In this study, the E-Bayesian estimation of the reliability parameter, R = P(Y < X < Z), when X, Y and Z are three independent inverse Rayleigh distribution with different parameters, were estimated based on ranked set sampling method. To assess the efficiency of the obtained estimates, we compute the average absolute bias and relative efficiency of the derived estimates and compare them with those based on the corresponding simple random sample through Monte Carlo simulations. Also, E-Bayesian estimation of R is compared with its maximum likelihood estimation in each method. Finally, three real data sets are used to analyze the estimation methods.