Optimum maintenance policy and sale date for a machine subject to random deterioration

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.