Analyze zero-failure evidence with clean reliability calculations. Test confidence goals, required samples, and lower bounds. Export reports, review tables, and plot outcomes with clarity.
Use zero-failure data to solve lower bound, sample size, confidence, or combined clean-run scenarios.
The chart updates after each calculation.
Sample software-development scenarios using the zero-failure lower-bound formula.
| Scenario | Successful Runs | Confidence Level | Reliability Lower Bound |
|---|---|---|---|
| API smoke tests | 10 | 90.00% | 81.1131% |
| CI pipeline passes | 29 | 95.00% | 90.4966% |
| Release validation runs | 59 | 95.00% | 95.1297% |
| Recovery drill streak | 99 | 99.00% | 95.4993% |
This calculator uses the classic zero-failure success-run form. It estimates a reliability lower bound when every observed run succeeds.
Reliability lower bound: R = (1 - C)^(1 / (n + 1)) Achieved confidence: C = 1 - R^(n + 1) Required successful runs: n = ceil( ln(1 - C) / ln(R) - 1 )Where:
Use this approach only when outcomes are pass or fail, failures are genuinely absent, and test conditions stay stable across runs.
It estimates a reliability lower bound from a streak of successful runs with zero failures. It also solves for required sample size, achieved confidence, and combined clean-run scenarios.
No. This form assumes zero observed failures. Once failures appear, use a broader reliability method such as an exact interval or a beta-binomial approach.
The extra one comes from the Bayesian update used by the success-run model. After n successes, the posterior form shifts to a distribution with n + 1 in the exponent.
Yes, when the runs are independent and collected under comparable conditions. In that case, adding the clean-run counts is a practical way to compute the combined lower bound.
No. Any binary pass-fail process can use it. Software teams often apply it to smoke tests, deployment checks, backup restores, and recovery drills.
Ninety, ninety-five, and ninety-nine percent are common. Higher confidence creates a stricter lower bound and usually requires more successful runs.
A clean streak does not prove perfect reliability. The calculator reports a conservative minimum reliability supported by the evidence at the chosen confidence level.
Independent runs, stable conditions, binary outcomes, and accurate failure detection matter most. Breaking those assumptions can make reliability look stronger than it really is.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.