Predictive maintenance consists in deciding whether or not to maintain
a system according to its state. In this paper, we address the case o
f one-unit systems, i.e. systems whose state is given by the value tak
en by one variable. The system is replaced in the case of breakdowns,
but also when a maintenance is decided, at a lowest cost than in the b
reakdowns case. We first propose a global approach to the problem and
provide a characterisation of the optimal maintenance, We then focus o
n the case when the state transition between two successive periods fo
llows a negative exponential distribution. (C) 1998 Elsevier Science B
.V. All rights reserved.