Integration of time-dependent covariates in recurrent events modelling : application to failures on drinking water networks

Claudio, Karim; Couallier, Vincent; Le Gat, Yves

Journal de la société française de statistique, Tome 155 (2014) no. 3, pp. 62-77.

L’extension linéaire standard du processus de Yule est un modèle adapté pour la modélisation des défaillances sur les réseaux d’eau potable, dans la mesure où il inclut dans le calcul du taux de défaillance les effets des défaillances passées, de l’âge et de différentes variables. Cependant, les fluctuations du nombre de défaillances au cours du temps montrent les limites de ce modèle dans la mesure où il n’intègre pas l’effet de variables exogènes évoluant avec le temps comme l’effet du climat. Une amélioration du modèle actuellement utilisé dans des outils comme PREVOIR$\copyright$ Canalisation est ainsi proposée, incluant à présent des variables temporelles. Ceci permet d’améliorer la prédiction du nombre de défaillances selon l’évolution du climat.

The standard Linear Extended Yule Process is a well-adapted stochastic model for water pipes failure modelling, as it takes into account the past number of pipe failures, the ageing and the effects of covariates in the failure rate. But fluctuations of failures along time in water network show the limits of the model, which does not consider time-dependent covariates, like frost effect. An improvement of the model actually used in a standard tool such as PREVOIR$\copyright$ Canalisation is therefore proposed that considers a time dependent covariate. This allows for dramatically improving the predictions of the number of pipe failures according to the climate.

Keywords: Dynamical intensity of counting process, Linear Extension of Yule Process (LEYP), Time-dependent covariate in water network failure models
Mot clés : Extension linéaire du processus de Yule (LEYP), Intensité dynamique d’un processus de comptage, Variable temporelle dans les modèles de défaillances des réseaux d’eau potable

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