On generalized shock models for deteriorating systems

Ji Hwan Cha, Maxim Finkelstein

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Standard assumptions in shock models are that failures of items are related either to the cumulative effect of shocks (cumulative models) or that they are caused by shocks that exceed a certain critical level (extreme shocks models). In this paper, we present useful generalizations of this setting to the case when an item is deteriorating itself, for example, when the boundary for the fatal shock magnitude is decreasing with time. Three stochastic failure models describing different impacts of shocks on items are considered. The cumulative effect of shocks is modeled in a way similar to the proportional hazards model. Explicit formulas for the corresponding survival functions are derived and several simple examples are considered.

Original languageEnglish
Pages (from-to)496-508
Number of pages13
JournalApplied Stochastic Models in Business and Industry
Issue number5
StatePublished - Sep 2013


  • cumulative shock model
  • extreme shock model
  • intensity process
  • reliability
  • shot-noise process


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