This paper presents an approach to maintenance planning which utilizes mathematics and economic theory to help select an optimal maintenance condition. The maintenance problem is discussed first with respect to short run (daily) routine operating decisions, and then with respect to long run decisions as they relate to equipment design and to maintenance facilities. The maintenance problem is then stated in mathematical terms. A cost minimizing maintenance model is described which takes account of such factors as deterioration and failure probabilities, manhours for preventive inspection and preventive repair, elapsed time for emergency diagnosis and repair, cost of setting up for periodic maintenance, cost of maintenance men, and cost of system downtime. A numerical example illustrates how the model can be used to determine the least cost combination of time between periodic maintenance, the number of maintenance men, and the number of periodics between inspections of each item for a required level of system operation.