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On a Terminating Shock Process with Independent Wear Increments

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: [email protected]
∗∗Postal address: Department of Mathematical Statistics, University of the Free State, PO Box 339, Bloemfontein 9300, Republic of South Africa. Email address: [email protected]
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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. 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.

Keywords

Brown–Proschan modelextreme shock modelcumulative shock modelvirtual agewear

MSC classification

Secondary: 60K10: Applications (reliability, demand theory, etc.) 62P30: Applications in engineering and industry
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 2 , June 2009 , pp. 353 - 362
Copyright
Copyright © Applied Probability Trust 2009 

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