Further Properties of a Model for a System Subject to Continuous Wear

A generalization of an earlier diffusion model for system subject to continuous wear is presented. It is assumed that the state of the system is modelled by Brownian motion with negative drift and an absorbing barrier at the origin. A repairman arrives according to a stationary renewal process and increases the state of the system by a random amount if the state does not exceed a threshold. Various properties of this model are investigated including the distribution of the state of the system at time t, the first passage time to state 0 and the probability that the state of the system exceeds a certain level throughout a specified interval.