Optimal Inspection and Maintenance for Stochastically Deteriorating Systems

Our motivation is the problem of determining condition based maintenance policies, for systems whose degradation may be modelled by a continuous time stochastic process. The process is modelled by a Lévy process; failure occurs when the degradation reaches a critical level. The system may be inspected or repaired at any time, and that the costs of inspections and repairs may depend on the of system degradation. Optimal inspection policies for systems which may be directly and perfectly observed are determined. We establish recursive relationships and integral equations based on the Lévy and obtains optimal solutions.