What this calculator does
The result sums binomial outcomes from K through N: Σ C(N,i)Rᶦ(1−R)ⁿ⁻ᶦ. It is broader than a simple parallel model because not every path has to survive.
When to use it
Use it for voting systems, multi-pump duty requirements, and arrays where a defined minimum capacity or channel count is required.
Inputs and formula
N is the installed identical path count, K is the number required, and R is each independent path's reliability for the same mission.
Worked example and interpretation
For 3 required of 5 paths with each path at 90% reliability, the calculation sums the probability of exactly three, four, or five successful paths.
Practical notes and limitations
Common power, environmental, software, or maintenance dependencies can invalidate independence. Map shared causes in a reliability block diagram before claiming redundancy benefit.