Redundancy Reliability Calculator

Work out redundancy reliability instantly with clear inputs, formula shown and shareable results.

About Redundancy Reliability Calculator

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.

Formulas

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

Worked example

With the default values below, Redundancy Reliability Calculator returns System Reliability of 99.94880%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Reliability Of One Unitaccepts 0.1–99.999 %: 92 %
Units In Parallelaccepts 1–20: 3
Units Required To Functionaccepts 1–20: 1
Cost Per Unitminimum 0: 180,000

Results

System Reliability: 99.94880%
Gain Over A Single Unit: 7.9488%
Cost Of Redundant Set: $540,000.00
System Unavailability: 0.05120%

Step by step

1Values used
2k-out-of-n reliability
3Full parallel
4System Reliability= 99.94880
5Gain Over A Single Unit= 7.9488
6Cost Of Redundant Set= 540,000.00
7System Unavailability= 0.05120

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax or compounding frequency into account.
Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Does redundancy always deliver the calculated gain?

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.

Is 2-out-of-3 better than 1-out-of-2?

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.