Classes of Virtual Age Models Adapted to Systems With a Burn-In Period

This paper proposes a new class of imperfect maintenance models for repairable systems subject to a burn-in period. Corrective maintenance and planned preventive maintenance are carried out over the course of the system´s life. Bathtub shaped intensities are adapted to characterize the reliability of systems developing a burn-in period. Imperfect maintenance models, such as virtual age models, allow us to describe maintenance efficiency. A previous study has pointed out that classical virtual age models can only be applied to continuously degrading systems, and not to systems with a burn-in period. A first attempt to adapt virtual age models with bathtub shaped intensity has then been proposed considering one specific virtual age, a particular intensity, and one kind of maintenance. In this paper, a general framework for adapting virtual age models to bathtub shaped intensities is presented. In particular, the concept of optimal maintenance supersedes the notion of perfect maintenance. The models can be suitable to every bathtub shaped intensity, and can consider multiple kinds of maintenance. Finally, an application to real data sets is presented.