Interval Estimation for the Stress-Strength Reliability with Bivariate Normal Variables

Abstract

We propose a procedure to obtain accurate confidence intervals for the stress-strength reliability R = P ( X > Y ) when ( X , Y ) is a bivariate normal distribution with unknown means and covariance matrix. Our method is more accurate than standard methods as it possesses a third-order distributional accuracy. Simulations studies are provided to show the performance of the proposed method relative to existing ones in terms of coverage probability and average length. An empirical example is given to illustrate its usefulness in practice.