Modelling imperfect maintenance of coating systems protecting steel structures

Steel structures such as bridges, tanks and pylons are exposed to outdoor weathering conditions. In order to prevent them from corrosion they are protected by organic coating systems. Unfortunately, the coating system itself is also subject to deterioration. In this paper we use the gamma process to model the coating deterioration in continuous time. The condition of the coating is represented by a continuous quantity. As soon as the condition exceeds the intervention level, maintenance is to be done. However, maintenance of coating systems is usually imperfect. Most maintenance optimization models do not take this into account. We incorporate imperfect maintenance in our deterioration model by assuming that maintenance actions have a random effect on the condition of the coating. This random effect makes that the time between two maintenance actions is a randomized hitting time. We consider a number of probability distributions for the random effect and we will derive (explicit) expressions for the distribution and the expected value of the time between two maintenance actions. It is shown that the time between two maintenance actions is Weibull distributed if the random reduction in condition is exponentially distributed and the expected deterioration follows a power law function. Obviously, the (expected) time between two maintenance actions plays an important role in evaluating the cost of a maintenance strategy. A number of (imperfect) maintenance actions are available to improve the condition of a coating: spot repair, repainting and replacement. Each action has a different (random) effect on the coating. We derive an expression for the expected average maintenance cost per time unit for a given sequence of maintenance actions. Subsequently, we consider the problem of finding the set of maintenance actions that minimizes the maintenance costs over a bounded horizon. This problem is formulated as a stochastic dynamic programming model.