Predictive maintenance: The one-unit replacement model

Predictive maintenance consists in deciding whether or not to maintain a system according to its state. In this paper, we address the case of one-unit systems, i.e. systems whose state is given by the value taken by one variable. The system is replaced in the case of breakdowns, but also when a maintenance is decided, at a lower cost than in the breakdowns case. We first propose a global approach to the problem and provide a characterisation of the optimal maintenance. We then focus on the case when the state transition between two successive periods follows a negative exponential distribution.