Likelihood and Bayesian Inference of the Stress-Strength Reliability Based on Record Values from Proportional and Proportional Reversed Hazard Rate Models

In this paper the likelihood and Bayesian inference of the stress-strength reliability are considered based on record values from proportional and proportional reversed hazard rate models. Then inference of the stress-strength reliability based on lower record values from some generalized distributions are also considered. Next the likelihood and Bayesian inference of the stress-strength model based on upper record values from Gompertz، Burr type XII، Lomax and Weibull distributions are considered. The ML estimators and their properties are studied. Likelihood-based confidence intervals، exact، as well as the Bayesian credible sets and bootstrap interval for the stress-strength reliability in all distributions are obtained. Simulation studies are conducted to investigate and compare the performance of the intervals.