Stochastic modeling of degradation branching processes

Abstract

Degradation branching is a common phenomenon in many real-life applications. The degradation of a location not only increases with time, but also propagates to other locations in the same system. While the degradation of an individual location has been studied extensively, research on degradation branching is sparse. In this paper, we develop a general stochastic degradation branching model that characterizes both the degradation growth and degradation propagation. The probabilistic properties of the general degradation branching processes are analyzed. Reliability metrics such as the mean time to failure, mean residual life, failure probability and others are also investigated. In particular, closed-form expressions for the expectation and variance of the degradation and selected reliability metrics are obtained when the time to branch follows an exponential distribution. The model is validated using actual crack growth data.