What AQL 1 really protects you from, and when to test 100%

"Sample to AQL 1" does not mean 99% of what you ship is good. The plan MIL-STD-105E gives for lots of 501 to 1,200 at AQL 1 (inspect 80, accept on 2 or fewer) accepts material running at 1% defective 95.3% of the time, at 2% 78.4% of the time and at 5% 23.1% of the time. It protects you from the occasional very bad lot; stop sampling and test every unit when the test does no damage and its cost per unit, divided by what one escape costs beyond the repair you would do anyway, is below your defect rate. Automated electrical test often clears that bar once the fixture exists, because its cost per unit is small.

The odds, plan by plan

The table gives the chance of accepting a lot at each defect rate, calculated exactly as a binomial sum for a large lot. The first five rows are the AQL 1.0 plans in MIL-STD-105E at general level II, normal inspection,¹ and the last three are zero-acceptance plans for comparison. MIL-STD-105E is public and was cancelled in 1995; later notices point to MIL-STD-1916 or ANSI/ASQ Z1.4.² If your contract names ISO 2859-1 or ANSI/ASQ Z1.4, take the plan from your licensed copy, because those paid standards were not read here. The n and c then go straight into the formulas at the end.

All of these odds assume a sample drawn at random across the lot, as MIL-STD-105E requires.¹ The first 80 off the line are not that.

Small batches get the weakest protection. A lot of 100 at AQL 1 is judged on 13 units, and a lot that is 10% defective still passes about one time in four. The binomial slightly misstates small lots, but the gap is modest: for 13 from 100 at 5% defective, the exact hypergeometric figure is 49.1% against 51.3%, and for 50 from 200 at 5% it is 23.7% against 27.9%.

AQL names the supplier's protection

NIST describes the acceptable quality level (AQL) as the baseline for which the producer wants a high chance of acceptance, and the lot tolerance percent defective (LTPD) as the level the consumer wants a low chance of accepting.³ The label "AQL 1" tells you only the first half. Your half is the rate at which acceptance falls to 10%, and for 80 and 2 that is 6.52% defective. For 13 and 0 it is 16.23%.

MIL-STD-105E says as much. The AQL "alone does not identify the chances of accepting or rejecting individual lots", you have to go to the operating characteristic curve, and choosing an AQL does not imply the supplier "has the right to supply any defective unit of product".¹ NIST adds that the main purpose of acceptance sampling is to decide whether a lot is likely to be acceptable, not to estimate its quality.⁴

Why AQL is not an outgoing quality figure

Suppose a line runs at a steady 3% and ships 12 lots of 1,000 a year under the 80 and 2 plan. The plan accepts 56.8% of lots, so 6.8 lots go through and 5.2 come back. Each accepted lot still carries about 3%. If rejected lots are simply returned, that is 188 escapes a year, and the plan says nothing about them.

A ceiling on outgoing quality exists only if every rejected lot is sorted 100% and defectives are replaced.³ Then the worst long-run outgoing rate for 80 and 2 is 1.71% for a large lot, or about 1.6% for a lot of 1,000, when incoming quality is 2.8%. MIL-STD-105E's own table gives a factor of 1.7 for this plan, which agrees.¹ So even with sorting, "AQL 1" can deliver worse than 1%. Without sorting, no ceiling exists at all.

The scheme also assumes a series of lots with switching rules: MIL-STD-105E moves to tightened inspection when 2 out of 5 or fewer consecutive lots are rejected.¹ One plan applied to one lot, with nobody tracking the history, gives you only the odds in the table. For an isolated lot, choose the plan by the limiting quality you cannot accept: MIL-STD-105E covers this in paragraph 4.11, and its Table VI-A prints 6.5% for 80 and 2 and 16% for 13 and 0, in line with the calculation here.¹

What c=0 changes

Zero acceptance gets about the same protection at the 10% point from fewer units, though it lets slightly more of a very bad lot through (3.4% against 1.1% at 10% defective). The 32 and 0 plan reaches 10% acceptance at 6.94% defective, close to the 6.52% of 80 and 2, with 40% of the sample.

The bill goes to the supplier. A lot at 1% is rejected 27.5% of the time under 32 and 0, against 4.7% under 80 and 2. To be accepted 95% of the time, the process has to run at 0.16% or better. So use c=0 when your process is well under the rate you are screening for and you can afford to sort or dispute a rejected lot. Asking for it on a process running at 1% buys frequent rejected batches.

How large a sample catches a given rate

For a 95% chance of finding at least one defective, the sample is about 3 divided by the rate, which is the rule of three.⁵ For 90% it is about 2.3 divided by the rate.

Turned round, a clean sample says little. No failures in 5 only shows, at 95% confidence, that the defect rate is below 45.1%. No failures in 80 shows below 3.7%, and it takes 300 to reach 1.0%. In a small lot the sample falls but stays a large share of the lot: to catch 1% in a lot of 200 with 95% confidence takes 155 units.

Those odds only count passes and fails, and a pull test gives you more. Pull force is a measurement: NASA's review of 780 results found it normally distributed, with averages at least 182% of the minimum.⁶ So record the five forces, not a tick. A mean well above the minimum with a tight spread says more about the setup than "no failures in 5", and a falling mean warns you before anything fails. Molex asks for at least five readings to confirm a setup and 25 for capability.⁷ Read as pass or fail alone, 5 pulls will almost always expose a setup making half its crimps bad (96.9%), catch one making 10% bad only 41.0% of the time, and tell you nothing about a run at 1,000 ppm.

What a batch costs in escapes

This illustration uses a lot of 1,000 under 80 and 2, with invented round costs: £0.20 to test one unit, and £50 for each defective that reaches the customer, the labour-and-parts figure used in the first pass yield example. "Sample and sort" means every rejected lot is then tested in full.

The break-even is the test cost divided by the escape cost, here 0.40%. Above it, test everything. Below it, testing nothing is cheaper on these costs, if you trust the rate. At a steady rate, sampling never comes out cheapest, as the table shows. The model assumes the test finds every defect and leaves out repair and fixture costs. Deducting a £14.50 repair from the escape cost moves the break-even to 0.56%, and a test that finds 90% moves it to 0.44%.

That changes when lots differ. Make 95 lots in 100 run at 0.1% and 5 in 100 at 10%. The expected cost per lot is then £298 with no test, £200 testing everything and £71 with sample and sort, because the plan rejects 98.9% of the bad lots. Sampling earns its place when the danger is a bad lot and each test costs real money. Cut the test to £0.02 a unit and testing everything wins again, at £20 against £49. At 30 s of labour and £30 an hour a test costs £0.25, and at 3 s it costs £0.025, so test time decides this more than any statistics.

Where that leaves assembly checks

Watch the unit, too. AQL can count defective units or defects per hundred units, can differ by defect class, and MIL-STD-105E lets the unit be almost anything.¹ At 1,000 ppm on 200 crimps the same harnesses are 18.1% defective or 20 defects per hundred units, so find out which your plan means. If the unit is the harness, 1% defective with 200 crimps means crimps running at 50.3 ppm. The first pass yield article gives the full table.

When someone still says "sample to AQL 1"

Ask for these answers, in writing:

1. Which n and c, from which edition of which standard, at which inspection level?
2. Which defects does it apply to, percent defective or defects per hundred units, which defect class, and is the unit a harness, a connector or a crimp?
3. What happens to a rejected lot: sorted 100% with defectives replaced, returned, or reworked and resubmitted?
4. Who tracks lot history for the switching rules?
5. Could a 100% electrical test with stored records replace it for electrical faults, leaving sampling for the checks that destroy parts?

Then work out your own odds, in Excel, for the rate you could not tolerate. For a large lot use =BINOM.DIST(c, n, p, TRUE). For a small lot, with D defectives in a lot of N, use =HYPGEOM.DIST(c, n, D, N, TRUE).

Notes

1. US Department of Defense, MIL-STD-105E, 1989, Tables I, II-A, V-A and VI-A and paragraphs 3.1, 3.4, 3.20, 3.23, 4.2, 4.4, 4.7 and 4.11. Cancelled and public, and not the standard your customer may specify. ↩ ↩² ↩³ ↩⁴ ↩⁵ ↩⁶ ↩⁷

2. EverySpec, MIL-STD-105E Notice 1, February 1995, and Notice 3, February 2008. ↩

3. NIST/SEMATECH e-Handbook of Statistical Methods, What kinds of lot acceptance sampling plans are there? ↩ ↩²

4. NIST/SEMATECH e-Handbook of Statistical Methods, What is acceptance sampling? ↩

5. Wikipedia, Rule of three (statistics). Accessed November 2026. The exact sample sizes here are from the calculation. ↩

6. A. Constante, C. Fitzgerald and A. Boutte, Analysis of Pull Force Test Results for Crimped Connections, NASA Goddard Space Flight Center. Aerospace data, abstract read. ↩ ↩²

7. Molex, Quality Crimping Handbook, order no. 63800-0029, copy hosted by DigiKey. Written for Molex terminals and tooling. ↩ ↩² ↩³

8. Cirris, Does repeating the hipot test damage your cable? Supplier guide, quoting MIL-STD-202 Method 301. ↩

9. Cirris, Using voltage to detect insulation defects. Supplier guide. ↩

10. Wiring Harness News, Electrically checking crimps. Trade article built around a CableEye tester. ↩

11. J. E. See, Visual inspection reliability for precision manufactured parts, Human Factors, 2015. Inspectors of nuclear weapon parts, not harnesses. The escape figures are from the calculation. ↩