Technical Note—A Note on Shot-Noise and Reliability Modeling

We discuss a reliability model that reflects the dynamic dependency between system failure and system stress. For example, the mortality rate for individuals who have had a heart attack declines with time. In particular, we use a shot-noise process to model “residual system stress,” which in turn drives a doubly stochastic Poisson process model for system failures. Intuitively, residual stress (or susceptibility to failure) may vary in a random manner yet be essentially unobservable, while system failures may be readily detectable and observable. Shot-noise distributions have a richness and subtlety that suggest untapped potential for applications. The doubly stochastic Poisson process provides a reasonable framework for modeling randomly varying rates of occurrence in a broad variety of settings.