Optimal maintenance of stochastically deteriorating systems

A machine maintenance problem were the deterioration of the machine is subject to additive random noise is considered. The objective is then to maximize the discounted net return of the machine. Furthermore, it is also required that the machine maintains a sufficiently good quality state with certain degrees of confidence in part or whole of the machine life span. This problem can be formulated as a constrained stochastic optimal control problem. It is then shown that the stochastic optimal control problem can be converted into an equivalent deterministic optimal control problem and subsequently solved by the technique of control parametrization. Numerical examples are presented to illustrate some of the interesting features of the model.