A RANDOM SHOCK MODEL FOR A CONTINUOUSLY DETERIORATING SYSTEM

摘要

A random shock model for a system whose state deteriorates continuously is introduced. It is assumed that the state of the system is modeled by a Brownian motion with negative drift and is also subject to random shocks. A repairman arrives according to a Poisson process and repairs the system if the state has been below a threshold since the last repair. Explicit expression is deduced for the stationary distribution of the state of the system. An optimization is also studied.