Abstract
A machine is bought for production purposes for a length of time and then sold. It is possible to do preventive maintenance while the machine is being used, if desired, in order to slow down the degradation of machine's capability with age. This degradation is due to a multitude of causes and can, at best, be characterized in a probabilistic framework. In this paper, a stochastic version of Pontryagin's maximum principle is used to obtain optimum preventive maintenance policy and sale date for a machine subject to random deterioration. It is shown that the optimum maintenance policy is bang-bang.
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