Bayes Estimation of the Stress-Strength Model Reliability When the Mean Strength Is Greater Than the Mean Stress

Order restricted Bayes estimators for the reliability of stress-strength model when the mean strength is greater than the mean stress are obtained with respect to inverted gamma and noninformative prior distributions, and their asymptotic properties are established. It is shown that the maximum likelihood estimator, restricted maximum likelihood estimator, unrestricted Bayes estimator, and restricted Bayes estimator of the reliability are all consistent and have the same limiting distribution. These estimators are compared with the corresponding unrestricted Bayes estimators by Monte Carlo simulation.