WHO TRS 929 Annex 4

Drum sampling plan calculator (square root of N plus 1)

Open the right drums, not the handiest ones at the front.

Enter how many drums, bags or IBCs arrived and how much you trust the lot, to get the n, p and r plans from WHO TRS 929 Annex 4 and a random list of container numbers to sample.

Last updated 2026-09-28. Math runs in your browser, no data leaves your computer.

Count the containers in one received lot, meaning one batch number from one supplier on one delivery. If a delivery mixes two batch numbers, run each batch on its own, because the plan assumes every container in N came from the same batch.

Number the containers before you start, so the random list below points at real drums on the floor. Mark each container you open, which is also what 21 CFR 211.84(c) asks of drug component samplers.

Count packages, not pallets, since four drums on a pallet are four sampling units in the WHO annex.

This only changes the wording of the result, because the WHO formulas treat every package the same way.

Pick the first option for any factory you have not received from before, because the WHO wording ties the r plan to a source that is not well known.

Match the numbering you chalked on the drums, so the random list lines up with the containers on the floor.

Before the booking, screen the name on the invoice. Shipment pre-check is on the paid plans, from USD 59 a month.

General guidance only. Verify against the cited primary sources before you commit to a shipment, declaration, or contract.

The three WHO plans, as published

Section 5.1 of WHO TRS 929 Annex 4 gives three plans for starting materials. The n plan is n = 1 + √N with simple rounding, the p plan is p = 0.4 × √N rounded up, and the r plan is r = 1.5 × √N rounded up, where N is the number of sampling units in the consignment. Appendix 5 works a lot of 40 containers and gets 7, 3 and 10.

The annex also prints Table 1, which lists n for N up to 90, p up to 225 and r up to 44. At a few points the table and the formula differ by one: for n at N = 3 and N = 13 and for r at N = 22 the formula gives one more than the table, and for p at N of 6 or fewer the table gives 2 where the formula gives 1. The tool shows both numbers and uses the larger, and for N of 4 or fewer it samples every container under the n plan, as section 5.1.1 says.

The r value can never be more than N, since the r samples are picked from the containers you already sampled. The random list uses your browser's cryptographic random generator, so draw it once, write the numbers on the sampling record and keep the list with the lot's paperwork.

Worked example. 80 drums from a new factory

The booking. A plant receives 80 drums of a surfactant, one batch, from a Zhejiang factory it has never bought from. The receiving tech applies the square root of N plus 1 rule, 1 + √80 = 9.94, so 10 drums, pulls them from the two nearest pallets and sends one composite for testing, which looks fine on paper.

The failure. The WHO annex keeps the n plan for uniform material from a recognized source, and a first delivery from a new factory is neither proven. Ten drums from two pallets are not random, and one composite can hide a few drums of a different material inside a pass. The choice is plain: sample the lot the way the r plan expects, or accept it on a single blended result.

The fix. Under the r plan every one of the 80 drums gets a quick identity check, and r = 1.5 × √80 = 13.4, rounded up to 14, randomly chosen drums get the full test individually. The tool draws the 14 drum numbers, the lab tests them one by one, the results agree, and the lot is released with a record that holds up.

Inspecting finished, packed goods at the factory before they ship? The AQL sampling plan calculator gives the ANSI/ASQ Z1.4 sample size and the accept and reject numbers for a pre shipment inspection.

Frequently asked

What is the square root of N plus 1 sampling rule?

It sets the number of containers to open in a received lot as 1 plus the square root of the number of containers, N. The WHO calls it the n plan in TRS 929 Annex 4, section 5.1.1, and rounds the result to the nearest whole number, so 40 drums gives 1 + 6.32 = 7.32, or 7 drums. The WHO also says that when N is 4 or fewer, every container is sampled.

When should I use the p plan or the r plan instead?

The WHO annex offers the p plan, 0.4 × √N rounded up, when the material is uniform, comes from a recognized source and the main purpose is identity: every container is sampled and pooled into p final samples. The r plan, 1.5 × √N rounded up, is for material suspected to be non uniform or from a source that is not well known: every container is sampled for identity, then r of those samples are tested in full. For a first order from a new Chinese factory, the r plan is the one that fits the WHO wording.

Is the square root of N plus 1 rule statistically valid?

Not on its own, and the WHO says so directly: the annex calls the n plan not statistically based and a guiding principle only, to be used with great caution. It also says the n plan is not recommended for a manufacturer's control laboratory that has to release or reject each consignment. Use it for routine lots from a supplier with a clean record, and move to a statistically based scheme when the stakes are higher.

Does the FDA require the square root of N plus 1 plan?

The rule in 21 CFR 211.84(b) for drug components asks for representative samples, with the number of containers based on appropriate criteria such as statistical criteria for component variability, confidence levels, precision, and the supplier's quality history. It does not name a formula. Many firms use square root of N plus 1 inside a written procedure, but the justification is theirs to make.

How is this different from AQL sampling?

AQL plans under ANSI/ASQ Z1.4 decide how many finished units to inspect and how many defects to accept, which suits cartons of packaged goods. This tool decides how many containers of a received bulk material to open and test, where the question is whether the lot is uniform and what it is, not a defect count.

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Sourzi shows what official files say. It is not customs or legal advice. For a binding answer, ask a licensed customs broker, a CBP ruling or an Australian Border Force Tariff Advice.

File dates and links are on Data sources.