Families of components, and systems, exposed to a compound poisson damage process

Abstract

A fairly common failure model in a wide variety of contexts is a cumulative damage process, in which shocks occur randomly in time and associated with each shock there is a random amount of damage which adds to previously incurred damage until a breaking threshold is reached. The multivariate life distributions that are induced when several "components," each with its own breaking threshold, are exposed to the same cumulative damage process are of interest in their own right, and are important examples in the general study of multivariate life distributions. This paper is a summary of some results about the very special, but central, case in which the cumulative damage process is a compound Poisson process. It is focused on the multivariate life distributions that arise when the component breaking thresholds are random and have a Marshall-Olkin multivariate exponential distribution. There are two relevant multivariate life distributions that can be derived, an intermediate distribution for the number of shocks (cycles) to failure and the final distribution for the actual times to failure. The results have application to the life distribution of a coherent system whose components are exposed to the damage process. (Author)