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On generalized shock models for deteriorating systems

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  • Ji Hwan Cha
  • Maxim Finkelstein

Abstract

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. Copyright © 2012 John Wiley & Sons, Ltd.

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  • Ji Hwan Cha & Maxim Finkelstein, 2013. "On generalized shock models for deteriorating systems," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 29(5), pages 496-508, September.
    • Handle: RePEc:wly:apsmbi:v:29:y:2013:i:5:p:496-508
    DOI: 10.1002/asmb.1933
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    Cited by:

    1. Hyunju Lee & Ji Hwan Cha, 2021. "On a multivariate IFR and positively dependent lifetime model induced by multiple shot-noise processes," Statistical Papers, Springer, vol. 62(2), pages 561-590, April.

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