An Adaptive Prescriptive Maintenance Policy for a Gamma Deteriorating Unit

In this paper, we propose an adaptive prescriptive maintenance policy that generalizes one recently proposed in the literature. The policy consists in performing a single inspection aimed at measuring the degradation level of the unit at a predetermined inspection time. Based on the outcome of this inspection, it is decided whether to immediately replace the unit or to postpone its replacement to a later time. In case of postponement, the usage rate of the unit may be changed if deemed convenient. The main novelty of the proposed policy is that, in case the replacement is postponed, the value of the usage rate in the remainder of the maintenance cycle (i.e., the time elapsing between the inspection time and the replacement time) is determined based on the measured degradation level at the inspection time. The optimal maintenance policy is defined by maximizing the long-run average utility rate. After each replacement the unit is considered as good as new. The lifetime of the unit is defined by using a failure threshold model. It is assumed that failures are not self-announcing and that failed units can continue to operate, albeit with reduced performance and/or additional costs.

Maintenance costs are computed considering the cost of preventive replacements, corrective replacements, inspections, logistic costs, downtime costs (which account for time spent in a failed state), and costs that account for the change of the unit working rate. These latter costs also include the possible penalty determined by failure to comply with contract clauses.

Keywords: Gamma process, Prescriptive maintenance, Adaptive maintenance policy, Renewal reward theorem.

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