Abstract
The aim of this paper is to study the asymptotic behavior of the Arithmetic Reduction of Intensity (ARI) and Arithmetic Reduction of Age (ARA) models as two imperfect maintenance models. These models have been proposed by Doyen & Gaudoin (2011), the failure process with bathtub failure intensity. The maintenance effect is characterized by the change induced by the failure intensity before and after a failure during the degradation period. To simplify the study, the asymptotic properties of the failure process are derived. Then, the asymptotic normality of several maintenance efficiency estimators can be proved in the case where the failure process without maintenance is known. Practically, the coverage rate of the asymptotic confidence intervals issued from those estimators is studied.
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