On the modeling of dependence between univariate Lévy wear processes and impact on the reliability function

Univariate Lévy processes have become quite common in the reliability literature for modeling accumulative deterioration. In case of correlated deterioration indicators, several possibilities have been suggested for modeling their dependence. The point of this article is the study of three different...

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Bibliographic Details
Published in:Applied stochastic models in business and industry 2024-05, Vol.40 (3), p.549-573
Main Authors: Mercier, Sophie, Verdier, Ghislain
Format: Article
Language:English
Subjects:
copula
Lévy copula
Lévy process
Mathematics
Modelling
multivariate degradation
Probability
Reliability
Stochastic processes
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Summary:Univariate Lévy processes have become quite common in the reliability literature for modeling accumulative deterioration. In case of correlated deterioration indicators, several possibilities have been suggested for modeling their dependence. The point of this article is the study of three different dependence models: use of a regular copula, superposition of independent univariate Lévy processes and use of a Lévy copula. The three methods are first presented and analyzed. In this way, it is shown that the multivariate process constructed through an ordinary copula cannot have independent increments in general, that is, it is not a Lévy process. The impact of a wrong choice for the model is next explored, based on data simulated from one model and next adjusted to all three models. It is shown that a wrong model can lead to either overestimate or underestimate the reliability function, which could be problematic in an application context.
ISSN:1524-1904
1526-4025
DOI:10.1002/asmb.2726