Stochastic survival models with events triggered by external shocks

Ji Hwan Cha, Maxim Finkelstein

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19 Scopus citations


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.

Original languageEnglish
Pages (from-to)183-195
Number of pages13
JournalProbability in the Engineering and Informational Sciences
Issue number2
StatePublished - Apr 2012

Bibliographical note

Funding Information:
We would like to thank two anonymous reviewers for their extremely helpful and profound comments. The work of the first author was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0093827). The work of the second author was supported by the NRF (National Research Foundation of South Africa) grant FA2006040700002.


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