Optimal Replacement Decisions for Structures under Stochastic Deterioration

The subject of this paper is determining optimal replacement decisions for components under stochastic deterioration. Using the discrete renewal theorem, three cost-based criteria for comparing maintenance decisions over unbounded horizons are determined in Sec. 2: (i) the average costs per unit time, (ii) the discounted costs over an unbounded horizon, and (iii) the equivalent average costs per unit time. By using these criteria, the cost of preventive maintenance can be balanced against the cost of corrective maintenance. In structural engineering, a distinction can often be made between a structure’s resistance and its design stress. A failure may then be defined as the event in which due to deterioration the resistance drops below the design stress or the failure level. Since deterioration is uncertain, it can best be regarded as a stochastic process. On the basis of a stochastic gamma process, the probabilities of failure per year, i.e. the probabilities that the resistance drops below the failure level per year, are calculated in Sec. 3. A case study on the maintenance of cylinders shows the usefulness of the replacement model in Sec. 4.