Optimisation of a single-component maintenance system: A smoothed perturbation analysis approach

In this paper we show how the technique of smoothed perturbation analysis can be applied to optimize threshold values in a maintenance model. We do so for a particular model in which a single component is minimally repaired up to an age threshold t and preventively replaced at age tp, where tp > t. With each maintenance action, such as minimal repair, replacement after failure or preventive replacement, costs are associated. These costs may depend on the sample path history of the component. We derive an estimator for the derivative of the cost performance with respect to t and tp.