Extended arithmetic reduction of age models for the failure process of a repairable system

In the reliability literature, imperfect repair processes, a kind of stochastic processes, are used to model the failure process of a repairable system. An imperfect repair process with the arithmetic reduction of age (ARA) modifies the age of the system but suffers from the drawback that if the initial intensity function is the power law, then the intensity after repairs remains parallel to the initial intensity. To address this drawback, this paper proposes a failure process model with an extended arithmetic reduction of age. In this model, a geometric repair factor is introduced to extend the arithmetic reduction of the age process. This process is compared with existing monotonic and non-monotonic imperfect repair processes. It is found that the proposed model performs better, in terms of the corrected Akaike information criterion, at modelling failure data with trend than the existing models, based on three real datasets.