Bounds for the joint survival and incidence functions through coherent system data

Bounds for the joint survival and incidence functions through coherent system data

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Article ID: iaor1998912
Country: United Kingdom
Volume: 29
Issue: 2
Start Page Number: 478
End Page Number: 497
Publication Date: Jun 1997
Journal: Advances in Applied Probability
Authors: ,
Keywords: competing risks
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 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.

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