Success Run Theorem Calculator

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.

Calculator

Use zero-failure data to solve lower bound, sample size, confidence, or combined clean-run scenarios.

White Theme
Whole number. Zero failures are assumed.
Common values are 90, 95, and 99.
Use the minimum acceptable reliability target.
Example: staging test passes.
Example: production validation passes.

Plotly Graph

The chart updates after each calculation.

Example Data Table

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%

Formula Used

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:

  • R = minimum reliability supported by the clean-run evidence
  • C = confidence level
  • n = count of consecutive successful runs with zero failures

Use this approach only when outcomes are pass or fail, failures are genuinely absent, and test conditions stay stable across runs.

How to Use This Calculator

  1. Select the mode that matches your question.
  2. Enter clean-run counts, confidence, or target reliability.
  3. Press Calculate to show results above the form.
  4. Review the metric cards, chart, and export options.

Frequently Asked Questions

1. What does this calculator estimate?

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.

2. Does it work when failures exist?

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.

3. Why does the formula use n + 1?

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.

4. Can I combine two separate clean test campaigns?

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.

5. Is this only for software teams?

No. Any binary pass-fail process can use it. Software teams often apply it to smoke tests, deployment checks, backup restores, and recovery drills.

6. What confidence level should I choose?

Ninety, ninety-five, and ninety-nine percent are common. Higher confidence creates a stricter lower bound and usually requires more successful runs.

7. Why is the lower bound below the observed pass streak?

A clean streak does not prove perfect reliability. The calculator reports a conservative minimum reliability supported by the evidence at the chosen confidence level.

8. What assumptions matter most?

Independent runs, stable conditions, binary outcomes, and accurate failure detection matter most. Breaking those assumptions can make reliability look stronger than it really is.

Related Calculators

mean time to recoveryteam capacity calculatorstory points per sprintlead time in weeks calculatorbuild-to-suit lease calculator

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.