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On the Failure Probability of Used Coherent Systems

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  • Majid Asadi
  • Amir R. Asadi

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 si=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.

Suggested Citation

  • Majid Asadi & Amir R. Asadi, 2014. "On the Failure Probability of Used Coherent Systems," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(10-12), pages 2468-2475, May.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:10-12:p:2468-2475
    DOI: 10.1080/03610926.2013.830744
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