On geometric reduction of age or intensity models for imperfect maintenance

There is an extensive literature on imperfect maintenance models. Among them, we have proposed in Doyen and Gaudoin (2004) [13] the classes of ARA and ARI models. These models express the effect of maintenance by an Arithmetic Reduction of Age (for ARA models) and an Arithmetic Reduction of Intensity (for ARI models). The aim of this paper is to study the possibility of building equivalent models with a Geometric Reduction of Age or Intensity: the GRA and GRI models. Several ideas leading to different possible models are presented. A list of potential GRI-GRA models is established. A brief illustration of their behavior is given based on simulated data and an application to real maintenance data is presented.