Optimal Repair and Inspection Rules under Uncertainty

Abstract

This paper focuses upon the optimal repair and inspection policies of infrastructure under uncertainty in the facility deterioration process. It is supposed that the condition of the facility, which is defined in continuous state, can only be observed by inspection. The optimal impulse control problem is formulated to find out the optimal timing for inspection and repairing so as to minimize the expected life-cycle costs, including the repairing cost, user’s cost, and inspection cost. The state-dependent rules are presented to determine the optimal timing for inspection and repairing based upon the observation of condition state by solving the second-order Fredholm integral equation. The paper concludes with numerical examples, for illustration.