On a terminating shock process with independent wear increments
Ji Hwan Cha and Maxim Finkelstein
Source: J. Appl. Probab.
Volume 46, Number 2
(2009), 353-362.
Abstract
In extreme shock models, only the impact of the current, possibly fatal shock is usually taken into account, whereas in
cumulative shock models, the impact of the preceding shocks is accumulated as well. In this paper we combine an extreme
shock model with a specific cumulative shock model. It is shown that the proposed setting can also be interpreted as a
generalization of the well-known Brown--Proschan model that describes repair actions for repairable systems. For a
system subject to a specific process of shocks, we derive the survival probability and the corresponding failure rate
function. Some meaningful interpretations and examples are discussed.
Primary Subjects: 60K10
Secondary Subjects: 62P30
Keywords: Brown--Proschan model; extreme shock model; cumulative shock model; virtual age; wear
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1245676092
Digital Object Identifier: doi:10.1239/jap/1245676092
Zentralblatt MATH identifier:
05578811
Mathematical Reviews number (MathSciNet):
MR2535818
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