On reliability estimation p (X1 < Y < X2) following Rayleigh-Pareto distribution in stress-strength model

In this paper, the reliability system R = P(X1 < Y < X2), of the stress-strength model was derived having strength (Y) subject to two stresses X1 and X2 follows the two parameters Rayleigh - Pareto distribution such as δ (scale) known and λ (shape) unknown parameters. We estimate the reliability function by using three estimation methods as maximum likelihood (ML), Percentile estimation (PE), and two shrinkage methods such that Shrinkage weight Estimator (SMW), and Shrinkage Function Estimator (SMF). To obtain the best estimate of the reliability function by using the Monte Carlo method depend on mean square error (MSE) criteria. The comparison showed that the (SMW) method is the best among the other methods.