A Prescriptive Maintenance Policy for a Gamma Deteriorating Unit

Most of the recent research in the field of maintenance is focused on using more and more information about the state of the system and its environment for predicting future events and making prescriptions about maintenance and operations. Indeed, these prescriptions take the form of recommendations that do not only describe what, how, and when to conduct the maintenance but also consist in advice on how to adjust the system operating conditions for the desired outcome. By following this general idea, this paper suggests a new maintenance policy for a degrading unit that generalizes a policy recently proposed in the literature by including the possibility of influencing the remaining useful life of the unit by changing its usage rate. In fact, this policy assumes that an inspection is performed at a prefixed time and that, based on the result of the inspection, it is decided whether to immediately replace the unit or to postpone its replacement to a second predetermined time and possibly adjust its working rate, if this latter option is deemed convenient. After each replacement the unit is considered as good as new. The degradation process of the unit is described by using a gamma process based model. The unit is assumed to fail when its degradation level passes an assigned threshold. It is supposed that failures are not self-announcing and that failed units can continue to operate, though with reduced performance and/or additional costs. Maintenance costs are computed considering the cost of a preventive replacements, corrective replacements, inspections costs, 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. This latter cost also includes the possible penalty determined by failure to comply with contract clauses. The optimal maintenance policy is defined by minimizing the long-run average reward rate.