Three models for the failure process of a repairable system

Development of models for the failure process of a repairable system has been an interesting research topic for decades. There have been many models developed in the literature. However, more research is still needed to deal with various difficulties raised in the practical applications, which includes the cases that most real systems are composed of more than one component and that the failure process may not be stochastically monotone. For such cases, we have recently developed three models, which are briefly discussed in this paper.