The Armed Forces of the Republic of China have a large number of motor vehicles for administrative use. The vehicles were acquired from different sources in different years. In general, the vehicles are old in age. The Armed Forces have established a plant to manufacture vehicles for replacement. Because the volume of production was low, the unit cost tended to be high. The private industry motor vehicles were also produced in an inefficient manner as compared to those produced in the United States. A logical alternative to reduce the cost is to combine the total demand and try to seek more efficient production. Unlike the private market, military vehicle replacement decisions are centralized. To help the decision maker to gain some insight on the optimal lifetime of a motor vehicle, a stochastic model is suggested in the paper.