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=P(X>Y)  for Gompertz lifetime models having the same shape parameters but different scale parameters under a set of upper record values. We obtain the maximum likelihood estimator (MLE), the approximate Bayes estimator and the exact confidence intervals of stress-strength reliability when the shape parameter is known. Also, when the shape parameter is unknown, the MLE, the asymptotic confidence interval and some bootstrap confidence intervals of stress-strength reliability are studied. Furthermore, a Bayesian approach is proposed for estimating the parameters and then the corresponding credible interval are achieved using Gibbs sampling technique via OpenBUGS software. Monte Carlo simulations are performed to compare the performance of different proposed estimation methods.