Acceptance Sampling Plan Calculator — MIL-STD-105E Tables and OC Curve

About ANSI/ASQ Z1.4, and what this page uses instead

The sampling tables most quality systems invoke are published as ANSI/ASQ Z1.4, which is a copyrighted standard sold by ASQ and by the ANSI webstore. It is not reproduced here, and nothing on this site is described as conforming to it.

What is reproduced is MIL-STD-105E, "Sampling Procedures and Tables for Inspection by Attributes", dated 10 May 1989 — a work of the United States Government whose cover page carries "Approved for public release; distribution is unlimited", and which is therefore in the public domain and legitimately mirrored, including by the Internet Archive and EverySpec. MIL-STD-105E was cancelled in 1995, and Z1.4 is its civilian successor; the maintainer of the widely used R implementation of both records that when the US military dropped support, ANSI and ISO adopted the standard with few or no changes to the central tables.

The practical consequence: if your drawing calls out Z1.4, read your own copy of Z1.4. This page will tell you what the public-domain predecessor says, which is a very good guide and is not a substitute for the document your contract names. If a plan here disagrees with your controlled copy, your controlled copy wins and we would like to hear about it.

Why "AQL 1.0" does not mean "1% is acceptable"

It is the most expensive misreading in the subject. The AQL is the quality level at which the plan is designed to accept most lots — not a threshold below which lots pass and above which they fail. A single sampling plan cannot draw that line, because it only ever sees the sample.

Take the plan this page opens on: a lot of 5,000, general level II, AQL 1.0, normal inspection → code letter L, n = 200, Ac = 5. Two hundred pieces out of five thousand feels thorough. The curve says otherwise. A lot that is genuinely 1% nonconforming is accepted 98.4% of the time, so the producer’s risk is a comfortable 1.6%. But a lot that is 4.6% nonconforming — nearly five times the agreed level — is still accepted one time in ten. That number is the limiting quality, it is marked on the curve, and it appears in no purchase order anywhere.

This is not a defect in the plan. It is what a 4% sample can do, and it is the reason acceptance sampling is a way of policing a stream of lots from a stable process rather than a way of sorting a single delivery. If you need to know that one particular lot is good, sampling cannot tell you and 100% inspection can.

The switching rules, which are not optional and are usually ignored

The tables are only half of the standard. The other half is a state machine: normal → tightened after two lots are rejected within five consecutive lots; tightened → normal after five consecutive lots are accepted; discontinue inspection under the standard entirely after five consecutive lots on tightened; and normal → reduced only after ten consecutive acceptances with steady production and the responsible authority’s agreement, with reduced dropping back to normal on the first rejection.

None of that is advisory. Applying the tables while ignoring the switching is the single most common way an otherwise correct sampling scheme is run wrongly, and it is what turns a scheme with teeth into a formality: the whole mechanism by which the standard punishes a deteriorating supplier is the switch to tightened.

This tool does the lookup, not the machine. The inspection state is an input you set, it is printed on the figure, and the figure says in as many words that the state is an input rather than a result — because a state machine needs persisted lot history and inventing one from whatever is in the grid would be inventing the one thing the inspector’s records are supposed to supply. The shipped sample is chosen to make the point: two of its ten lots are rejected within five consecutive lots, so a scheme run properly would already be on tightened inspection. Switch the option and watch Ac fall from 5 to 3 on the same sample of 200.

Arrows, and the sample size that is not your code letter’s

Most cells of the master tables hold an arrow rather than a plan, and the instruction printed under the table is "use the first sampling plan below the arrow". The half of that rule people drop is the sample size: when you follow the arrow you take the sample size of the plan you land on, not the one printed beside your own code letter.

A lot of 5,000 at AQL 0.010 is a good example. Level II gives code letter L, whose own sample size is 200 — but that cell is an arrow, and following it down lands on Q: n = 1,250, Ac = 0. Taking 200 pieces and accepting on zero is a different plan with a different OC curve, and it is the classic error. When an arrow has been followed, this tool says so, names the letter it landed on and prints both sample sizes.

The standard adds one more instruction in the same footnote: if the sample size reaches or exceeds the lot size, carry out 100 percent inspection. That fires on the small lots and on the tight AQLs, and the figure says it rather than quietly reporting a sample bigger than the delivery.

Which distribution the curve comes from

Binomial is the default and is exact for percent-nonconforming sampling when the lot is large relative to the sample: Pa = Σ C(n,d)·p^d·(1−p)^(n−d) for d = 0 to Ac. Nothing is approximated and nothing is tabled.

Hypergeometric is exact when the lot is finite and the sample is a large fraction of it, because real sampling is without replacement. On a lot of 300 at level II‑plus discrimination the sample is 80 pieces — over a quarter of the lot — and the two curves visibly differ: the binomial puts Pa at the AQL at 95.3% where the exact finite-lot answer is 98.2%, and the limiting quality at 6.5% where the exact answer is 5.8%. Treating a lot of 300 as inexhaustible flattens the curve and understates how much a sample of 80 tells you. The tool warns when the sample passes 10% of the lot and points at the option.

Poisson is the approximation MIL-STD-105E itself used to tabulate most of its own OC curves — §4.12.1 says binomial for AQLs of 10 or less at sample sizes of 80 or less, Poisson everywhere else. Selecting it is how the standard’s printed OC tables are reproduced exactly, which is what /validation does. Above AQL 10 the tool switches to Poisson whatever you choose, because those AQLs are defects per hundred units rather than a proportion and there is no p for a binomial to use.

The three disagree, and the disagreement is the point of naming them: on the default plan the limiting quality at 10% acceptance is 4.59% by the exact binomial and 4.64% by the Poisson the standard printed. The figure says which one drew the curve.

Common questions

Is this an ANSI/ASQ Z1.4 table?

No. It is MIL-STD-105E, the public-domain US Government standard that Z1.4 succeeded, and the two are widely reported to share their central tables. Z1.4 is a paid standard, none of it is reproduced here, and no conformance to it is claimed. If your contract names Z1.4, use your controlled copy of Z1.4.

What sample size do I need for a lot of 1,000 at AQL 2.5?

General inspection level II puts a lot of 1,000 in the 501–1,200 band, which is code letter J: n = 80, Ac = 5, Re = 6 on normal inspection. Enter the lot size and pick the AQL to see it with its curve — and to see that a lot at 11.3% nonconforming, four and a half times the agreed level, still gets accepted one time in ten under that plan.

Why did my sample size not change when I switched to tightened inspection?

Because tightened inspection is usually the same sample with a smaller acceptance number, not a bigger sample. Code letter L at AQL 1.0 is n = 200 with Ac = 5 on normal and n = 200 with Ac = 3 on tightened. You inspect the same pieces and accept on fewer defects.

On reduced inspection Ac is 2 and Re is 5. What happens if I find 3?

You accept the lot and go back to normal inspection. Reduced is the only one of the three tables where the acceptance and rejection numbers are not consecutive, and the gap is deliberate: finding more than Ac is evidence that the qualification for reduced inspection no longer holds, even though it is not enough to reject the lot.

Can this decide whether to ship a lot?

No. It is a calculation aid. It reads a public-domain table and computes a probability; the disposition of a lot, and whether the plan satisfies your contract, your customer and your quality system, remain yours. Nothing here is validated for use as a record under any regulated quality system.

Where can I check the numbers?

The /validation page reproduces the standard’s own tabulated OC values for two plans — code letter C at n = 5 and code letter L at n = 200 — against the shipped code, at the precision the standard prints. The tests also read Table I back, all 105 cells, against page images of the scan.

Is my data uploaded anywhere?

No. The whole calculation runs as JavaScript in this browser tab. Lot sizes and defect counts by supplier are exactly the kind of data most quality agreements forbid putting into a cloud service, and nothing on this site accepts any of it.