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On New Classes of Extreme Shock Models and Some Generalizations

Part of: Special processes Applications

Published online by Cambridge University Press:  14 July 2016

Ji Hwan Cha  and
Maxim Finkelstein
Ji Hwan Cha*
Affiliation:
Ewha Womans University
Maxim Finkelstein*
Affiliation:
University of the Free State and Max Planck Institute for Demographic Research
*
∗Postal address: Department of Statistics, Ewha Womans University, Seoul, 120-750, Korea. Email address: jhcha@ewha.ac.kr
∗∗Postal address: Department of Mathematical Statistics, University of the Free State, 339 Bloemfontein 9300, South Africa. Email address: finkelm.sci@ufs.ac.za
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Abstract

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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. A shock model which combines these two types is called a ‘combined shock model’. In this paper we study new classes of extreme shock models and, based on the obtained results and model interpretations, we extend these results to several specific combined shock models. For systems subject to nonhomogeneous Poisson processes of shocks, we derive the corresponding survival probabilities and discuss some meaningful interpretations and examples.

Keywords

Extreme shock modelcombined shock modelwearvirtual ageprobability approximation

MSC classification

Secondary: 60K10: Applications (reliability, demand theory, etc.) 62P30: Applications in engineering and industry
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 1 , March 2011 , pp. 258 - 270
Copyright
Copyright © Applied Probability Trust 2011 

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