Optimal maintenance policy for a system with preventive repair and two types of failures

• We develop a maintenance model with preventive repair and two types of failures.
• Our model has three types of forms corresponding to three types of actual system.
• An algorithm and two theorems are employed to obtain optimal maintenance policy.
• We examine how the system parameters affect the optimal maintenance policy.

Maintenance policy is one of the most critical issues in operations management. In reality, the proper functioning of productive systems is affected by so many complicated factors that even preventive repair cannot eliminate the possibility of system failures of different types. A cost-effective maintenance strategy is usually desired. In this paper, a geometric process maintenance model with preventive repair and two types of failures (repairable failure and unrepairable failure) is studied. A maintenance policy (T,N)(T,N) is proposed, where preventive repair will be conducted when the successive operating time reaches TT, and the system will be replaced by a new one when an unrepairable failure or the NNth repairable failure occurs. The optimal policy (T∗,N∗)(T∗,N∗) is obtained such that the average cost rate (i.e., the long-run average cost per unit time) is minimized. The model is generalized to reflect three different types of maintenance systems. An algorithm is proposed to obtain the optimal policy (T∗,N∗)(T∗,N∗). Numerical experiments are conducted to examine the impacts of system parameters on the optimal maintenance policy.