Mixed-Effects Nonhomogeneous Poisson Process Model for Multiple Repairable Systems

The nonhomogeneous Poisson process (NHPP) has become a useful approach for modeling failure patterns of recurrent failure data revealed by minimal repairs from an individual repairable system. Sometimes, multiple repairable systems may present system-to-system variability owing to operation environments or working intensities of individual systems. In this paper, we go over the application of generalized mixed-effects models to recurrent failure data from multiple repairable systems based on the NHPP. The generalized mixed-effects models explicitly involve between-system variation through randomeffects, along with a common baseline for all the systems through fixed-effects for non-normal data. Details on estimation of the parameters of the mixed-effects NHPP models and construction of their confidence intervals are examined. An applicative example shows prominent proof of the mixed-effects NHPP models for the purpose of reliability analysis.