Comparison of Some of Estimation methods of Stress-Strength Model: R = P(Y < X < Z)

Abstract

In this study, the stress-strength model R = P(Y < X < Z) is discussed as an important parts of reliability system by assuming that the random variables follow Invers Rayleigh Distribution. Some traditional estimation methods are used to estimate the parameters namely; Maximum Likelihood, Moment method, and Uniformly Minimum Variance Unbiased estimator and Shrinkage estimator using three types of shrinkage weight factors. As well as, Monte Carlo simulation are used to compare the estimation methods based on mean squared error criteria.

Keywords

• Stress-Strength Model, Inverse Rayleigh Distribution, Least Square Estimator, Maximum Likelihood Method Estimator, Moment method, Uniformly Minimum Variance Unbiased Method, Shrinkage Methods.