Estimation of Reliability in a Multicomponent Stress-Strength Model Based on a Marshall-Olkin Bivariate Weibull Distribution


During this paper, we tend to think about a system that has k s-freelance and identically distributed strength parts, and every component is constructed by a combine of s-dependent parts. These parts (X1,Y1),(X2,Y2),...,(Xk,Yk) follow a Marshall-Olkin bivariate Weibull distribution, and each part is exposed to a typical random stress T that follows a Weibull distribution. The system is regarded as operating solely if a minimum of s out of k (1 ≤ s ≤ k) strength variables exceed the random stress. The multicomponent reliability of the system is given by Rs,k=P (a minimum of s of the (Z1,...,Zk) exceed T) where Zi=min(Xi,Yi), i=1,...,k. We tend to estimate Rs,k by using frequentist and Bayesian approaches. The Bayes estimates of Rs,k are developed by using Lindley's approximation, and also the Markov Chain Monte Carlo strategies, due to the shortage of explicit forms. The asymptotic confidence interval, and the very best likelihood density credible interval are created for Rs,k. The reliability estimators are compared by using the estimated risks through Monte Carlo simulations.

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