Repair efficiency estimation in the ARI1 imperfect repair model

International audienceThe aim of this paper is to study the estimation of repair efficiency in an imperfect repair model, called Arithmetic Reduction of Intensity model with memory one (ARI1). This model, first introduced by Doyen and Gaudoin, has a very simple failure intensity, and repair efficiency is characterized by a single parameter. Thanks to that simplicity, the asymptotic almost sure behavior of the failure and cumulative failure intensities of ARI1 model can be derived. Then, the almost sure convergence and asymptotic normality of several estimators (including maximum likelihood) of repair efficiency can be proved in the case where the wear out process without repair is known. The influence of the number of observed failures on the quality of the repair efficiency estimation is empirically studied. Finally, repair efficiency is estimated on a real maintenance data set