Interval Estimation of Stress-Strength Reliability Based on Lower Record Values from Inverse Rayleigh Distribution

Abstract

We consider the estimation of stress-strength reliability based on lower record values when and are independently but not identically inverse Rayleigh distributed random variables. The maximum likelihood, Bayes, and empirical Bayes estimators of are obtained and their properties are studied. Confidence intervals, exact and approximate, as well as the Bayesian credible sets for are obtained. A real example is presented in order to illustrate the inferences discussed in the previous sections. A simulation study is conducted to investigate and compare the performance of the intervals presented in this paper and some bootstrap intervals.