulations are carried out to compare the performances of the different estimators.

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