Conditionally independent generalized competing risks for maintenance analysis

Yann Dijoux (1) , Laurent Doyen (2) , Olivier Gaudoin (1)

1 SMS - Statistique et Modélisation Stochatisque
2 SAGAG - Statistique Appliquée et de Géométrie Aléatoire de Grenoble

A complex repairable system is subjected to corrective maintenance (CM) and condition-based preventive maintenance (PM) actions. In order to take into account both the dependency between PM and CM and the possibility of imperfect maintenances, a generalized competing risks model have been introduced in Doyen and Gaudoin (2006). In this paper, we study the particular case for which the potential times to next PM and CM are independent conditionally to the past of the maintenance process. We address the identifiability issue and find a result similar to that of Cooke (1993) for usual competing risks. We propose a realistic model with exponential risks and derive the maximum likelihood estimators of its parameters.

Mots clés: reliability; imperfect maintenance; competing risks; point processes

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Yann Dijoux, Laurent Doyen, Olivier Gaudoin. Conditionally independent generalized competing risks for maintenance analysis. T. Bedford, J. Quigley, L. Walls, B. Alkali, A. Daneshkhah and G. Hardman. Advances in Mathematical Modeling for Reliability, IOS Press, Amsterdam, pp.88-95, 2008, 978-1-58603-865-6. ⟨hal-00305307⟩