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Bounds for the Joint Survival and Incidence Functions Through Coherent System Data

Part of: Survival analysis and censored data Distribution theory - Probability Operations research and management science

Published online by Cambridge University Press:  01 July 2016

J. V. Deshpande  and
S. R. Karia
J. V. Deshpande*
Affiliation:
University of Poona
S. R. Karia*
Affiliation:
University of Poona
*
∗ Postal Address: Department of Statistics, University of Poona, Pune-411007, India.
∗ Postal Address: Department of Statistics, University of Poona, Pune-411007, India.
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Abstract

In the series system (competing risks) set-up the observed data are generally accepted as the lifetime (T) and the identifier (δ) of the component causing the failure of the system. Peterson (1976) has provided bounds for the joint survival function of the component lifetimes in terms of the joint distribution of (T, δ). In the case of more complex coherent systems, there are various schemes of observation in the literature. In this paper we provide bounds for the joint and marginal survival functions of the component lifetimes in terms of the joint distribution of the data as obtained under existing and new schemes of observation. We also tackle the reverse problem of obtaining bounds for the joint distributions of the data for given marginal distributions of the component lifetimes and the distribution of the system lifetimes.

Keywords

AUTOPSY MODELCOHERENT SYSTEMSCONTINUOUS MONITORINGINCIDENCE FUNCTIONSMINIMAL PATH AND CUT SETSSUBSURVIVAL FUNCTION

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 90B25: Reliability, availability, maintenance, inspection 60E99: None of the above, but in this section
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 29 , Issue 2 , June 1997 , pp. 478 - 497
Copyright
Copyright © Applied Probability Trust 1997 

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References

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