First and Last Passage Times of Spectrally Positive Lévy Processes with Application to Reliability

Christian Paroissin () and Landy Rabehasaina ()
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Christian Paroissin: Université de Pau et des Pays de l’Adour
Landy Rabehasaina: Université de Franche-Comté

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 2, 351-372

Abstract: 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 (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.

Keywords: First-passage time; Last-passage time; Scale function; Failure time; Lévy process; Gamma process; Compound Poisson process; Brownian motion with drift; 60K10; 60J75 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11009-013-9360-9

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