  Most of the reliability literature on modeling the effect of repairs on
systems assumes the failure rate functions are monotonically increasing. For
systems with non-monotonic failure rate functions, most models deal with
minimal repairs (which do not affect the working condition of the system) or
replacements (which return the working condition to that of a new and identical
system). We explore a new approach to model repairs of a system with a
non-monotonic failure rate function; in particular, we consider systems with a
bathtub-shaped failure rate function. We propose a repair model specified in
terms of modifications to the virtual age function of the system, while
preserving the usual definitions of the types of repair (minimal, imperfect and
perfect repairs) and distinguishing between perfect repair and replacement. In
addition, we provide a numerical illustration of the proposed repair model.
