Success-Run Sample Size Calculator (Zero-Failure Reliability and Confidence)
The success-run theorem tells you how many parts must pass with zero failures before you can claim a given reliability at a given confidence. It is the quick answer behind the familiar 95/95 or 90/90 sample sizes used in process validation, special process qualification and aerospace test plans.
Your numbers
Statistical confidence that the true reliability is at least the value below.
0.95 means 95% of parts conform. Enter 0.99 for 99%.
Used only to show the sample as a share of the lot.
Test, inspection and consumed material cost per sampled part.
Your results
Assumes a binomial model, random sampling and a pass criterion of zero failures. Your customer specification or test plan governs the sample size you must actually use.
Sample size vs required reliability
Sweeps Required reliability (as a fraction) from 0.8 to 0.99, holding your other inputs fixed.
Validation evidence from your ERP data
Optional: we can review how lot results and sample plans are captured in your ERP and suggest a cleaner evidence trail.
Optional. The tool and every export work without this. No spam.
How to use the calculator
Pick the confidence level, enter the reliability you need to demonstrate as a fraction, and read the sample size. Round-up is already applied. Enter the lot size to see what share of the lot you would consume and the cost per test to see the budget. Use the chart to see how quickly the sample grows as you push reliability from 80% toward 99%.
- Zero failures allowed: one failure means you must retest with a larger plan.
- Use destructive-test cost per part for the budget line.
- Compare 95% and 99% confidence to see the price of extra certainty.
The formula behind it
With zero failures in n trials, the probability of that outcome is R to the power n. Setting that equal to 1 minus C and solving gives n = ln(1 - C) / ln(R). At 95% confidence and 95% reliability that is about 59 parts; at 95/99 it is about 299. The sample grows roughly in proportion to 1 / (1 - R), which is why each extra nine of reliability is expensive.
Common mistakes
The most common error is treating the result as a probability that a part is good. It is a lower confidence bound on the conforming rate. Others are sampling from a single batch and claiming it for the whole process, mixing variable and attribute data, and forgetting that the plan is only valid if the samples are random and representative. For variable data, a tolerance interval or Cpk study often needs fewer parts.
Frequently Asked Questions
What is the 95/95 sample size?
At 95% confidence and 95% reliability with zero failures allowed, the success-run theorem gives 59 samples. For 95/99 you need 299, and for 90/90 you need 22. Those are the numbers most validation plans quote.
What if I get one failure?
The zero-failure plan is then not met. You can move to a larger plan that allows one failure, which needs roughly twice the sample, or investigate the cause, fix it and restart the demonstration.
Does lot size change the result?
For large populations it does not. For very small lots the binomial model is conservative, and a hypergeometric plan can need fewer parts. The calculator shows the sample as a share of the lot so you can spot that case.
Is this the same as AQL sampling?
No. AQL plans control the risk of accepting a lot at a given defect level. The success-run approach demonstrates a minimum reliability with stated confidence, typically for validation or qualification rather than routine lot acceptance.
If sample plans and validation records live in your ERP or QMS, we can help pull lot, result and acceptance data into one place so the evidence is ready for audit.
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