Minimax Estimators for the Stress Strength Reliability Based on the Generalized Rayleigh Distribution

Abstract

The analysis of strength-stress reliability R=P(Y<X) is widely considered as one of the fundamental tools in reliability engineering and survival analysis. In this research we examine the state of strength that is represented as X and the stress that is represented as Y. Recent studies confirm the importance or robust estimation methods in reliability analysis, for this context, the reliability R=P(Y<X) is estimated utilizing minimax strategy that follows the statistical decision theory, under six different loss functions namely; Quadratic (M1), Relative Squared Error (M2), Entropy (M3), Log-Squared(M4), Least Absolute Deviations(M5), and Linear-Exponential (M6) loss functions when these states( stress and strength) follows the generalized Rayleigh distribution. Monte Carlo simulations will be made to make comparisons between the proposed estimators, and the simulation results have shown that the LinEx (M6) loss function consistently achieved the lowest mean squared error in the majority of symmetrical and asymmetrical cases. In contrast, the RSE (M2) loss function excels in specific scenarios, particularly when the stress sample size is larger than the strength sample size. Furthermore, the entire loss function exhibits the property of consistency as its performance improves with increasing sample sizes.