A prescriptive maintenance policy for a two-unit system in the presence of production constraints

In this paper, we propose a prescriptive maintenance policy for a two-unit system subject to degradation. We suppose that the system is inspected only once during its mission duration, that both mission duration and inspection time are predetermined, and that the inspection allows to know the exact value of the degradation level of the units. It is assumed that units fail when their degradation level exceeds a given failure threshold, that failures are not self-announcing, and that maintenance activities can be performed at the inspection time only. Moreover, it is also assumed that maintenance activities can involve only prescriptive actions that consist in tuning the usage rate of the units when this is deemed convenient. The production rate depends on the usage rate. Higher usage rates incur higher usage costs. On the other hand, reducing the usage rate of a unit slows its degradation process and reduces the risk of failure. The production rate of a failed unit is zero. We assume that there exists a target production rate for the system and that missing the target triggers economic penalties conceived to compensate for the loss of production. Both low usage rates and failures can incur penalties. The tuning of the usage rate is made via a condition-based rule that uses the information gained through the inspection. Objective of the policy is to find the optimal trade-off between usage costs and penalties. The optimal policy is found by minimizing the expected overall cost.