Availability for repairable series systems with random repair times

The failure pattern of repairable components is often modeled by an alternating renewal process which implies that a failed component is perfectly repaired and maintenances frequency is certain. In practice, repair is often imperfect and frequency is uncertain. This paper assuming number of repairs of the failed component is stochastic, and proposes a generalized availability model for repairable series systems. Availability and some asymptotic quantities in these models are derived. Finally, an example illustrates the application of these models.