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AQL sampling plan (ISO 2859-1 / ANSI Z1.4): theory, guide and example

How acceptance sampling by AQL works: code letters, inspection levels, accept and reject numbers, what the operating characteristic curve really tells you, and a worked incoming inspection example.

Ľubomír Blažek
Automotive quality manager · updated 2026-10-25

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Open the free AQL Sampling Plan tool and click Load sample: it reproduces the case study below.

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Theory: deciding about a lot from a sample

Inspecting every unit of every delivery is expensive. Acceptance sampling inspects a random sample and decides about the whole lot. ISO 2859-1 (equivalent to ANSI/ASQ Z1.4) is the most widely used system. Three inputs define the plan:

  • Lot size: larger lots get larger samples, but not proportionally.
  • Inspection level: II is standard; I is cheaper and less discriminating; III is stricter; S-1 to S-4 are for expensive or destructive tests.
  • AQL (acceptance quality limit): the worst average defect rate considered acceptable, agreed with the supplier.

Lot size and level give a code letter; code letter and AQL give the sample size n and the acceptance number Ac. If the sample contains Ac or fewer defectives, the lot is accepted; Re = Ac + 1 or more, it is rejected.

The operating characteristic (OC) curve

The OC curve shows, for each true defect rate of the lot, the probability that it will be accepted. It reveals two risks: the producer’s risk (a good lot at the AQL is rejected, typically about 5 %) and the consumer’s risk (a bad lot is accepted). The LTPD is the defect rate accepted only 10 % of the time.

Key point

AQL plans protect against bad lots on average; they do not guarantee that an individual accepted lot is good.

Step by step

  1. Lot size of the delivery.
  2. Inspection level, usually II.
  3. AQL from the supplier agreement.
  4. Read n, Ac, Re and take n units at random from the whole lot.
  5. Enter the number of defectives found to get the decision, and check the OC curve.

Example: incoming inspection of 1,000 brackets

A delivery of 1,000 brackets is inspected at level II, AQL 1.0 % (the tool’s default):

  • Code letter J, sample size n = 80, accept on 2, reject on 3.
  • OC curve: a lot with 1 % defectives is accepted 95 % of the time, with 2 % about 78 %, with 5 % still 23 %.
  • LTPD ≈ 6.5 %: only lots that bad are reliably (90 %) rejected.

The inspector finds 1 defective bracket in the 80: the lot is accepted. The quality engineer notes that a 2 % defective supplier would pass most deliveries, so for the critical hole position the plan is supplemented by a supplier capability requirement (Cpk ≥ 1.33) instead of relying on sampling.

Common mistakes

  • Taking the sample from the top of the first box instead of at random.
  • Reading AQL as the maximum defect rate of accepted lots.
  • Using AQL sampling for safety-critical characteristics.

Note: always verify plans for contractual use against the current edition of ISO 2859-1.

Frequently asked questions

Does AQL 1 % mean that 1 % defective lots are rejected?

No. AQL is the quality level that the plan accepts most of the time (typically about 95 % of lots). Lots with a defect rate somewhat worse than the AQL are still often accepted. The OC curve shows the exact probabilities.

Is sampling compatible with zero-defect targets?

Not really: any plan with Ac ≥ 1 accepts some defective lots by design. For critical characteristics, use process control and error-proofing at the source, or c = 0 plans.