AQL Sampling Plan (ANSI/ASQ Z1.4)

1. Code letter. Table I (MIL-STD-105E p.13) gives the sample size code letter for the lot size and inspection level, for example lot 2000 at level II gives K.
2. Plan. Tables II-A, II-B and II-C (pp.14–16) give normal, tightened and reduced single sampling plans. The code letter row and AQL column give the sample size n, the acceptance number Ac and the rejection number Re.
3. Arrows. Where the cell is an arrow, follow it in the same AQL column to the first cell with Ac and Re, and use that row's sample size. The sample size can therefore differ from the one the code letter first suggests.
4. Sample not smaller than the lot. If n equals or exceeds the lot size, inspect every unit.
5. Decision. Accept with Ac or fewer nonconforming units, reject with Re or more. Reduced plans can have a gap between Ac and Re: a result in the gap accepts the lot, but normal inspection resumes for the next lot (4.10.1.4, p.8). Under reduced inspection a rejected lot also returns the next lot to normal inspection (4.7.4, p.6).
6. Pa and LTPD. Pa is the probability of accepting a lot when the process runs exactly at the AQL. LTPD is the quality at which Pa falls to 10 %, solved numerically to 0.01 %.

The distribution follows MIL-STD-105E 4.12.1 (p.9), the same basis as the standard's operating characteristic curves in Table X:

Example: n = 125, Ac = 3, p = 1.0 % gives λ = 1.25 and Pa ≈ 96.2 %; the LTPD is 5.34 %, matching Table X-K-1 (p.52).

For reduced inspection Pa counts every result below Re, because a result in the Ac–Re gap still accepts the lot. Reduced Pa is therefore higher than a count up to Ac alone would give.

Why not the hypergeometric distribution? The hypergeometric describes drawing without replacement from one fixed lot with a known number of nonconforming units (a Type A curve). Z1.4 is designed for a continuing series of lots and describes the long-run acceptance rate for a process at quality p (a Type B curve); its published curves use the binomial and Poisson distributions, and this tool uses the same so its numbers can be checked against Table X. When the sample is a small fraction of the lot the difference is negligible. When it is a large fraction, the hypergeometric curve is steeper, so this tool slightly overstates Pa for poor lots.

Page numbers refer to the printed pages of MIL-STD-105E, 10 May 1989 edition, available from EverySpec.

• Attributes, single sampling. The tool counts nonconforming units, or above AQL 10 the total nonconformities in the sample (the AQL itself is then stated per hundred units). Double and multiple sampling plans are not covered, and neither is sampling by variables, which ANSI/ASQ Z1.9 handles.
• A continuing series of lots. The AQL scheme assumes a steady stream of lots inspected under the switching rules. For an isolated lot, choose a plan by limiting quality instead, such as ISO 2859-2.
• Switching rules are yours to apply. Moving between normal, tightened and reduced inspection (4.7, p.6) depends on the results of earlier lots, which the tool does not track. Pick the inspection state the rules put you in.
• Random samples. Pa and LTPD assume the sample is drawn at random from the lot and follow the distributions in 4.12.1. LTPD here is solved to 0.01 %, so it can differ in the last digit from the three-figure values in Table X.
• Which standard. MIL-STD-105E was cancelled in 1995. ANSI/ASQ Z1.4 replaced it with the same table values, and ISO 2859-1 is the international counterpart. ISO 2859-1 (1999 onward) removed this gap in reduced inspection (Re = Ac + 1). This tool follows MIL-STD-105E / ANSI/ASQ Z1.4 and keeps the gap.

• Reading the AQL as a guarantee. The AQL is the quality the plan accepts most of the time, not the worst quality a customer will receive. A process running exactly at the AQL still has some lots rejected (Pa is about 87–99.4 % for normal single plans), and lots worse than the AQL can still be accepted; the LQ / LTPD shows how bad a lot must be before it is usually rejected.
• Staying on normal inspection. The protection the scheme offers depends on switching to tightened inspection when lots start failing (2 rejected out of 5 or fewer consecutive lots). A single plan used on its own gives much weaker protection than the published AQL suggests.
• Ignoring the arrows. Sampling the size the code letter first suggests, instead of following the arrow to the plan that has an acceptance number, gives a plan the standard does not contain.
• Mixing up the two kinds of AQL. Up to 10 the AQL is percent nonconforming; above 10 it is nonconformities per hundred units, where one unit can carry several nonconformities. Either way, Ac and Re are compared with the raw count in the sample: do not convert the count to a per-hundred-units figure first.
• Sampling a fixed percentage or the easiest units. A sample of, say, 10 % of the lot, or units taken from the top of the box, is not the plan in the table and does not have the Pa shown here.
• Staying on reduced inspection after a gap result or a rejection. Under reduced inspection, a count between Ac and Re accepts the lot and a count at Re or above rejects it; either way the next lot returns to normal inspection.