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QR Batch Failure Estimator

Estimate a print batch’s failure rate from your own sample scan results: enter how many codes you tested and how many failed, and get the estimated failure rate with a 95% confidence interval.

Enter your numbers

Wilson 95% confidence interval (z = 1.96): centre = (p + z² / 2n) / (1 + z² / n), half-width = z · √(p(1 − p) / n + z² / 4n²) / (1 + z² / n), where p is failures / sample size. The interval reflects sampling uncertainty in your own test — it is not a measured property of the batch.

Result

Estimated failure rate
5.00%
95% confidence interval: 2.15% to 11.18%
Expected failures in batch of 100050
Plausible range in batch22 to 112
Sample tested100 codes, 5 failed

Plan reprints against the top of the interval, not the point estimate: with a small sample, the true failure rate could plausibly be that high.

How to use the QR Batch Failure Estimator

How this estimator works

You test a sample of codes from the batch and count how many fail to scan. The failure rate in your sample is the point estimate for the whole batch, and the Wilson interval shows how far the true batch rate could plausibly be from that estimate given the sample size. A small sample gives a wide interval; a large sample narrows it. The interval is about sampling uncertainty in your test, not a guarantee about any particular code.

Taking a sample you can trust

Test codes pulled from across the run, not just the top of the pile: early, middle, and late sheets, and from each printer or plate if several are involved. Scan each sampled code the way the audience will — at the real distance, in the real light, with an ordinary phone — and count a code as failed if it does not scan on the first reasonable attempt. A tidy sample tested under ideal conditions tells you less than a messy sample tested honestly.

What to do with the result

If the top of the interval is above the failure level your job can absorb, reprint or re-test before shipping. If the interval is too wide to decide, test more codes rather than guessing — doubling the sample narrows the interval noticeably. Keep the failed codes: checking what they have in common, such as one corner of the sheet or one ink, often finds the cause faster than statistics alone.

Frequently Asked Questions

What does the confidence interval mean?

Roughly this: if you repeated the same sampling many times, about 95% of the intervals computed this way would contain the true batch failure rate. It is a statement about the procedure and your sample size, not a promise that the true rate sits inside this particular interval.

How many codes should I sample?

More is better, and the interval shows you the payoff: doubling the sample narrows it noticeably. As a working rule, sample across the whole run — early, middle, and late — rather than taking one handful from the top of the pile.

Why use the Wilson interval instead of the simple percentage?

The simple percentage pretends the sample is the whole batch. The Wilson interval accounts for the fact that a sample can mislead, especially a small one, and it behaves sensibly at the extremes — for example, zero failures in a small sample does not mean a zero failure rate.

Does this validate the QR payloads?

No. This estimates scan failures from your sample outcomes. Checking that payloads are correctly formatted is a different job — validate the payloads separately before printing.