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AQL attribute sampling plan

Enter lot size, inspection level and AQL to find how many units to sample, how many defects to accept and the real risk of accepting bad lots or rejecting good ones.

Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.

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Lot and plan

AQL up to 10: percent nonconforming items. Above 10: nonconformities per 100 units.

Operating characteristic
Inspection effort

Rejected lots are 100% screened (rectifying inspection). Total time feeds the cost of poor quality.

—Single sampling plan
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Plans for the same code letter and AQL

Tables II-A (normal), II-B (tightened) and II-C (reduced), with arrows already resolved.

Operating characteristic curve

Probability of accepting the lot versus true quality. Points: AQL (producer’s risk) and limiting quality (consumer’s risk).

Tap the chart to see the values.

Average outgoing quality (AOQ)

With 100% screening of rejected lots. The peak of the curve is the AOQL.

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Next step

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Cost of poor quality with this inspection →

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Method, assumptions and references

Equations used

Code letter = Table I (lot size × inspection level); n = sample size of the letter (A = 2 … R = 2000)
Ac and Re = Table II-A (normal), II-B (tightened) or II-C (reduced); arrow: first plan in the direction shown, with its n
Binomial: Pa(p) = Σ (d = 0…Ac) C(n, d) pᵈ (1 − p)ⁿ⁻ᵈ; Poisson: Pa = Σ e^(−np) (np)ᵈ ÷ d!
α = 1 − Pa(AQL); β = Pa(LQ); AOQ = Pa · p · (N − n) ÷ N; ATI = n + (1 − Pa)(N − n)

Assumptions and limits

  • Single sampling, random sample from the whole lot, items classified as conforming or nonconforming. Double and multiple plans are not covered here.
  • Tables II-A and II-B are the same in ISO 2859-1, NBR 5426 and ANSI/ASQ Z1.4. Table II-C follows Z1.4 and NBR 5426 (with a gap between Ac and Re); in ISO 2859-1:1999 reduced plans have Re = Ac + 1.
  • The AQL protects the producer over a series of lots; for an isolated lot, use limiting quality (ISO 2859-2) and check β.

Standards and technical documents

  • ISO 2859-1:1999 (Amd 1:2011): Sampling procedures for inspection by attributes — Part 1: Sampling schemes indexed by acceptance quality limit (AQL) for lot-by-lot inspection
  • ISO 2859-2:2020: Sampling schemes indexed by limiting quality (LQ) for isolated lot inspection
  • MIL-STD-105E: Sampling Procedures and Tables for Inspection by Attributes, 1989
  • Montgomery, D. C. Introduction to Statistical Quality Control, 8th ed. Wiley, 2019, ch. 15
  • Schilling, E. G.; Neubauer, D. V. Acceptance Sampling in Quality Control, 3rd ed. CRC Press, 2017

U.S. regulations

  • ANSI/ASQ Z1.4-2003 (R2018): Sampling Procedures and Tables for Inspection by Attributes
  • ANSI/ASQ Z1.9-2003 (R2018): Sampling Procedures and Tables for Inspection by Variables for Percent Nonconforming
  • 21 CFR Part 820 (QMSR): sampling plans used for acceptance must rest on a valid statistical rationale

Frequently asked questions

What sample size for a lot of 2,000 units?

At general level II the code letter is K: 125 units. With AQL 1.0 on normal inspection, accept the lot with up to 3 nonconforming and reject with 4.

What do the arrows in the table mean?

When a cell has no plan, the arrow points to the first plan available below or above. Use that plan’s sample size, not the one of the original letter.

Does AQL 1.0 mean I accept 1% defects?

No. It is the worst average tolerated over a series of lots. With plan 125/3/4, a lot with 5% defects still passes about 12% of the time; the OC curve shows the real risk.

When do I switch to tightened inspection?

When 2 of 5 consecutive lots are rejected on normal. Return to normal after 5 consecutive lots are accepted on tightened.