On generalized shot noise-type stochastic failure model

Abstract

We discuss a reliability model that reflects the dynamic dependency between system failure and system stress induced by environmental shock process. 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, e.g., when the boundary for the fatal shock magnitude is decreasing with time. Mathematically, this approach is closer to the paper by Lemoine & Wenocur (1986) and is based on the consideration of the shot noise process-type stochastic intensity as a model for shocks accumulation. Some illustrative examples are also discussed. © 2012 Taylor & Francis Group.