Estimation of the stress-strength reliability for the exponential-Rayleigh distribution

In this current paper, we consider the problem of estimating the stress-strength parameter Psi = P(X < Y). This is done by using Bayesian and non-Bayesian approaches when X and Y are independent random variables from two exponential-Rayleigh distributions with different shape parameters but the same scale parameter. Maximum likelihood and Bayes estimators are used to estimate and construct the asymptotic confidence interval and credible interval of Psi. Finally, an intensive simulation study is performed to compare the proposed methods and analyze a real data set for illustrative purposes.