The equations follow for parallel redundancy with a switch probability of success of 1:

The following approximate formula are used to calculate the reliability of a k-out-of-n type parallel system when the switch probability of success is equal to P S < 1.

For example, for a 1–out-of-2 system:

This formula is derived based on the assumption that all spares are in hot standby mode and that the failure of the switch may not lead to system failure if only standby units are failed. This formula gives correct results for the trivial cases where the probability of switch failure is 0 or 1. It gives reasonably approximate results for all other cases.