Optimal periodic inspection of a deterioration process with sequential condition states

The condition of components subject to visual inspections is often evaluated on a discrete scale. If at each inspection a decision is made to do nothing or to perform preventive or corrective maintenance, the proposed decision model allows us to determine the optimal time between periodic inspections, such that the expected average costs per unit of time are minimized. The model which describes the uncertain condition over time is based on a Markov process with sequential phases. The key quantities involved in the model are the probabilities of having to perform either preventive or corrective maintenance before or after an inspection. The costs functions for two scenarios are presented: a scenario in which failure is immediately detected without the need to perform an inspection and a scenario in which failure is only detected by inspection of the object. Analytical results for a special case and algorithmic results for a broad class of Markov processes are derived. The model is illustrated using an application to the periodic inspection of road bridges.