Some Properties of Incomplete Repair and Maintenance Models

We consider an incomplete repair model, that is, the impact of repair is not minimal as in the homogeneous Poisson process and not "as good as new" as in renewal processes but lies between these boundary cases. The repairs are assumed to impact the failure intensity following a virtual age process of the general form proposed by Kijima. In previous works field data from an industrial setting were used to fit several models. In most cases the estimated rate of occurrence of failures was that of an underlying exponential distribution of the time between failures. In this paper it is shown that there exist maintenance schedules under which the failure behavior of the failure-repair process becomes a homogeneous Poisson process. Further, examples of optimal maintenance under incomplete repair are given.