Multivariate stress-strength reliability model and its evaluation for coherent structures

Consider a system which has n independent components (or subsystems) each consisting of m dependent elements. Let X(i) = (X(i)(1), X(i)(2),..., X(i)(m)), i = 1, 2,.... n denote the random strength vector of the ith component, where X(i)(j) denotes the random strength of the jth element of the ith component. The elements of the components are subjected to a common random stress Y = (Y(1), Y(2),..., Y(m)) over time. In this paper, we setup a multivariate stress-strength model based on the conditional ordering between Xis and Y and evaluate the reliability of coherent structures in this setup. (C) 2008 Elsevier Inc. All rights reserved.