Journal
JOURNAL OF APPLIED PROBABILITY
Volume 38, Issue 2, Pages 438-448Publisher
APPLIED PROBABILITY TRUST
DOI: 10.1017/S0021900200019951
Keywords
shock model; random sums; reliability; regular variation
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In this paper we study random variables related to a shock reliability model. Our models can be used to study systems that fail when k consecutive shocks with critical magnitude (e.g. above or below a certain critical level) occur. We obtain properties of the distribution function of the random variables involved and we obtain their limit behaviour when A tends to infinity or when the probability of entering a critical set tends to zero. This model generalises the Poisson shock model.
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