Reliability of a Multicomponent Stress-strength Model Based on a Bivariate Kumaraswamy Distribution with Censored Data

Abstract

In this paper, we consider a system which has k statistically independent and identically distributed strength components and each component is constructed by a pair of statistically dependent elements with doubly type-II censored scheme. These elements (X₁, Y₁), (X₂, Y₂), ⋯, (X_k, Y_k) follow a bivariate Kumaraswamy distribution and each element is exposed to a common random stress T which follows a Kumaraswamy distribution. The system is regarded as operating only if at least s out of k (1 ≤ s ≤ k) strength variables exceed the random stress. The multicomponent reliability of the system is given by R_s,k=P(at least s of the (Z₁, ⋯, Z_k) exceed T) where Z_i = min(X_i, Y_i), i = 1, ⋯, k. The Bayes estimates of R_s,k have been developed by using the Markov Chain Monte Carlo methods due to the lack of explicit forms. The uniformly minimum variance unbiased and exact Bayes estimates of R_s,k are obtained analytically when the common second shape parameter is known. The asymptotic confidence interval and the highest probability density credible interval are constructed for R_s,k. The reliability estimators are compared by using the estimated risks through Monte Carlo simulations.