Development of two mathematical models for age-based maintenance policies of production systems with different operational states

Maintenance management along with production planning and control are two major components of production systems and operation management. In this paper, a production system that has two operational states plus a failure state is considered. In this system, maintenance actions are carried out based on the age-based policy which means the maintenance is performed after passing a specified time from the age of the system or after a system failure whichever occurs first. According to the random variables of the system failure, i.e., transition among the states of the system, two approaches are proposed to model the age-based policy considering different scenarios and their respective probabilities that may occur in the age-based policy. Both models aim to optimize the expected cost of the system per time unit, while the optimal time to terminate the production cycle and conduct preventive maintenance is determined as the main decision variable of the models. Some numerical examples employing different statistical distributions for the system failure mechanism, e.g., Weibull, gamma, normal, are also provided.