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.