AQL 2.5 Sampling Table: Sample Sizes and Acceptance Numbers Explained

The most common failure in an inspection brief is not a wrong number but a missing one. A buyer specifies AQL 2.5 and assumes that determines how much of the order gets opened. It does not. The sample size was fixed by two other decisions before the AQL was ever consulted, and those two decisions — the lot presented and the inspection level agreed — are the ones that decide how much evidence the verdict rests on.

What Are the Two Tables Behind Every AQL 2.5 Plan?

ISO 2859-1 publishes sample size code letters in one table and sampling plans in another. The first takes the lot size across the top and the inspection level down the side, and returns a letter between A and R. The second takes that letter in the left column and an AQL value across the top, and returns a sample size with an accept number above a reject number.

Reading them in the wrong order produces most of the confusion in the market. A buyer who starts at the AQL has already lost the decision that mattered. Start at the lot size, move to the letter, take the sample, and only then read the accept and reject pair. Everything downstream — how long the visit takes, how much the inspection costs, what the plan can detect — was decided by step two.

How Do You Find the Sample Size Code Letter?

Enter Table 1 with the size of the lot being presented and read across to the column for the agreed inspection level. A lot of 500 pieces under General Inspection Level II lands in the 281 to 500 band and returns H. The lot is what is offered at one time for one inspection, not the purchase order quantity: an order of 2,000 pieces shipped as four lots of 500 inspects four times at code letter H, which is a materially different outcome to inspecting once at code letter K.

This is why split shipments need to be addressed before they happen. Splitting a lot to stay under a convenient sample size band is a recognised way to weaken a plan without changing a word of the specification. The remedy is simple and belongs in the purchase order: lots are defined by the shipping schedule agreed at order placement, and re-splitting afterwards requires written approval.

What Sample Size Does Each Code Letter Carry?

The letters run from A to R, and for the sizes that matter to bag programmes the progression is not linear. It roughly doubles every two or three letters, which means the cost of inspection scales far more slowly than the size of the order. A 3,000-piece order is examined to the tune of 125 units; a 30,000-piece order draws 315. The plan buys information about the process, not coverage of the cartons.

What Are the Accept and Reject Numbers at AQL 2.5?

The accept number, written Ac, is the largest number of defects the sample may hold and still pass. The reject number, Re, is the count at which the lot fails. The two always differ by one, and there is no band between them. At code letter H the pair is 3 and 4: three defects in fifty units releases the lot, and a fourth fails it. Both numbers count defects, not defective units — one unit carrying two listed faults contributes two.

That distinction decides real outcomes. A lot with two badly made units, each carrying two major faults, produces a count of four and fails even though only two units were touched. Buyers who prefer to count defective units rather than defects can ask for that convention, but it has to be stated before the visit, because it loosens the plan by roughly the number of faults a single unit typically carries.

Why Do the Smallest Code Letters Force a Change of Plan?

Below about 32 units the arithmetic stops working. There is no sensible way to express 2.5% of eight units, so the table cannot offer the plan being asked for and prints an arrow instead. The arrow points to the first plan that does exist, usually one with a different sample size or a different AQL column. Following the arrow is mandatory: a plan that ignores it is not a plan from the standard at all.

In practice this affects sample orders and top-up orders, where lots are small because the quantity is small rather than because anything has been split. A 40-piece replacement shipment draws code letter D and a sample of eight units, and at AQL 2.5 that plan accepts nothing and rejects at one. The practical response for very small lots is usually a full check or an agreed concession, not a battle over which arrow applies.

What Do the Arrows in the Table Mean?

There are two places arrows appear, and they point in different directions for different reasons. A down arrow beneath an AQL column means no plan exists at that combination of sample size and AQL: shift down the column until you meet a valid row, and use the accept and reject pair printed with it, adjusting the sample size to match. An up arrow appears where the plan would be uneconomically tight and points to a larger sample with a higher accept number.

Both changes should be recorded on the report. An inspection executed at a sample size that differs from the code letter is legitimate only if it followed an arrow, and if nobody wrote down which arrow, nobody can verify it. Reports that quote a sample size without showing its derivation are the single most common sign that the plan was improvised.

How Does the Table Change Under Tightened or Reduced Inspection?

The tables repeat for each switching state, and this is where the same AQL 2.5 label stops meaning the same thing. Under tightened inspection the sample size is unchanged but the accept and reject pair moves down by roughly one: a lot that passed comfortably last month now sits on the boundary. Under reduced inspection the sample falls to about 40% of normal, with its own accept and reject pair and its own rules for leaving the state.

For a buyer comparing quotations, this is the trap. Two vendors both writing AQL 2.5 may be running plans that differ by a full unit of tolerance and by 60% of the sample size, purely because their programmes sit in different states. Ask for the state, then compare. A programme that has never been tightened is either very good or rarely inspected.

What Does Double Sampling Look Like on the Same Table?

Double sampling is the optional third table, and it exists to reduce the average number of units examined on good lots. A first sample is drawn and read against two thresholds: below the first, accept; above the second, reject; in between, draw a second sample and judge the combined result against cumulative numbers. Clean lots are cleared on the small first sample; only the borderline ones consume the extra work.

The attraction is cost, but the hidden cost is complexity. Two sets of accept and reject numbers, a decision rule between samples, and a second visit or a longer one when the first lands in the middle. Single sampling remains the right default for bag programmes precisely because every party can read the outcome without reference to a second decision. State single sampling unless the double plan has been agreed and priced.

Where Does the Inspection Level Change the Answer?

The inspection level is chosen before the plan and it moves the sample harder than the AQL ever does. Taking the standard 500-piece order: Special Level S-4 draws 13 units, General Level I draws 20, Level II draws 50, and Level III draws 80. Each step changes both the cost of the visit and the ability of the plan to detect a poor lot, and none of them changes a single character in the AQL 2.5 description.

How Should the Sampling Table Be Reproduced in a Specification?

Do not reproduce it. Instead specify the standard by edition, the inspection level, single versus double sampling, the AQL by defect class, and the switching state at the start of the programme. Those five references reconstruct the plan exactly and leave no room for a homemade table drifting away from the original — which is what happens when somebody copies eight rows out of a spreadsheet three years ago and nobody re-checks it.

Once those five lines are written the table becomes verifiable rather than believed. Any lot quantity can be run through the AQL sampling table and the resulting sample size checked against the report. The guard against the one-in-three risk described above — a lot re-split to change its code letter — is dealt with at quotation stage, alongside the numbers set out in why the bulk window is 35-50 days: inspection closes the window, it does not sit inside it.

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