Estimation of P (X < Y) for Gompertz distribution based on upper records

This article discusses the problem of estimation of stress-strength reliability (R = P (X < Y)) based on upper records assuming that the stress (X) and the strength (Y) follow the independent Gompertz distribution. Uniformly minimum variance unbiased estimator and maximum likelihood estimator with exact/asymptotic confidence intervals for stress-strength reliability are obtained. Bayes estimators under squared error loss function and highest posterior density intervals are also calculated. The performances of the estimators are then compared based on their bias and mean squared error. A real data set is used to illustrate the proposed methodology.