Stress-strength reliability estimation for p(T<X<Z) using exponentiated inverse Rayleigh distribution

In this research, the reliability of the stress-strength model is introduced and derived for the probability P(T<X<Z) of a component strength X relation between two stresses T and Z follows to have Exponentiated Inverse Rayleigh Distribution (EIRD) with different unknown shape parameters and common known scale parameter. Three methods to estimate the parameters of EIRD are discussed by using the Maximum Likelihood, Ordinary and Weighted Least Square methods, and compare between these estimates based on a simulation study by the mean squared error criteria for both small, medium and large samples. the most important result, that this comparison confirms on the performance of the maximum likelihood estimator works the best for all studded experiments.