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STOCHASTIC SURVIVAL MODELS WITH EVENTS TRIGGERED BY EXTERNAL SHOCKS

Published online by Cambridge University Press:  27 April 2012

Ji Hwan Cha  and
Maxim Finkelstein
Ji Hwan Cha
Affiliation:
Department of Statistics, Ewha Womans University, Seoul 120-750, Korea E-mail: [email protected]
Maxim Finkelstein
Affiliation:
Department of Mathematical Statistics, University of the Free State, 339 Bloemfontein 9300, South Africa and Max Planck Institute for Demographic Research, Rostock, Germany E-mail: [email protected]
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Abstract

In most conventional settings, the events caused by an external shock are initiated at the moments of its occurrence. In this paper, we study the new classes of shock models: (i) When each shock from a nonhomogeneous Poisson processes can trigger a failure of a system not immediately, as in classical extreme shock models, but with delay of some random time. (ii) When each shock from a nonhomogeneous Poisson processes results not in an ‘immediate’ increment of wear, as in classical accumulated wear models, but triggers its own increasing wear process. The wear from different shocks is accumulated and the failure of a system occurs when it reaches a given boundary. We derive the corresponding survival and failure rate functions. Furthermore, we study the limiting behavior of the failure rate function where it is applicable.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 2 , April 2012 , pp. 183 - 195
Copyright
Copyright © Cambridge University Press 2012

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References

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