caa a22 4500 605519951 CHVBK 20210128100732.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s11009-013-9360-9 doi (NATIONALLICENCE)springer-10.1007/s11009-013-9360-9 First and Last Passage Times of Spectrally Positive Lévy Processes with Application to Reliability [Elektronische Daten] [Christian Paroissin, Landy Rabehasaina] 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 (Reliab Eng Syst Saf 94:33-43, 2009). 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. Springer Science+Business Media New York, 2013 First-passage time nationallicence Last-passage time nationallicence Scale function nationallicence Failure time nationallicence Lévy process nationallicence Gamma process nationallicence Compound Poisson process nationallicence Brownian motion with drift nationallicence Paroissin Christian Laboratoire de Mathématiques et de leurs Applications - UMR CNRS 5142, Université de Pau et des Pays de l'Adour, Avenue de l'Université, 64013, Pau cedex, France aut Rabehasaina Landy Laboratoire de Mathématiques - UMR CNRS 6623, Université de Franche-Comté, 16 Route de Gray, 25030, Besançon cedex, France aut Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/2(2015-06-01), 351-372 1387-5841 17:2<351 2015 17 11009 https://doi.org/10.1007/s11009-013-9360-9 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11009-013-9360-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Paroissin Christian Laboratoire de Mathématiques et de leurs Applications - UMR CNRS 5142, Université de Pau et des Pays de l'Adour, Avenue de l'Université, 64013, Pau cedex, France aut NATIONALLICENCE 700 1- Rabehasaina Landy Laboratoire de Mathématiques - UMR CNRS 6623, Université de Franche-Comté, 16 Route de Gray, 25030, Besançon cedex, France aut NATIONALLICENCE 773 0- Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/2(2015-06-01), 351-372 1387-5841 17:2<351 2015 17 11009