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AOQ and AOQL Calculator for Rectifying Inspection

Acceptance sampling only protects you if rejected lots are screened or returned. AOQ tells you how many defectives still escape after that screening step, and the AOQL is the ceiling no matter how bad the supplier gets. This calculator shows both, and a chart that makes the hump in the curve obvious.

Your numbers

Lot size N

units

Number of pieces in each submitted lot.

Sample size n

units

Pieces inspected from each lot.

Acceptance number c

Maximum defectives in the sample for the lot to be accepted.

Incoming process percent defective p

2.5 %

True percent nonconforming in the lots you receive.

Your results

Average outgoing quality AOQ

1.5564

Percent defective in product leaving inspection, after rejected lots are 100 percent screened and defectives replaced with good parts.

Approximate AOQL

1.5778

Worst-case average outgoing quality over all possible incoming quality levels, in percent.

Expected defectives in sample (n x p)

Probability of acceptance (fraction)

0.6767

Probability of acceptance Pa

67.7%

Share of lots expected to pass at this incoming quality (Poisson approximation of the binomial).

AOQL factor f for this c

1.372

Uses the Poisson approximation, accurate when n is small relative to N and p is small. For small lots or large p, use the hypergeometric or binomial model.

Save results:

Outgoing quality (AOQ, %) as incoming defect rate changes

Sweeps Incoming process percent defective p from 0.2 to 12, holding your other inputs fixed.

Outgoing quality by supplier from your ERP

Optional: we review how to compute AOQ and acceptance rates from your existing inspection lot history.

Optional. The tool and every export work without this. No spam.

How to use the calculator

Enter the lot size, the sample size and the acceptance number from your sampling plan. Then drag the incoming percent defective slider to see how the probability of acceptance and the outgoing quality change. The chart sweeps incoming quality from 0.2 to 12 percent so you can see where outgoing quality peaks. The primary results are AOQ at your chosen incoming quality and the approximate AOQL.

Use your actual plan values from ANSI/ASQ Z1.4 or your own supplier agreement.
Set p to a recent supplier history value to see typical outgoing quality.
Read the AOQL as the worst case you will ever ship under this plan.

The formula behind AOQ and AOQL

With rectifying inspection, accepted lots ship with their defectives in the uninspected part (N minus n). Rejected lots are fully screened and defectives replaced, so they ship clean. That gives AOQ = Pa x p x (N - n) / N. The probability of acceptance Pa is the chance the sample holds c or fewer defectives, here computed with the Poisson sum exp(-m) x (1 + m + m^2/2 + ...) where m = n x p. The AOQL is the maximum of that curve, approximated as f / n with f = 0.368, 0.841, 1.372 and 1.946 for c = 0 to 3.

Worked example and how to read it

Take N = 1000, n = 80, c = 2 and p = 2.5 percent. The sample is expected to hold 2 defectives, Pa is about 68 percent and AOQ is about 1.6 percent. The AOQL comes out near 1.6 percent as well, since 2.5 percent sits near the peak. If your customer needs 1 percent or better, this plan is not enough on its own. You need a larger sample, a lower c, or tighter supplier controls. Notice the curve falls on both sides of the peak: very good lots pass clean, very bad lots are mostly rejected and screened.

Common mistakes

The biggest one is quoting AOQL for a plan where rejected lots are not actually screened. If rejected lots are only returned and replaced with unscreened lots, the math does not apply. Also remember AOQ is an average over many lots, not a promise about any single lot. Finally, the Poisson shortcut overstates risk for small lots, so check the hypergeometric result when N is under about 10 times n.

Do not apply AOQL to destructive tests where screening is impossible.
Include lots that were accepted on deviation in your real history.
Recalculate when you change n or c after a supplier rating change.

Frequently Asked Questions

What is the difference between AOQ and AOQL?

AOQ is the average percent defective in outgoing product at one specific incoming quality level. AOQL is the maximum AOQ across all possible incoming quality levels, so it is the guaranteed upper bound for the plan, provided rejected lots are fully screened.

Does AOQL apply if we just return rejected lots?

No. The AOQ and AOQL formulas assume every rejected lot is 100 percent inspected and defectives are removed or replaced with good units. If rejected lots go back to the supplier unscreened, you have no outgoing quality guarantee from the plan.

Why is the AOQL only approximate here?

The tool uses the standard Poisson factors f for c = 0 to 3 and a finite lot correction. The exact AOQL needs the binomial or hypergeometric distribution and a numeric search, which differs by a few percent at small sample sizes.

Can I use this for ANSI Z1.4 plans?

Yes, enter the n and Ac from the Z1.4 table for your code letter and AQL. Z1.4 itself does not guarantee an AOQL, but the calculation tells you what your plan delivers when rejected lots are screened.

If your receiving results already sit in SAP QM, Infor, Epicor or another ERP, we can pull lot history and compute outgoing quality by supplier automatically. Ask for a short review of your inspection data.

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