Simple accurate approximations of the control limit policy in condition based maintenance

In this paper, we consider a component exhibiting a continuous monotone degradation. The degradation process is random and modelled as a Gamma process. The maintenance policy is condition based and follows the control limit policy with a preventive limit and a given failure limit. The inspection cost is non-negligible. Therefore, the component monitoring is periodic. Our objective is to minimize the annual average maintenance cost subject to a constraint on the minimum average availability. The decision variables are the preventive limit and the time between inspections. We propose a new simple (i.e., it involves basic spreadsheet calculations) and accurate (i.e., relative average error below 1.5%) approximations of the annual average maintenance cost and of the average availability. The empirical results show that our optimisation problem satisfies a balancing phenomenon, which stabilizes the optimal expected number of inspections per cycle as the degradation per unit of time increases. Moreover, we find that doubling the corrective maintenance cost increases the optimal annual average cost by a small factor of 12%. This is achieved by reducing the optimal time between inspections. These results show the benefit of jointly considering the preventive limit and the time between inspections in the maintenance optimisation.