On a cumulative damage process and resulting first passages times

Abstract

AbstractThe reliability of a product is often affected by a damage process. In this paper we consider a shock model where at random times a shock causes a random damage. The cumulative damage process is assumed to be generated by a position‐dependent marking of a doubly stochastic Poisson process. Some characteristics of this process are described. For general and special cases the probability that the damage process does not cross a certain threshold before a time t is calculated. Copyright © 2004 John Wiley & Sons, Ltd.