no. 3
Numéro spécial : fiabilité
Testing an “Exponential Delay Time model” against a “Random Sign Censoring model” in Reliability
[Test du modèle “Delay Time” exponentiel contre le modèle “Random Sign Censoring” en Fiabilité]
Journal de la société française de statistique, Tome 155 (2014) no. 3, pp. 104-119.

Nous nous intéressons dans cet article à un système industriel sujet à différentes causes de pannes et sur lequel deux types de maintenance peuvent être effectuées : soit une maintenance corrective dans le cas d’une panne critique, soit une maintenance préventive afin de réduire le risque d’une panne critique. Des modélisations basées sur la notion de risques concurrents ont été proposées dans la littérature. Mais peu d’inférence statistique a été menée sur ces modèles. En particulier, il existe très peu de tests statistiques permettant de décider quel modèle pourrait le mieux s’ajuster à un jeu de données précis.

L’objectif de cet article est justement d’introduire un test non-paramétrique permettant de décider entre deux de ces modèles de fiabilité : le modèle “Delay Time” avec loi exponentielle et le modèle “Random Sign Censoring”. Nous introduisons une statistique de test et prouvons sa normalité asymptotique. Nous terminons l’article en étudiant par simulation le comportement de notre procédure dans le cas de petits échantillons et en présentant une application du test sur un jeu de données réelles.

In this paper we consider an industrial system subject to different causes of failure and different types of maintenance: a corrective maintenance is performed after a critical failure and a preventive maintenance can be performed in order to decrease the risk of critical failure. The recurrence of these types of maintenance has been often modeled in a competing risks framework.

However rather few statistical inference has been carried out in these models. In particular, there is a need to introduce statistical tests in order to help the engineers to select the model which better fits their data. Thus, in this paper, we introduce a nonparametric test with aim to decide between a Delay Time model with exponential distribution and a Random Sign model. We prove the asymptotic normality of our test statistic and we carry out a Monte Carlo simulation to learn how works our test on finite sample sizes. An application on a real dataset is also given.

Keywords: Asymptotic distribution, Censoring, Competing risks, Corrective Maintenance, Delay Time model, Nonparametric test, Preventive Maintenance, Random Sign Censoring Model
Mot clés : Censure, Loi asymptotique, Maintenance Corrective, Maintenance Préventive, Modèle “Delay Time”, Modèle “Random Sign Censoring”, Risques concurrents, Test non-paramétrique 
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Dauxois, Jean-Yves; Jomhoori, Sarah; Yousefzadeh, Fatemeh. Testing an “Exponential Delay Time model” against a “Random Sign Censoring model” in Reliability. Journal de la société française de statistique, Tome 155 (2014) no. 3, pp. 104-119. http://archive.numdam.org/item/JSFS_2014__155_3_104_0/

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