Piecewise NHPP models with maximum likelihood estimation for repairable systems

Non-homogeneous Poisson process (NHPP) models are widely used for repairable system analysis. Different NHPP models have been developed for different applications. It has been noticed that almost all the existing models apply only a single model for the entire system development or operation period. However, in some circumstances, such as when the system design or the system operation environment experiences major changes, a single model will not be appropriate to describe the failure behavior for the entire timeline. In this paper, we proposed a piecewise NHPP model for repairable systems with multiple stages. The maximum likelihood estimation (MLE) for the model parameters is also provided.