Passage times of perturbed subordinators with application to reliability

TL;DR

This paper analyzes the distribution of passage times in perturbed subordinators, a class of degradation models, and explores their application to reliability, including maintenance policy considerations.

Contribution

It extends classical degradation models by considering both first- and last-passage times for perturbed subordinators, providing new insights into their distribution and reliability applications.

Findings

Derived distributions for first-passage times

Derived distributions for last-passage times

Proposed maintenance policy based on passage times

Abstract

We consider a wide class of increasing L\'evy 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.