Optimization of preventive maintenance schedule and production lot size

In this research, a developed mathematical model is proposed to optimize the preventive maintenance age and lot size for a single-unit production system producing a single item. The system is assumed to start in an in-control state producing items of acceptable quality and then after a period of production time the system may shift to an out-of-control state producing non-conforming items. The time for the system to shift is a random variable that is assumed to follow a general probability distribution. It is assumed that failure may occur at any time after the system shift to the out-of-control state. The system failure time is also assumed to follow a general probability distribution. The proposed model considers average total values of the maintenance, inventory holding, non-conforming items, and shortage costs. The results found indicated that the introduction of failure possibility decreased the production lot size for a specific preventive maintenance age. Sensitivity analysis is carried out to assess the effect of four cost parameters on model performance. Furthermore, the model is extended to consider the effects of: combining inspection with preventive maintenance; and introducing non-negligible preventive maintenance duration.