Analysis of the reliability and the maintenance cost for finite life cycle systems subject to degradation and shocks

This paper deals with a deteriorating system subject to two different causes of failure: internal continuous degradation and sudden shocks. The degradation process is modelled using a gamma process. It is assumed that the system fails when the deterioration level reaches a critical threshold. Furthermore, sudden shocks arrive at the system at random times following a non-homogeneous Poisson process. When a sudden shock takes place, the system fails. To control the system reliability, a condition-based maintenance is applied. Under this maintenance policy, availability measures of the system are obtained. It is shown that these measures fulfil Markov renewal equations. A recursive method is developed to compute these measures. Furthermore, the maintenance cost of this system is analysed. Traditionally, the maintenance cost is analysed assuming an infinite time span. However, most systems have a finite life cycle and the application of the asymptotic approach is questionable. In this paper, the maintenance cost is analysed considering a finite life cycle. A recursive method, which combines numerical integration and Monte Carlo simulation, is developed to obtain the expected cost rate in the finite life cycle and its associated standard deviation.