A random shock model for a continuously deteriorating system

Purpose – A random shock model for a system whose state deteriorates continuously is introduced and stochastically analyzed. It is assumed in the model that the state of the system follows a Brownian motion with negative drift and is also subject to random shocks. A repairman arrives at the system according to a Poisson process and repairs the system if the state has been below a threshold since the last repair.Design/methodology/approach – Kolmogorov's forward differential equation is adopted together with a renewal argument to analyze the model stochastically. The renewal reward theorem is used to obtain the long‐run average cost per unit time.Findings – An explicit expression is deduced for the stationary distribution of the state of the system. After assigning several costs to the system, an optimization is also studied as an example.Practical implications – The present model can be used to manage a complex system whose state deteriorates both continuously and jumpwise due to the continuous wear and r...