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 i th component, where X i j denotes the random strength of the j th element of the i th 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 X i s and Y and evaluate the reliability of coherent structures in this setup.