Point and Interval Estimation of Stress-Strength Model for Exponentiated Inverse Rayleigh distribution

This paper deals with finding a formula for the stress-strength reliability function for complete data when the strength (X) falls between the stress (T) and the stress (Z) ; where X,T,Z are independent random variables and follow the Exponentiated Inverse Rayleigh Distribution with unknown shape parameters and common known scale parameter , and estimate this formula with the Maximum Likelihood Estimate method (MLE) and the Bayesian method using Non-informative priors and informative priors under Weighted Square Error Loss Function ( WSELF ) ,Also the interval estimation had been done for the reliability function that based on the Maximum Likelihood Estimator .Simulation study is used to determine the best estimator; the results showed that Bayesian estimation using informative priors based on Weighted Square Error Loss Function is the best estimator For the equal sizes , and Bayesian estimation using Non-informative priors based on Weighted Square Error Loss Function is the best estimator when the size of the stress sample (Z) larger than the size of (X,T) , and Maximum Likelihood Estimator is the best estimator For the rest sizes