Generalized Shock Models Based on a Cluster Point Process

Abstract

We review the principal progress of shock models during the last three decades. Our new model, the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$delta$</tex> -shock model, and its latest developments are also introduced. Furthermore, for adapting shock models to a wider reliability field, we put forward a generalized framework for studying shock models, based on cluster point processes with cluster marks. In addition, we provide a noteworthy case under this framework as a concrete example in reliability with an insurance background, and give the asymptotic distribution of the risk process.