Semiparametric inference for an extended geometric failure rate reduction model

The aim of this paper is twofold. First a new imperfect maintenance model is introduced. This model is an extension of Finkelstein's Geometric Failure Rate Reduction model, using the modification proposed by Bordes and Mercier for extending the Geometric Process. Second, based on the observation of several systems, the semiparametric inference in this model is studied. Estimators of the euclidean and functional model parameters are derived and their asymptotic normality is proved. A simulation study is carried out to assess the behavior of these estimators for samples of small or moderate size. Finally, an application on a real dataset is presented.