  We review basic modeling approaches for failure and maintenance data from
repairable systems. In particular we consider imperfect repair models, defined
in terms of virtual age processes, and the trend-renewal process which extends
the nonhomogeneous Poisson process and the renewal process. In the case where
several systems of the same kind are observed, we show how observed covariates
and unobserved heterogeneity can be included in the models. We also consider
various approaches to trend testing. Modern reliability data bases usually
contain information on the type of failure, the type of maintenance and so
forth in addition to the failure times themselves. Basing our work on recent
literature we present a framework where the observed events are modeled as
marked point processes, with marks labeling the types of events. Throughout the
paper the emphasis is more on modeling than on statistical inference.
