On a terminating renewal shock process with an independent wear process

Abstract

In this article, we study shock models that can stochastically describe, for example, collapses of different structures. For this purpose, we consider a combination of an extreme shock model and a specific cumulative shock model, where shocks occur according to a renewal process. A new interpretation of the previous shock model studied by the authors, where shocks arrive according to a nonhomogeneous Poisson process, is given. Based on this interpretation, the results are extended to the case when the shock process follows a renewal process. Some examples are discussed. © 2012 Copyright Taylor and Francis Group, LLC.