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Stochastic properties of a cumulative damage threshold crossing model

Part of: Distribution theory - Probability Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Nader Ebrahimi
Nader Ebrahimi*
Affiliation:
Northern Illinois University
*
∗Postal address: Division of Statistics, Northern Illinois University, DeKalb, IL 60115, USA. Email address: nader@math.niu.edu.
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Abstract

In this paper we describe a model for survival functions. Under this model a system is subject to shocks governed by a Poisson process. Each shock to the system causes a random damage that grows in time. Damages accumulate additively and the system fails if the total damage exceeds a certain capacity or threshold. Various properties of this model are obtained. Sufficient conditions are derived for the failure rate (FR) order and the stochastic order to hold between the random lifetimes of two systems whose failures can be described by our proposed model.

Keywords

Poisson processstochastic orderingfailure rate orderingIFRNBUPF2 propertyTP2 property

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 60E15: Inequalities; stochastic orderings 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 3 , September 1999 , pp. 720 - 732
Copyright
Copyright © Applied Probability Trust 1999 

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