Stress-Strength Reliability Estimation for the Type I Extreme-Value Distribution Based on Records

Abstract

In this paper, we consider the stress-strength reliability for record data when the distribution of random stress and strength have the type I extreme-value distribution. First, classical inference methods, namely uniformly minimum variance unbiased estimate (UMVUE) and maximum likelihood estimate (MLE), are used for. Second, Bayesian inference of are considered for gamma priors assumption. When the common parameter of stress and strength variables is known, the exact Bayes estimate and Bayesian credible interval of are obtained. Markov Chain Monte Carlo (MCMC) method are used to derive the Bayes estimate and highest probability density (HPD) credible interval of when the common parameter is unknown. Finally, Monte Carlo simulations are performed to compare the performance of the obtained estimates. A real data set about the weather temperature is analyzed to illustrate the performances of the derived estimators in the paper.