Virtual age models with time-dependent covariates: A framework for simulation, parametric inference and quality of estimation

International audienceA repairable system faces some failures and imperfect maintenances throughout its lifetime. If several identical and independent systems are considered together, some differences may arise between the systems, such as the geographical location or the maintenance team for example, which are constant information, or the weather conditions, which vary with time. This observed heterogeneity will influence more or less the failure process. In this paper, we include these data in a generalized virtual age model with the use of covariates. Then we estimate simultaneously the effect of the maintenances, that of the covariates, and the intrinsic wear of the systems. We also propose two simulation methods as well as a numerical estimation procedure. Then we assess the quality of the estimation of the parameters with a thorough simulation study