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Identifiability problems in coherent systems

Published online by Cambridge University Press:  14 July 2016

Shmuel Nowik
Shmuel Nowik*
Affiliation:
Tel-Aviv University
*
∗ Postal address: Raymond and Beverly Sackler Faculty of Exact Sciences, School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel.
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Abstract

Given a coherent system, let Z be the age of the machine at breakdown, and I the set of parts failed by time Z. Assume that the component lifetimes are independent. Assume further that the lifetime distributions are mutually absolutely continuous and that each possesses a single positive atom at the common essential infimum. We prove that the joint distribution of (Z, I) identifies the lifetime distribution of each part if and only if there is at most one component belonging to all cut sets. If we relax the mutual absolute continuity assumption by allowing isolated intervals of constancy, then a necessary and sufficient condition for identifiability is that no two parts be in parallel.

Keywords

COMPETING RISKSCOHERENT RELIABILITY SYSTEMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 4 , December 1990 , pp. 862 - 872
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

This research formed part of the author's M.Sc. thesis at Tel-Aviv University.

References

[1] Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
[2] Meilijson, I. (1981) Estimation of the lifetime distribution of the parts from the autopsy statistics of the machine. J. Appl. Prob. 18, 829–838.Google Scholar
[3] Meilijson, I. (1985) Competing risks on coherent reliability systems. Technical report, Tel-Aviv University.Google Scholar
[4] Rall, L. B. (1969) Computational Solution of Nonlinear Operator Equations. Wiley, New York.Google Scholar