A condition-based maintenance of a dependent degradation-threshold-shock model in a system with multiple degradation processes

This paper proposes a condition-based maintenance strategy for a system subject to two dependent causes of failure: degradation and sudden shocks. The internal degradation is reflected by the presence of multiple degradation processes in the system. Degradation processes start at random times following a Non-homogeneous Poisson process and their growths are modelled by using a gamma process. When the deterioration level of a degradation process exceeds a predetermined value, we assume that a degradation failure occurs. Furthermore, the system is subject to sudden shocks that arrive at the system following a Doubly Stochastic Poisson Process. A sudden shock provokes the total breakdown of the system. Thus, the state of the system is evaluated at inspection times and different maintenance tasks can be carried out. If the system is still working at an inspection time, a preventive maintenance task is performed if the deterioration level of a degradation process exceeds a certain threshold. A corrective maintenance task is performed if the system is down at an inspection time. A preventive (corrective) maintenance task implies the replacement of the system by a new one. Under this maintenance strategy, the expected cost rate function is obtained. A numerical example illustrates the analytical results.