On the failure probability of used coherent systems

Abstract

In analyzing the lifetime properties of a coherent system, the concept of "signature" is a useful tool. Let T be the lifetime of a coherent system having n iid components. The signature of the system is a probability vector s=(s1, s2,., sn), such that s i=P(T=Xi:n), where, Xi:n, i=1, 2,., n denote the ordered lifetimes of the components. In this note, we assume that the system is working at time t>0. We consider the conditional signature of the system as a vector in which the ith element is defined as pi(t)=P(T=Xi: n|T>t) and investigate its properties as a function of time. © 2014 Taylor & Francis Group, LLC.