A proposed measure of residual life of live components of a coherent system

Abstract

The concept of the signature of a coherent system is useful to study the stochastic and aging properties of the system. Let X 1:n,X 2:n,⋯,X n:n denote the ordered lifetimes of the components of a coherent system consisting of n i.i.d components. If T denotes the lifetime of the system, then the signature vector of the system is defined to be a probability vector s = (s 1,s 2,⋯,s n) such that s i = P(T = X i:n), i=1,2,⋯,n. Here we consider a coherent system with signature of the form s=(s 1,s 2,⋯s i,0⋯,0), where s k>0, k=1,2,⋯,i. Under the condition that the system is working at time t , we propose a time dependent measure to calculate the probability of residual life of live components of the system, i.e., X k:n, k=i+1,⋯,n. Several stochastic and aging properties of the proposed measure are explored. © 2006 IEEE.