A multivariate degradation model with dependence due to shocks

Sophie Mercier (1) , Anne Barros (2) , Antoine Grall (3)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 NTNU - Norwegian University of Science and Technology [Trondheim]
3 LM2S - Laboratoire Modélisation et Sûreté des Systèmes

The aim of this paper is to model degradation phenomena in a multi-unit context , with dependence between components induced by a common and external stressing random environment. The stress arrives by shocks and each shock induces a sudden increase to the deterioration level of each component. The model induces a two-step dependence between components: …rstly, all components are simultaneously impacted by a shock; secondly, for a given shock, the deterioration increments of the di¤erent components are correlated. This leads to a multivariate degradation model. A method of moments is proposed, for the estimation of the model parameters. Assuming the components to belong to a system with a given failure zone, the system reliability is next provided and the in ‡uence of the model parameters on the system lifetime is studied. Numerical experiments illustrate the study.

Mots clés: Failure zone; Multivariate Lévy process; Multivariate compound Poisson process; Stochastic comparison; Upper set

Domaines: Probabilités [math.PR]

Sophie Mercier, Anne Barros, Antoine Grall. A multivariate degradation model with dependence due to shocks. MMR 2015: Ninth International Conference on Mathematical Methods in Reliability, 2015, Tokyo, Japan. ⟨hal-01355141⟩