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Realistic variation of shock models

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  • Gut, Allan
  • Hüsler, Jürg

Abstract

The standard assumptions in shock models are that the failure (of a system) is related either to the cumulative effect of a (large) number of shocks or that failure is caused by a shock that exceeds a certain critical level. The present paper is devoted to both types but with variation of the scheme. We consider that a shock can partly harm the system which implies a lower critical boundary for the following shocks to be fatal. For the cumulative model we deal with the case that only the sum of the most recent shocks implies a system failure. In addition, we consider the combination of both models with some link functions.

Suggested Citation

  • Gut, Allan & Hüsler, Jürg, 2005. "Realistic variation of shock models," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 187-204, September.
  • Handle: RePEc:eee:stapro:v:74:y:2005:i:2:p:187-204
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    References listed on IDEAS

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    1. Li, Haijun & Shaked, Moshe, 1995. "On the first passage times for Markov processes with monotone convex transition kernels," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 205-216, August.
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