Age-based preventive maintenance for passive components submitted to stress corrosion cracking

This paper deals with an age-based preventive maintenance for critical systems or structures subject to a gradual degradation phenomenon such as stress corrosion cracking. We analyze a system subjected to different cracks. A crack can be only detected when its length exceeds a detection threshold. When the length of the crack reaches a given threshold, the system fails. The length of the crack is modeled using a gamma process. Furthermore, when the number of cracks detected in the system attains a fixed value, the system fails. Corrective maintenance actions are performed after a system failure. A preventive maintenance is performed when the age of the system is TT. Maintenance actions replace the system by a new one with an associated cost. The problem is to determine an optimal planned replacement time TT, minimizing the expected cost rate of the system. The analytical solution to the problem is obtained under some general assumptions. A numerical example is shown to illustrate the problem.