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On identifiability in the autopsy model of reliability theory

Part of: Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Robin Antoine ,
Hani Doss  and
Myles Hollander
Robin Antoine*
Affiliation:
The University of the West Indies
Hani Doss*
Affiliation:
Florida State University
Myles Hollander*
Affiliation:
Florida State University
*
∗ Postal address: Department of Mathematics, The University of the West Indies, St. Augustine, Republic of Trinidad and Tobago, West Indies.
∗∗ Postal address: Department of Statistics, The Florida State University, Tallahassee, FL 323063033, USA.
∗∗ Postal address: Department of Statistics, The Florida State University, Tallahassee, FL 323063033, USA.
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Abstract

A coherent system is observed until it fails. At the instant of system failure, the set of failed components and the failure time of the system are noted. The failure times of the components are not known. We consider whether the component life distributions can be determined from the distributions of the observed data.

Meilijson (1981) gave a condition on the structure of the system that was sufficient for the identifiability of the component distributions, under the assumption that the component life distributions are continuous and have common essential extrema. Nowik (1990) gave necessary and sufficient conditions for identifiability under the more restrictive condition that the component distributions have atoms at their common essential infimum and are mutually absolutely continuous. We give a necessary condition for identifiability, which we show to be equivalent to Nowik's condition, under the assumption that the distributions are continuous and strictly increasing. We derive a sufficient condition for identifiability, more general than Meilijson's, for the case in which the component distributions are assumed to be analytic. We also show that our necessary condition for identifiability is both necessary and sufficient when the component life distributions are assumed to belong to certain parametric families.

Keywords

COHERENT SYSTEMFATAL SETINCIDENCE MATRIXIDENTIFIABLE

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 4 , December 1993 , pp. 913 - 930
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

Research supported by Air Force Office of Scientific Research Grants No. 90–0202 and 91–0048.

References

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