Derivation of an Exact Expression for Mean Time to Repair

The mean time to repair for a failed component is a necessary number for availability calculations. For a device with a constant failure intensity, one half of the time between tests is often taken to be the mean time to repair. This is an approximation. This paper derives an exact expression for mean time to repair and discusses its limiting behavior. For constant failure intensity, approximating the mean time to repair by one half of the test interval is valid when the product of failure intensity and test interval is small. As this product increases, mean time to repair approaches the "test interval" minus the "mean time to failure". An example illustrates these concepts.