Availability of a system subject to hidden failure inspected at constant intervals with non-negligible downtime due to inspection and downtime due to repair/replacement

For systems with hidden or unrevealed failures, a common practice is to inspect the system regularly, since failures can only be detected upon inspection. Recent works in the literature have studied the availability of a system under periodic inspection, assuming perfect repair/replacement with non-negligible downtime due to repair/replacement for a detected failure. In some situations, however, not only downtime due to repair/replacement but also downtime due to inspection is non-negligible regardless whether a failure was detected or not. In this paper, we consider the availability of a system subject to hidden failure inspected at constant interval with both non-negligible downtime due to inspection and non-negligible downtime due to repair/replacement.