Quality & Statistics

AQL Sampling Calculator

Sample size and accept/reject numbers from lot size, inspection level, and AQL, for normal or tightened inspection.

Accept if defects ≤ Ac

Lot or batch sizeunitsInspection levelAQL

Sampling plan

Sample

—

Accept ≤

—

Reject ≥

—

Code letter: —
Lots accepted at the AQL: —
Limiting quality (10% accepted): —

What AQL means

The AQL (acceptance quality limit; “acceptable quality level” in older editions) is the worst average quality a supplier’s process can run at and still have most lots accepted. It is given either as percent nonconforming (defective units) or as nonconformities (defects) per 100 units.

It is not a promise that every accepted lot is at least that good. A sampling plan only controls the odds: lots at the AQL are accepted most of the time, and lots much worse than the AQL are rejected most of the time. The operating-characteristic figures beside the calculator show those odds for the plan you pick.

How a sampling plan is chosen

Pick the inspection level (II unless your procedure says otherwise).
Find the sample size code letter from the lot size and level (Table I below).
With the code letter and AQL, read the sample size n, acceptance number Ac, and rejection number Re from the master table for normal or tightened inspection.
Where the table shows an arrow instead of numbers, follow it to the first plan below or above and use that row’s sample size — so the letter can change.
If the sample size is at least the lot size, inspect every unit.

Decision

Nonconforming found ≤ Ac → accept the lot; ≥ Re → reject the lot

The plans here come from MIL-STD-105E, which is public domain. ANSI/ASQ Z1.4 uses the same tables, and ISO 2859-1 uses the same normal and tightened single-sampling plans. Reduced inspection is left out on purpose: Z1.4 and ISO 2859-1:1999 give different reduced plans and switching criteria, so use the edition your contract names.

Sample size code letters (Table I)

Lot size	S-1	S-2	S-3	S-4	I	II	III
2 – 8	A	A	A	A	A	A	B
9 – 15	A	A	A	A	A	B	C
16 – 25	A	A	B	B	B	C	D
26 – 50	A	B	B	C	C	D	E
51 – 90	B	B	C	C	C	E	F
91 – 150	B	B	C	D	D	F	G
151 – 280	B	C	D	E	E	G	H
281 – 500	B	C	D	E	F	H	J
501 – 1,200	C	C	E	F	G	J	K
1,201 – 3,200	C	D	E	G	H	K	L
3,201 – 10,000	C	D	F	G	J	L	M
10,001 – 35,000	C	D	F	H	K	M	N
35,001 – 150,000	D	E	G	J	L	N	P
150,001 – 500,000	D	E	G	J	M	P	Q
500,001 and over	D	E	H	K	N	Q	R

Code letter	A	B	C	D	E	F	G	H
Sample size	2	3	5	8	13	20	32	50

Code letter	J	K	L	M	N	P	Q	R
Sample size	80	125	200	315	500	800	1,250	2,000

Worked example

A lot of 1,000 units, general inspection level II, AQL 2.5% for major defects, normal inspection:

Table I

1,000 is in 501 – 1,200 → code letter J → n = 80

Table II-A (normal), J at AQL 2.5

Ac = 5, Re = 6

Inspect 80 units at random. Five or fewer defectives: accept. Six or more: reject. If the process really runs at 2.5% defective, this plan accepts about 98% of lots; at 5% it accepts about 79%, and at 10% about 18%.

Under tightened inspection the same lot gets Ac = 3, Re = 4 with the same 80 units, which accepts about 86% of lots at 2.5% defective — a stronger push on a supplier whose recent lots have been failing.

Inspection levels

Level	When it is used
II	The default general level.
I	Less discrimination is needed; smaller samples.
III	Greater discrimination is needed; larger samples.
S-1 to S-4	Small samples are necessary (for example destructive or costly tests) and larger sampling risks can be tolerated.

Special levels don’t combine well with very small AQLs. The standard’s own example: S-1 never goes beyond code letter D (8 units), but AQL 0.10 needs at least 125 units, so the arrow takes you to the 125-unit plan anyway.

Switching between normal and tightened

Switch	Rule (MIL-STD-105E 4.7, 4.8)
Start	Begin on normal inspection.
Normal → tightened	2 lots rejected out of 5 or fewer consecutive lots on original inspection.
Tightened → normal	5 consecutive lots accepted on original inspection.
Stop inspection	5 lots in total rejected while on tightened inspection: stop accepting product until the supplier has taken corrective action, then resume on tightened.

Apply the rules separately for each class of defect (critical, major, minor).

Frequently asked questions

Which AQL should I use?

It is a contract decision between buyer and supplier. In consumer-product inspection a common convention is zero tolerance for critical defects, 2.5 for major, and 4.0 for minor, but nothing in the standard requires those values.

Why did the code letter change?

For some combinations of code letter and AQL the master table has no plan, only an arrow. You follow the arrow to the nearest plan and use its sample size — for example, AQL 0.65 at code letter G points up to letter F (20 units, Ac 0).

Does a larger lot need a proportionally larger sample?

No. Sample size grows much more slowly than lot size: 80 units for a lot of 1,000, 200 units for a lot of 10,000, and 500 units for a lot of 100,000 at level II.

What about AQLs above 10?

AQLs above 10 are only defined for nonconformities per 100 units, since one unit can carry several defects. The calculator switches its acceptance odds to a Poisson model for those.

Can I accept a lot with an Ac = 0 plan if I find no defects?

Yes — zero found means accept, one or more means reject. The standard also allows using the Ac = 1 plan with its larger sample instead of an Ac = 0 plan, where the table offers one.