ESTIMATION OF P [Y < X] FOR BURR-XII DISTRIBUTION USING RECORD VALUES: CLASSICAL AND MCMC APPROACHES

In some situations, only observations that exceed or only those that fall below the current extreme value are recorded. Examples include meteorology, hydrology and industrial stress testing. In this paper, it is shown how record data can be used to provide inference for the stress-strength reliability model, R = P [Y < X] when X and Y are two independent Burr-XII distributions with different one shape parameters, but having the same another shape parameter. Our focus then shifts to the problem of estimating R when the available data is in the form of record values. The maximum likelihood estimator (MLE) and two bootstrap confidence intervals of R are proposed. Also, we propose to apply Markov Chain Monte Carlo (MCMC) approaches to study the Bayesian estimation of R based on upper record values. Assuming known common shape parameter, the MLE of R is obtained. The exact distributions of the MLEs of the unknown parameters are used to construct the exact confidence interval of R. Bayes estimators are obtained by Lindley's approximations, and also by using MCMC approach. Analysis of a real data set has been presented for illustrative purposes. Monte Carlo simulations are performed to compare the different proposed methods.