Estimation of Reliability under Stress-Strength Model in a Bivariate Exponential Set-Up

Abstract

The exact expression of R=P (Y <X) is derived when the random strength (X) and the random stress ( Y) jointly follow a bivariate exponential distribution due to Gumbel. A natural estimator ( $\widehat{R}$ ) of R is proposed for which consistency and asymptotic normality are ensured. Simulation studies are reported to examine the closeness between $\widehat{R}$ and R, and to compare $\widehat{R}$ with Tong's estimator under near independent situations.