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.

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