THE NUMBERS, EXPLAINED
How to use this calculator.
Supported threshold is one: the system works if at least one component works. Independent failures over the same interval are required; no shared-cause model.
Start with your inputs
Enter independent component reliability (fractions). Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Independent component reliability (fractions) | 0.9,0.8 |
A worked example
With the example inputs above, at-least-one reliability (%) is 98. Change the inputs to explore your own scenario.
| Result | Example answer |
|---|---|
| At-least-one reliability (%) | 98 |
| All components fail (%) | 2 |
How this is calculated
At-least-one reliability (%)
Multiply component failure probabilities and subtract from one.
All components fail (%)
Multiply all component failure probabilities.
Symbols and units
- a
- Independent component reliability (fractions)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions and limits
Supported threshold is one: the system works if at least one component works. Independent failures over the same interval are required; no shared-cause model.
Calculations use the values you enter. Blank or invalid inputs show an error instead of silently substituting zero. Results are displayed to useful precision; calculations retain the underlying numeric precision.
Questions about this tool
What does the result tell me?
At-least-one reliability (%); All components fail (%). The result applies to the method and inputs described above. Check the units and assumptions before using it in a decision.
Why might another calculator differ?
Differences in units, rounding, timing or model definitions can produce different answers. Compare the input definitions and the method, rather than only the final number. For this tool: Supported threshold is one: the system works if at least one component works. Independent failures over the same interval are required; no shared-cause model.
Are my inputs stored or sent to AI?
Calculations on this page happen in your browser. The separate AI question finder sends its submitted conversation to OpenAI; these calculator fields are not sent. Favourites and recent tool names are stored locally. A shared link contains the inputs you choose to include.
Further reading
NIST Reliability Parallel or Redundant Model ↗
Background reading; this does not imply endorsement or independent review of SumFizz.
Review status
Software example and browser checks are recorded in our quality report. No external expert review is claimed. Created with coding assistance; calculations run as ordinary browser code.
Read the quality report →