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* Corresponding author 1 LMAP - Laboratoire de Mathématiques et de leurs Applications Pau 2 Laboratoire de Mathématiques - UMR CNRS 6623 LMB - Laboratoire de Mathématiques de Besançon

Abstract : We consider a wide class of increasing Lévy processes perturbed by an independent Brownian motion as a degradation model. Such family contains almost all classical degradation models considered in the literature. Classically failure time associated to such model is defined as the hitting time or the first-passage time of a fixed level. Since sample paths are not in general increasing, we consider also the last-passage time as the failure time following a recent work by Barker and Newby. We address here the problem of determining the distribution of the first-passage time and of the last-passage time. In the last section we consider a maintenance policy for such models.

Keywords : First-passage time last-passage time scale function failure time Lévy process gamma process compound Poisson process Brownian motion with drift

Autor: Christian Paroissin - Landy Rabehasaina -



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