AQL sampling: how the sample size is set, what the inspection levels do, and what a pass really means

The lot size and inspection level set the sample; the AQL sets how many defects it may hold. How the tables work, when to use each level, and the odds that a bad lot passes anyway.

Filed under Line watch and quality control

Short answer: AQL sampling is how an inspector decides whether a whole production lot is acceptable by checking a random sample of it. The lot size and the inspection level set a code letter; the code letter sets the sample size; the AQL you choose for each defect class sets how many defects the sample may contain before the lot fails. The tables come from ANSI/ASQ Z1.4 and ISO 2859-1. The part most buyers miss: an AQL of 2.5 is not a promise that the lot is under 2.5% defective. It is the process average the plan is built to accept most of the time. A lot at twice that rate can still pass.

AQL sampling is the arithmetic under every pre-shipment inspection report, and it is the part buyers most often copy from a template without reading. Our pre-shipment inspection note covers the visit itself: when to book it, what the inspector checks, what a fail looks like. This note covers the numbers: how the sample size is set, what the general and special inspection levels do, what switching rules are, and what an AQL actually protects you from. You can run any of the plans below in our AQL calculator.

What AQL sampling is, and what it is not

Nobody checks every unit in a 5,000-piece order. Checking all of them takes days, costs more than the risk is worth, and a tired inspector on unit 4,000 misses things. The NIST/SEMATECH engineering statistics handbook puts it simply: "Acceptance sampling is "the middle of the road" approach between no inspection and 100% inspection." The idea started with ammunition testing in World War II, where the problem was obvious: "If every bullet was tested in advance, no bullets would be left to ship."

The handbook is also clear about the limit of the method: "the main purpose of acceptance sampling is to decide whether or not the lot is likely to be acceptable, not to estimate the quality of the lot." The inspection report gives you a decision, accept or reject. It does not tell you the true defect rate of the lot, and treating "passed" as "almost no defects" is where the trouble starts.

The tables everyone uses descend from a US military standard. Wikipedia's summary: "MIL-STD-105E was cancelled in 1995 but is available in related documents such as ANSI/ASQ Z1.4, "Sampling Procedures and Tables for Inspection by Attributes."" ISO 2859-1 is the international version. For a buyer the two give the same sample sizes and acceptance numbers in everyday use, and inspection firms will work to either.

How the sample size is set: lot size, inspection level, code letter

Three inputs set an AQL sampling plan:

1. Lot size. The number of units in the batch being inspected, counted in the unit you sell. If you sell sets, count sets, and say so in the purchase order.
2. Inspection level. How much inspection you are buying. This decides the sample size.
3. AQL per defect class. How many defects the sample may contain. This decides the accept and reject numbers.

Lot size and inspection level give a code letter; the code letter gives the sample size. QIMA, one of the large inspection firms, gives the standard worked example: "Example: A shipment of 4,000 units inspected at General Inspection Level II gives code letter L." and "Example: Code letter L at AQL 2.5 requires a sample of 200 units." At that AQL the acceptance number is 10: ten or fewer defective units in the 200 and the lot passes, eleven or more and it fails.

Inspection level and AQL are often mixed up. Renaud Anjoran of Sofeast, an ASQ Certified Quality Engineer, separates them cleanly: the level gives the number of pieces to check and the AQL limits give the upper limit on defectives. "They are separate concepts, but many people say “AQL inspection levels”, meaning “the levels for random inspections”."

General inspection levels I, II and III

The general levels change the sample size for the same lot. Sofeast's example for a 5,000-piece order at the general levels: 80 pieces at Level I, 200 at Level II and 315 at Level III.

• Level II is the default, and it is what you get if the purchase order does not say otherwise.
• Level I checks fewer pieces. It can make sense for a supplier with a long record of passed lots on a simple product. Sofeast's warning is worth keeping: "However, settling on this level by default, in order to spend less time/money on inspections, is very risky."
• Level III checks more pieces. Sofeast's rule of thumb: "If a supplier recently had quality problems, this level is appropriate." It is also a sensible choice for a first production lot, a new mold, or a product where a field failure is expensive.

A larger sample does not change the AQL. It makes the plan better at telling a good lot from a bad one, which the next section shows in numbers.

Special inspection levels S-1 to S-4

The special levels give very small samples. Quoting ISO 2859-1, Sofeast notes: ["“Four additional special levels, S-1, S-2, S-3 and S-4 […] may be used where relatively small sample sizes are necessary and larger sampling risks can be tolerated” (ISO 2859-1 standard)."](https://qualityinspection.org/inspection-level/) They are not a cheaper way to run the whole inspection. They are used for specific checks inside an inspection that otherwise runs at a general level. Insight Quality Services lists the usual reasons: the test destroys the unit, the test is slow or expensive to run, or the result tends to be the same on every unit in the lot.

Their example is a 2,000-piece order of cushions inspected at General Level II for workmanship, with one check pulled out: "However, you’ll also use Special Level S-1 to check the package measurements and do barcode scan tests — a 5-package sample size." Carton dimensions, barcode scans, drop tests and long run-in tests are the typical special-level checks. Workmanship, function and appearance stay at the general level.

What a pass actually means: the AQL is not a ceiling

This is the part that costs buyers money. Wikipedia defines the acceptable quality limit as the level that "is the worst tolerable process average" that is still considered acceptable. That is a process average, not a limit on any single lot. The NIST handbook states the producer's side of the design plainly: "The producer would like to design a sampling plan such that there is a high probability of accepting a lot that has a defect level less than or equal to the AQL." The buyer's side is a different number, the lot tolerance percent defective (LTPD): "The consumer would like the sampling plan to have a low probability of accepting a lot with a defect level as high as the LTPD." Sampling plans carry both risks, and Wikipedia is careful to add: "These are primarily statistical risks and do not necessarily imply that a defective product is intentionally being made or accepted."

The way to see both risks at once is the operating characteristic (OC) curve, which plots the chance a lot passes against its true defect rate. In NIST's words: "The OC curve is the primary tool for displaying and investigating the properties of a LASP" (a lot acceptance sampling plan). Here are a few points for the common plan above, sample 200 with acceptance number 10. We calculated these with the standard binomial formula; they are not from the tables.

A lot with twice the AQL's defect rate passes more often than not. The sample size changes that. For the same 5,000-piece order at AQL 2.5, the Level I plan (80 pieces, accept on 5 or fewer) passes a 5%-defective lot about 79% of the time, and the Level III plan (315 pieces, accept on 14 or fewer) passes it about 39% of the time. A five-piece check that allows no defects, the size of a typical special-level check, passes a 5%-defective lot about 77% of the time, which is why special levels belong on attributes that do not vary from unit to unit.

None of this makes AQL sampling weak. It makes it a tool with a known error rate, and the buyer chooses that error rate when choosing the level and the AQL. QIMA's caution runs the other way too: "Set it too strict and good shipments get rejected, damaging supplier relationships and delaying production."

Switching rules: normal, tightened and reduced inspection

The standards were written for a continuing stream of lots from the same supplier, not a single shipment. They start every supplier at normal inspection and move between severities based on results. One summary of the ISO 2859-1 rules: "Switch to tightened if 2 of 5 consecutive lots are rejected." Tightened inspection generally keeps the sample size and lowers the acceptance numbers. After a run of accepted lots on tightened, the plan returns to normal. Reduced inspection uses smaller samples, is allowed only after a sustained run of accepted lots with steady production and the buyer's approval, and ends at the first problem: "Return to normal if a lot is rejected under reduced inspection." Insight Quality Services quotes the standard on one detail people get wrong: inspection levels are "kept unchanged when switching between normal, tightened, or reduced".

In practice, Sofeast admits, "very very few buyers follow those switching rules" Most importers inspect each shipment at normal severity forever. For a supplier you will buy from for years, writing the switching rules into the quality agreement is cheap and fair: a supplier with a clean record earns smaller inspections, and a slipping one gets tighter checks automatically.

Single, double and multiple sampling plans

Everything above is a single sampling plan: one sample, one decision. The tables also give double and multiple plans. In a double plan the first sample can pass the lot, fail it, or be inconclusive, and if it is inconclusive NIST describes the next step: "If the outcome is (3), and a second sample is taken, the procedure is to combine the results of both samples and make a final decision based on that information." Double plans inspect fewer units on average when lots are clearly good or clearly bad. They are harder to run and harder to argue about, so most consumer-goods inspections stay with single sampling.

What to write into the purchase order

Wikipedia puts the reason for agreeing this in advance well: "In order to avoid argument, buyers and sellers agree on an AQL standard, chosen according to the level of risk each party assumes, which they use as a reference during pre-shipment inspection." A sampling clause that holds up has six lines:

• Standard and edition: ANSI/ASQ Z1.4 or ISO 2859-1, single sampling, normal inspection.
• Inspection level: General Level II unless there is a reason, and Level III for a first lot or a new mold.
• AQL per defect class: for example critical 0, major 2.5, minor 4.0, with the defect list attached so "major" means the same thing to both sides.
• Special-level checks: which tests run at S-1 to S-4 (carton size, barcode scan, drop test) and which stay at the general level.
• The counting unit: pieces, sets or cartons, and how a lot is defined if the order ships in several containers.
• What happens on a fail: rework and re-inspection at the supplier's cost, and the balance payment tied to a passed report. See payment terms.

The reference for "acceptable" is the signed sample, not the drawing alone; our note on the golden sample covers why. Sampling also starts long before the shipment: first article inspection approves the process, and AQL sampling checks that the process held.

Where JCH fits

JCH builds the inspection plan with the buyer before the purchase order is placed: the level, the AQL by defect class, the special-level checks and the defect list. Jack's engineering team and vetted partner network then inspect to that plan at first article, in process and before shipment. The inspection step shows where each check sits in a program. If you have a lot size and a product and want to see the plan before you commit to it, the AQL calculator gives the sample size and accept and reject numbers in a few seconds, and we are glad to review the result with you.

Straight answers

What is AQL sampling?

AQL sampling is a method for deciding whether a production lot is acceptable by inspecting a random sample of it. The lot size and inspection level give a code letter and sample size from the ANSI/ASQ Z1.4 or ISO 2859-1 tables, and the AQL chosen for each defect class gives the number of defective units the sample may contain before the lot is rejected.

What sample size does AQL 2.5 require?

The AQL does not set the sample size; the lot size and inspection level do. For example, a lot of 4,000 units at General Inspection Level II gives code letter L, a sample of 200 units. At AQL 2.5 that plan accepts the lot with 10 or fewer defective units and rejects it with 11 or more.

Does AQL 2.5 mean the lot has no more than 2.5% defects?

No. The AQL is the process average the sampling plan is designed to accept most of the time. A lot with a higher defect rate can still pass. With a 200-unit sample and an acceptance number of 10, a lot that is truly 5% defective passes a little more than half the time.

What is the difference between General Inspection Levels I, II and III?

They change the sample size for the same lot. Level II is the default. Level I inspects fewer units and suits a supplier with a strong record on a simple product. Level III inspects more units and suits a first production lot, a new mold or a supplier with recent quality problems.

When are special inspection levels S-1 to S-4 used?

For individual checks where a small sample is enough or necessary, such as destructive tests, slow tests, or attributes that do not vary from unit to unit like carton dimensions and barcode scans. The rest of the inspection still runs at a general level.

How this note was made: researched and drafted with AI assistance, checked against the sources listed below and edited at JCH Design & Manufacturing.