Availability of a series system with replacement and repair

Abstract

We consider two models for the reliability of a series system of components with spares, serviced by a single service facility. Replacement of failed components by a spare has pre-emptive priority over repair of the failed components; the models differ in whether interrupted repairs resume from where they left off, or restart from the beginning. We find the availability of such systems: numerical results indicate that this is insensitive to the shape of the repair-time and replacement-time distributions. We also obtain the distribution of system downtime for these models.