In this paper, we consider a system which has s-independent and identically distributed strength components, and each component is constructed by a pair of s-dependent elements. These elements follow a Marshall-Olkin bivariate Weibull distribution, and each element is exposed to a common random stress which follows a Weibull distribution. The system is regarded as operating only if at least out of strength variables exceed the random stress. The multicomponent reliability of the system is given by (at least of the exceed ) where , . We estimate by using frequentist and Bayesian approaches. The Bayes estimates of have been developed by using Lindley's approximation, and the Markov Chain Monte Carlo methods, due to the lack of explicit forms. The asymptotic confidence interval, and the highest probability density credible interval are constructed for . The reliability estimators are compared by using the estimated risks through Monte Carlo simulations.
Index Terms-Marshall-Olkin bivariate Weibull distribution, stress-strength, stress-strength model.
0018-9529
<p>In this study, we consider a multicomponent system which has k independent and identical strength components X1,...,Xk and each component is exposed to a common random stress Y when the underlying distributions are Weibull. The system is regarded as operating only if at least s out of k (1 ≤ s ≤ k) strength variables exceeds the random stress. We estimate the reliability of the system by using frequentist and Bayesian approaches. The Bayes estimate of the reliability has been developed by using Lindley's approximation and the Markov Chain Monte Carlo methods due to the lack of explicit forms. The asymptotic confidence interval and the highest probability density credible interval are constructed for the reliability. The comparison of the reliability estimators is made in terms of the estimated risks by the Monte Carlo simulations.</p>
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