A Prescriptive Maintenance Policy for Systems with a Bathtub-Shaped Degradation Rate

In this paper, we propose a prescriptive maintenance policy for systems whose degradation evolves according to a non-homogeneous gamma process, where the degradation rate function (here intended as the derivative of the mean degradation function) has a bathtub-shaped temporal evolution. We introduce a usage variable that represents the rate at which the system operates, with a nominal level corresponding to standard operating conditions. At each inspection, this rate can be reduced by selecting one level within a finite set of admissible ones. The usage rate directly influences the degradation rate: lower usage rates slow down the degradation process, but each reduction involves a cost that increases with its deviation from the nominal level and with the duration for which that reduction is applied. In this work, the system operates over a finite time horizon and is subject to periodic inspections that are perfect, instantaneous, and non-destructive. Failures are not self-announcing. At each inspection, the usage rate to be applied until the next inspection is selected, with the possibility of performing preventive or corrective maintenance. The optimal policy is obtained by minimizing the expected total cost over the finite horizon.
Numerical studies are carried out by varying the number of available usage-rate levels and the length of the operating horizon. The obtained results, compared to those obtained by adopting a similar (simpler) policy that allows for corrective and preventive replacements only, show that within the considered experimental scenarios, allowing for usage-rate reductions significantly reduces the expected cost.

Keywords: prescriptive maintenance, non-homogeneous gamma process, bathtub-shaped degradation rate, finitehorizon maintenance policy, average total cost.