Passage times of perturbed subordinators with application to reliability

Christian Paroissin (1) , Landy Rabehasaina (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

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.

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

Domaines: Probabilités [math.PR]

Christian Paroissin, Landy Rabehasaina. Passage times of perturbed subordinators with application to reliability. 2011. ⟨hal-00656837⟩