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

Consider a system which has nn independent components (or subsystems) each consisting of mm dependent elements. Let Xi=(Xi1,Xi2,…,Xim), i=1,2,…,ni=1,2,…,n denote the random strength vector of the iith component, where Xij denotes the random strength of the jjth element of the iith component. The elements of the components are subjected to a common random stress Y=(Y1,Y2,…,Ym) 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.