Bivariate Gamma wear processes for track geometry modelling, with application to intervention scheduling

Sophie Mercier (1) , Carolina Meier-Hirmer (2) , Michel Roussignol (3)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 R&D - SNCF - Département recherche et développements
3 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

This paper discusses the intervention scheduling of a railway track, based on the observation of two dependent randomly increasing deterioration indicators. These two indicators are modeled through a bivariate Gamma process constructed by trivariate reduction. Empirical and maximum likelihood esti-mators are given for the process parameters and tested on simulated data. An EM algorithm is used to compute the maximum likelihood estimators. A bi-variate Gamma process is then tted to real data of railway track deterioration. Intervention scheduling is deened, ensuring that the railway track remains of good quality with a high probability. The results are compared to those based on both indicators taken separately, and also on one single indicator. The policy based on the joint information is proved to be safer than the other ones, which shows the potential of the bivariate model.

Mots clés: Gamma wear process; Lévy process; dependent stochastic processes; reliability; track maintenance

Domaines: Probabilités [math.PR]; Statistiques [stat]

Sophie Mercier, Carolina Meier-Hirmer, Michel Roussignol. Bivariate Gamma wear processes for track geometry modelling, with application to intervention scheduling. Structure and Infrastructure Engineering, 2012, 8 (4), pp.357-366. ⟨10.1080/15732479.2011.563090⟩. ⟨hal-01576989⟩