Scheduling Preventive Maintenance Considering the Saturation Effect

During the useful life period of a costly system, it has been a common practice to perform imperfect preventive maintenances (PMs) with the purpose of failure prevention and useful life extension. Nevertheless, a system cannot be restored to an as-good-as-new state even though the imperfect PM actions are performed with a high frequency. This is known as the saturation effect and it is commonly overlooked in the existing literature. Motivated by a PM problem in a manufacturing company, this study proposes two PM models to capture the dynamics of the saturation effect. The first model divides the system deterioration into recoverable damage and irreversible intrinsic fatigue. The PMs are assumed to be effective only in healing the first type of damage. When the intrinsic fatigue for some complex systems cannot be well defined, we propose another model that generalizes the existing virtual age models by allowing the proportion of virtual age reduction to depend on the PM frequency. The long-run average costs of the two models are derived, and optimization of the cost models is investigated. The proposed PM models are then applied to two types of mechanical systems in the manufacturing company. The case study shows that ignorance of the saturation effect will make inferior maintenance policy that incurs substantial losses. The proposed models are also shown to be robust in the sense that the parameter estimation errors cannot significantly increase the system operational cost rate.