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For k-out-of-n redundancy the system works if at least k of n units work, giving the binomial sum of terms C(n,k) R^k (1-R)^(n-k) from k to n. Full parallel redundancy is the special case k = 1, where system unreliability is (1-R)^n — three units at 92% each give 99.95% availability.
k-out-of-n reliability
R_system = sum from k to n of C(n,k) x R^k x (1-R)^(n-k)
Full parallel
R_system = 1 - (1 - R)^n
Only if failures are independent. Common-cause failures — shared power supply, shared cooling, identical design defect — bypass redundancy entirely and often dominate real system unavailability.
For availability, 1-out-of-2 is better. For safety systems that must avoid false trips as well as failures to act, 2-out-of-3 voting balances both, which is why it is standard in process safety.