Shocks, runs and random sums

Abstract:

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 k tends to infinity or when the probability of entering a critical set tends to zero. This model generalises the Poisson shock model.

Año de publicación:

2001

Keywords:

• reliability
• Regular variation
• Shock model
• Random sums

Fuente:

scopus