On new classes of extreme shock models and some generalizations

Ji Hwan Cha, Maxim Finkelstein

Research output: Contribution to journalArticlepeer-review

125 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)258-270
Number of pages13
JournalJournal of Applied Probability
Volume48
Issue number1
DOIs
StatePublished - Mar 2011

Keywords

  • Combined shock model
  • Extreme shock model
  • Probability approximation
  • Virtual age
  • Wear

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