Survival of systems with protection subject to two types of external attacks

Ji Hwan Cha, Maxim Finkelstein, Francois Marais

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3 Scopus citations


We consider a large system that, due to its importance and (or) large economic value, should be protected from possible harmful attacks. The attacker executes two types of attacks modeled by the corresponding shock processes: those that target the repairable defense system and those that target the non-repairable 'main' system itself. The quality of the performance of the defense system, i.e., the ability to neutralize the attacks on the main system depends on its state defined by the accumulated damage. In order to obtain the survival probabilities for the main system, we develop a new class of state-dependent extreme shock models, where the accumulated damage caused by the shock process of one type affects the probability of failure from shocks of the other type.

Original languageEnglish
Pages (from-to)79-91
Number of pages13
JournalAnnals of Operations Research
Issue number1
StatePublished - Jan 2014

Bibliographical note

Funding Information:
Acknowledgements The authors would like to thank the referees and the editor for helpful comments and suggestions, which have improved the presentation of this paper. The work of the first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2011-0017338). The work of the first author was also 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.


  • Extreme shock model
  • Poisson process
  • Probability of survival
  • State-dependent shock model


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