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AQL sampling simulator: what an incoming inspection really catches

A supplier ships 60 lots. You know its real defect rate; the inspector does not. Every lot is inspected with the ISO 2859-1 normal single sampling plan. See which lots get through, how the OC curve explains it, and when the switching rules would tighten or reduce the inspection.

Lot 1,000 · level II · AQL 1 → code letter J, n 80, Ac 2, Re 3 (normal inspection)
60 lots, one square each

Number = defectives found in the sample. Green accepted, red rejected. Orange ring: 2 of 5 consecutive lots rejected, switch to tightened. Blue ring: switching score reached 30, reduced inspection possible.

OC curve of the plan
0 %50 %100 %fraction defective → 10 %AQL

At 1.0 %: Pa = 95.3 %. Binomial model.

Result of this run
Lots accepted
97 %
Parts inspected
6,640
Incoming defects
9,233 ppm
Shipped to the line
8,083 ppm
  • Tightened inspection: not triggered
  • Switching score: 33 · reached 30 at lot 59

The run stays on normal inspection so the lots can be compared; the tightened and reduced plans of ISO 2859-1 are not simulated. Rejected lots are screened 100 %.

Your own plan with OC curve, AOQL and PDF: AQL sampling plan calculator · ISO 2859-1 switching rules

Five guided lessons

  1. A supplier exactly at the AQL. See that a lot at the AQL is usually, not always, accepted.
  2. A bad supplier still gets through. See the consumer’s risk.
  3. The supplier gets worse. See the switching rule catch a deteriorating supplier.
  4. An excellent supplier. See the switching score build up towards reduced inspection.
  5. Inspection does not make quality. Compare defects coming in with defects going out.

Acceptance sampling in five steps

  1. Lot size and inspection level give the sample size code letter (ISO 2859-1 table 1, general level II by default).
  2. Code letter and AQL give the plan: sample size n, acceptance number Ac and rejection number Re (table 2-A for normal inspection).
  3. Draw n parts at random from the whole lot, not from the top layer of the box.
  4. Count the defectives d. Accept the lot if d ≤ Ac, reject it if d ≥ Re.
  5. Record the result and apply the switching rules over the series of lots.

Worked example: lot of 1,000, AQL 1.0

Lot size 1,000 at level II gives code letter J, so n = 80 with Ac 2, Re 3. The probability of acceptance is P(d ≤ 2) from the binomial distribution:

Supplier fraction defectivePa (n 80, Ac 2)Meaning
0.5 %99 %Good supplier, almost always accepted
1 % (the AQL)95 %Producer’s risk about 5 %
2 %78 %Twice the AQL, mostly accepted
4 %38 %Four times the AQL, still accepted more than one lot in three
6.5 %10 %About the limiting quality for 10 % consumer’s risk

Common mistakes with AQL

  • Reading AQL as the maximum defect rate of each lot.
  • Using one plan forever without the switching rules, which removes most of the customer’s protection.
  • Taking the sample from one place in the lot, which breaks the randomness the tables assume.
  • Using AQL for critical or safety characteristics, where only zero defects is acceptable.
  • Treating sampling as a quality strategy. It sorts lots; it does not reduce the supplier’s defect rate.

Frequently asked questions

Does AQL 1.0 mean that lots with more than 1 % defects are rejected?

No. The AQL is the worst tolerable process average. Lots at the AQL are accepted with high probability (typically 90 to 99 %), and lots well above the AQL can still be accepted. For n 80, Ac 2 a lot with 4 % defective is accepted about 38 % of the time. The OC curve shows the full picture.

What is the OC curve?

The operating characteristic curve gives the probability of accepting a lot for every possible fraction defective. Its shape depends on the sample size and the acceptance number, not on the AQL label. A steeper curve separates good and bad lots better.

What are producer’s risk and consumer’s risk?

Producer’s risk (α) is the chance of rejecting a good lot, usually quoted at the AQL. Consumer’s risk (β) is the chance of accepting a bad lot, usually quoted at the limiting quality (LQ or LTPD). With a single sample both cannot be small unless the sample is large.

What are the ISO 2859-1 switching rules?

Inspection starts at normal. Two of five or fewer consecutive lots rejected → tightened. Five consecutive lots accepted on tightened → back to normal. Switching score of 30 plus steady production and approval → reduced. A rejected lot on reduced (or irregular production) → back to normal. Five cumulative lots rejected on tightened → discontinue acceptance.

How is the switching score calculated?

It starts at 0 on normal inspection. For plans with Ac 0 or 1, add 2 for every accepted lot, otherwise reset to 0. For Ac 2 or more, add 3 if the lot would have been accepted with the acceptance number one step tighter, otherwise reset to 0. Reduced inspection can be considered from 30.

Is AQL sampling acceptable in the automotive industry?

Many automotive customers require zero-defect acceptance (c = 0) for attribute sampling, and IATF 16949 expects defect prevention at the source rather than sorting. AQL plans are still common at incoming inspection for non-critical characteristics and in consumer goods. Always check the customer-specific requirements.

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