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

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  • Ji Cha
  • Maxim Finkelstein
  • Francois Marais

Abstract

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. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Ji Cha & Maxim Finkelstein & Francois Marais, 2014. "Survival of systems with protection subject to two types of external attacks," Annals of Operations Research, Springer, vol. 212(1), pages 79-91, January.
    • Handle: RePEc:spr:annopr:v:212:y:2014:i:1:p:79-91:10.1007/s10479-013-1315-6
    DOI: 10.1007/s10479-013-1315-6
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    References listed on IDEAS

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    1. Chen, Jinyuan & Li, Zehui, 2008. "An extended extreme shock maintenance model for a deteriorating system," Reliability Engineering and System Safety, Elsevier, vol. 93(8), pages 1123-1129.
    2. Finkelstein, Maxim & Marais, Francois, 2010. "On terminating Poisson processes in some shock models," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 874-879.
    3. Austin J. Lemoine & Michael L. Wenocur, 1986. "Technical Note—A Note on Shot-Noise and Reliability Modeling," Operations Research, INFORMS, vol. 34(2), pages 320-323, April.
    4. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael & del Carmen Segovia, Maria, 2009. "Replacement policy in a system under shocks following a Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 497-502.
    5. Gut, Allan & Hüsler, Jürg, 2005. "Realistic variation of shock models," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 187-204, September.
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