Bayesian and Classical Estimation of Strength-Stress Reliability for Gompertz Distribution Based on Upper Record Values

In this paper, we consider the problem of estimating stress- strength reliability R = Pr(X > Y ) for Gompertz lifetime models hav- ing the same shape parameters but different location parameters under a set of upper record values. We obtain the maximum likelihood es- timator (MLE), the approximate Bayes estimator and the exact con- dence intervals of stress-strength reliability when the shape parameter is known. Also, when the shape parameter is unknown, the MLE, the asymptotic condence interval and some bootstrap condence intervals of stress-strength reliability are studied. Furthermore, a Bayesian ap- proach is proposed for estimating the parameters and then the corre- sponding credible interval are achieved using Gibbs sampling technique via OpenBUGS software. Monte Carlo simulations are performed