Abstract
This paper exhibits a stochastic model which describes the evolution of a
material submitted to inspections. When an inspection takes place, a decision depending on the observed state of the material is taken. If the
material is in not too bad state, no service is rendered, only the date of
the next inspection is chosen. If the material is in a bad working state,
a service takes place. Roughly speaking, the failure rates of the material
are constant, the inspection and repair rates are general. We define the
average cost function corresponding to the utilization of this material and
we show how it can be computed. Then we determine the inspection rates
which give the optimal maintenance policy using a simulated annealing
algorithm. We observe experimentally that the best durations between inspections are deterministic ones.