AQL sample size calculator

Enter the lot size, inspection level and AQL, and get how many units to inspect and how many defectives accept or reject the lot. The calculator reads the ISO 2859-1 tables for you, arrows included, and shows the path it took.

Sampling plan

80units to sample

Code letter

Accept up to (Ac)

Reject at (Re)

Pull 80 units at random from the lot. With 2 or fewer defectives in the sample, accept the lot. With 3 or more, reject it.

How the table was read

Lot of 1,000 units at level II: code letter J (80 units).
AQL 1.0 on normal inspection: Ac 2, Re 3.

Same letter, other AQLs (normal)

AQL	Sample	Ac	Re
0.65	80	1	2
1.0	80	2	3
1.5	80	3	4
2.5	80	5	6
4.0	80	7	8
6.5	80	10	11

Same lot and AQL under the three severities

Severity	Letter	Sample	Ac	Re
Normal	J	80	2	3
Tightened	J	80	1	2
Reduced	J	32	1	2

How to build an AQL sampling plan

A single sampling plan under ISO 2859-1 (ANSI/ASQ Z1.4, MIL-STD-105E) comes from two tables:

1. Code letter: Table 1, crossing the lot size with the inspection level (II is the default)

2. Plan: the master table for the severity (2-A normal, 2-B tightened, 2-C reduced), crossing the code letter with the AQL: sample size n, acceptance number Ac, rejection number Re

3. Decision: with Ac or fewer defectives in the sample, accept the lot. With Re or more, reject it

Draw the sample at random from the whole lot. A unit with several defects counts once when the AQL is in percent nonconforming. Above AQL 10, the tables only apply to nonconformities per 100 units, and then every defect counts.

Worked example

The values already in the calculator: a lot of 1,000 units, level II, AQL 1.0, normal inspection.

Table 1: a lot of 501 to 1,200 at level II gives code letter J, which means 80 units
Table 2-A, row J, column 1.0: Ac 2, Re 3
Inspect 80 units drawn at random. With 0, 1 or 2 defectives, accept the lot. With 3 or more, reject it

For the same lot, same letter J:

AQL	Sample	Ac	Re
0.65	80	1	2
1.0	80	2	3
2.5	80	5	6
4.0	80	7	8

Many plants use one AQL per defect class, for example 0.65 for major and 2.5 for minor defects. The 80-unit sample is the same, and each class has its own Ac and Re.

Under the other severities, same letter J and AQL 1.0: tightened is 80 units with Ac 1, Re 2. Reduced is 32 units with Ac 1, Re 2.

When the table shows an arrow

Not every letter and AQL pair has a plan. Take a small lot with a low AQL: 20 units at level II gives letter C (5 units), but at AQL 1.0 the cell for letter C has an arrow pointing down. The first plan below it is letter E: 13 units, Ac 0, Re 1. The sample becomes 13, not 5. This is the most common mistake when reading the table: taking the Ac of the new plan with the sample size of the old letter.

An arrow pointing up works the same way: use the first plan above it and that row’s sample size. When the sample comes out as large as the lot or larger, the standard says to inspect 100% of the lot.

How to read the result

Sample size: how many units to inspect, drawn at random from the whole lot.
Ac: the most defectives the lot can have in the sample and still be accepted.
Re: the number of defectives that rejects the lot. In the current tables, Re = Ac + 1.
Ac 0, Re 1: a single defective rejects the lot. You get this with a low AQL and a small sample.
Accepting a lot does not prove it is good. The plan protects the average over a series of lots. A single lot worse than the AQL can still pass by luck, which is why the switching rules to tightened inspection exist.

Reduced inspection: which table this calculator uses

The calculator follows Table 2-C of ISO 2859-1:1999, where Re = Ac + 1. ANSI/ASQ Z1.4 (like MIL-STD-105E) has a different reduced table with a gap between Ac and Re (for example Ac 1, Re 3): a count between the two accepts the lot but sends you back to normal inspection. ISO 2859-1:1999 removed that gap. If your contract cites Z1.4, check the reduced numbers there. The normal and tightened plans are the same in both.

Common mistakes

Using the original letter’s sample size after following an arrow. The sample size is the one of the row where the plan sits.
Sampling a fixed percentage of the lot (say 10%). The standard does not work that way: the sample grows much more slowly than the lot.
Pulling the sample from the top of the pallet or the start of the run. It has to be random across the lot.
Treating the AQL as the quality target. AQL 1.0 does not mean 1% defective is fine for the customer. It is the quality at which the plan accepts most lots.
Staying on normal inspection forever. The switching rules to tightened inspection are part of the system and are what protects the customer when a supplier gets worse.

To measure how much of the process falls inside the spec, instead of only accepting or rejecting lots, use the Cpk calculator and the control chart generator. And before relying on inspection by measurement, check the gage with a gage R&R study.

Sources

ISO 2859-1:1999, Sampling procedures for inspection by attributes, Part 1: Sampling schemes indexed by acceptance quality limit (AQL) for lot-by-lot inspection, Tables 1, 2-A, 2-B and 2-C.
ANSI/ASQ Z1.4, Sampling Procedures and Tables for Inspection by Attributes (successor to MIL-STD-105E).
ABNT NBR 5426:1985, the Brazilian standard, with the same code letters and the same normal and tightened plans.

Frequently asked questions

How do you calculate an AQL sample size?

Two lookups. In Table 1, the lot size and inspection level give the sample size code letter. In the master table for the inspection severity (normal, tightened or reduced), the code letter and the AQL give the sample size and the Ac and Re numbers. Example: a lot of 1,000 at level II is letter J; at AQL 1.0 on normal inspection, sample 80 units, Ac 2, Re 3.

What does AQL mean?

AQL is the acceptance quality limit: the worst percent nonconforming that, averaged over a series of lots, you still consider acceptable. It is agreed between customer and supplier. Common values are 0.65 for critical or major defects, 1.0 to 1.5 for major defects and 2.5 to 4.0 for minor defects.

Which inspection level should I use?

Level II, unless the contract or customer says otherwise. Level I takes smaller samples and level III larger ones, for when you need better discrimination. The special levels S-1 to S-4 are for costly or destructive tests where only small samples are practical.

What do the arrows in the AQL table mean?

An arrow means there is no plan for that code letter at that AQL. Follow the arrow to the first plan below or above it, and use the sample size of the row where that plan sits, not the one of your original letter. If that sample is as large as the lot or larger, inspect the whole lot.

What is the difference between normal, tightened and reduced inspection?

You start on normal. When 2 out of 5 consecutive lots are rejected, you switch to tightened, which accepts fewer defectives for the same sample. After 5 consecutive lots accepted on tightened, you go back to normal. Reduced uses smaller samples and needs a good track record plus approval from whoever is responsible for quality.

Is ANSI Z1.4 the same as ISO 2859-1?

Mostly. Both come from MIL-STD-105, and the code letters and the normal and tightened single sampling plans match. The main difference is reduced inspection: ISO 2859-1:1999 removed the gap between Ac and Re that Z1.4 still has, so the reduced plans differ.

MetrologyGage R&R calculatorParts, operators and trials become repeatability, reproducibility, %R&R and ndc.Open →QualityCp and Cpk calculatorPaste measurements, set the limits and get Cp, Cpk, Pp and Ppk with a histogram.Open →QualityControl chart (X̄-R, I-MR)Paste your data and get the control limits, the chart and the out-of-control points.Open →QualityDPMO and sigma level calculatorDefects, units and opportunities become DPMO, PPM, yield and sigma level, with FPY and RTY.Open →QualityPareto chart makerPaste causes and counts and see the vital few, the cumulative curve and the ABC classes.Open →QualityFMEA: RPN and Action PrioritySeverity, occurrence and detection become RPN and AP (AIAG-VDA), with the risks ranked.Open →