The Help of Regenerative and Semi-Regenerative Methods for Studying a Preventive Maintenance Model

We consider an item the behavior of which is described by a stochastic process (Φt)t≥0 taking values in a finite states space E. Let (Ew, Ef ) be a partition of the states space E : the states of Ew are the working states of the item, the states of Ef are the failure states. If no preventive maintenance was planned, the item would evolve until it reaches a failure state, the transition rates from working states to other working states or to failures states being constant. Indeed a supervisation by way of inspections occurs as follows : when an inspection takes place, if the item is observed in a state which is not too damaged, then no service is rendered and the date of the next inspection is chosen according to a distribution which depends on the observed state. Il the item is observed in a too damaged state, a service (named preventive maintenance) is rendered. When the item failed, it is repaired. The repair, service and inspection rates are not supposed to be constant. At the end of a repair or of a service, the item is in a not too damaged state which can be chosen depending randomly on the state it is just leaving. This model was introduced in [8] and studied by adding supplementary variables in order to obtain a Markov process. In this talk we will emphasize regenerative technics.