Mathematical model for maintenance planning of machine tools

Abstract

Preventive maintenance planning of machine tools may be a complex task for tools with multiple components. For manufacturing processes with high setup and downtime costs, components replacement should be combined to avoid too many production stoppages and therefore reduce costs. The combination that minimizes costs should take into account the lifetime distribution and the age of each component at the replacement time. Replacing too soon may imply a high number of replacements for a given component, while replacing too late may imply a high number of failures that lead to shutdowns, increasing costs. In this paper, a tool is seen as a series system, which means that whenever a component fails, a corrective action is needed and at least the failed component has to be replaced. In the literature, some of the models and heuristics for maintenance planning of series systems consider that a minimal repair is made when a component fails, while other models propose static approaches, i.e., the same combination and the same interval is used over time regardless of the ages of the components involved. This paper aims to propose a dynamic approach and presents a mathematical model to determine both the next time to perform a preventive maintenance task and the components that should be replaced in order to minimize the total cost. The model also intends to determine the components to be replaced preventively when unexpected events occur (such as the failure of a tool component or the machine, the shortage of raw material, etc.) or during planned stoppages (such as the end of a production order, machine preventive maintenance task, etc.).