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 ( $\hat{R}$ ) of R is proposed for which consistency and asymptotic normality are ensured. Simulation studies are reported to examine the closeness between $\hat{R}$ and R, and to compare $\hat{R}$ with Tong's estimator under near independent situations.

Keywords

Gumbel's bivariate exponential distribution estimator consistency asymptotic normality simulation.

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