On the Failure Probability of Used Coherent Systems |
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| Authors: | Majid Asadi Amir R Asadi |
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| Institution: | 1. Department of Statistics, University of Isfahan, Isfahan, Iran;2. School of Mathematics, Institute of Research in Fundamental Sciences (IPM), Tehran, Iranm.asadi@stat.ui.ac.ir;4. Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran |
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| 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. |
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| Keywords: | Order statistics Stochastic order Signature vector Residual lifetime k-out-of-n systems |
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