1Where √n+1 comes from.
The formula is WHO’s “n plan”, from its 2005 guidelines for sampling pharmaceutical products: n = 1 + √N, where N is the number of containers in the consignment, rounded by simple rounding, with every container sampled when N is 4 or fewer. Samples from the n containers are identity-tested one by one and, if they agree, combined into one composite sample for analysis.¹
WHO attaches heavy qualifications. The guidelines are written mainly for regulators, inspectorates and procurement agencies, and their sampling plans are “not necessarily appropriate for manufacturers”. The n plan “is not statistically based and should be used only as a guiding principle”, should be used “with great caution” and only for uniform material from a recognised source, and is “not recommended for use by control laboratories of manufacturers who are required to analyse and release or reject each received consignment”. WHO also says sampling plans are not recommended for sampling starting materials for identification tests.¹
| Plan | Formula | When WHO says it may be used | What is sampled |
|---|---|---|---|
| n plan | n = 1 + √N | Uniform material from a recognised source, with great caution | n containers, each identity-tested, then composited |
| p plan | p = 0.4√N, rounded up | Uniform material from a recognised source, mainly to test identity | Every container identity-tested, then pooled into p final samples |
| r plan | r = 1.5√N, rounded up | Material suspected to be non-uniform, from a source not well known, or herbal | Every container identity-tested, then r chosen at random and tested individually |
For a consignment of 25 drums, WHO’s table gives 6 for the n plan, 2 for the p plan and 8 for the r plan.¹
2What FDA requires in the US.
Section 211.84(b) requires “representative samples of each shipment of each lot”. The number of containers sampled and the amount taken from each “shall be based upon appropriate criteria such as statistical criteria for component variability, confidence levels, and degree of precision desired, the past quality history of the supplier, and the quantity needed for analysis and reserve”.²
FDA’s CGMP questions and answers say “The CGMP regulations do not specify the number of containers to be sampled from each received shipment.” Each manufacturer decides, provided its plan “is scientifically sound, leads to representative samples, and complies with the principles established at § 211.84(b)”. For identity, FDA explains that a container either is or is not what its label says, and that contents can be substituted in distribution and warehousing, so manufacturers need an approach that gives “a high degree of confidence that each container in each shipment contains the material purported by the label”. Testing every container “may be valuable particularly for components purchased from distributors”.³
Identity can be tested on a composite sample only if the manufacturer shows that one nonconforming container would not be masked, or runs an additional test on the composite that ensures every container sampled holds the same material.³ For glycerin, propylene glycol and other components at high risk of diethylene glycol and ethylene glycol contamination, FDA’s May 2023 guidance goes further and recommends that identity testing, including the limit test, cover samples from all containers of all lots.⁴
3What EU GMP requires.
Annex 8 starts from every container: “The identity of a complete batch of starting materials can normally only be ensured if individual samples are taken from all the containers and an identity test performed on each sample.” Sampling only some containers is permissible “where a validated procedure has been established to ensure that no single container of starting material has been incorrectly labelled”.⁵ Chapter 5 requires identity testing of each batch of starting material according to Annex 8.⁶
The validation must consider the manufacturer and supplier, the manufacturer’s quality system, the conditions the material is made under, and the material and the products it goes into. Annex 8 says a reduced procedure could be accepted for material from a single-product manufacturer or plant, or coming directly from the manufacturer or in its sealed container with a history of reliability and regular audits. It is “improbable” that one could be validated for material from brokers whose source is unknown or unaudited, or for material used in parenteral products.⁵
Beyond identity, the quality of a batch can be assessed on a representative sample. The number of samples is “determined statistically and specified in a sampling plan”, as is the number that may be blended into a composite.⁵
EMA’s questions and answers apply this to glycerol, propylene glycol and low-
4What else the sampling plan should cover.
ICH Q7 asks API manufacturers for sampling methods that specify the number of containers, which part of each container to sample and how much to take, based on a plan that considers the material’s criticality and variability, the supplier’s quality history and the quantity needed for analysis.⁸ For packaging materials, Annex 8 asks the plan to consider the quantity received, the quality required, the type of material, the production method and what audits show of the supplier’s quality system, with the number of samples determined statistically.⁵ WHO says sampling plans for packaging materials should be based on defined sampling standards, such as BS 6001-1, ISO 2859 or ANSI/ASQC Z1.4-1993.¹
5How it runs in Seal.
In Seal, the approved sampling plan is resolved against the containers that actually arrived. The raw materials blueprint records container selection, sampling location, quantity, tools, resealing and custody, and keeps the contributing containers of a composite sample, so a container with no identity result keeps the receipt on hold rather than being covered by its neighbours. How many containers are sampled and identity-tested comes from your approved strategy; Seal does not impose a universal rule.
In sample management, a pool keeps every contributor and its actual amount, including exclusions and the resulting container. In the LIMS, incoming inspection connects the supplier lot, its CoA, the sampling plan and the analytical work, and inventory uses the authorised disposition without copying the decision into another application.
References
- 1WHO guidelines for sampling of pharmaceutical products and related materials, WHO Technical Report Series No. 929, Annex 4, WHO, 2005. https:/
/ cdn. who. int/ media/ docs/ default- source/ medicines/ norms- and- standards/ guidelines/ quality- control/ trs929- annex4- guidelinessamplingpharmproducts. pdf (read 6 November 2026) - 221 CFR 211.84, Testing and approval or rejection of components, drug product containers, and closures, eCFR. https:/
/ www. ecfr. gov/ current/ title- 21/ chapter- I/ subchapter- C/ part- 211/ subpart- E/ section- 211. 84 (read 6 November 2026) - 3Questions and Answers on Current Good Manufacturing Practice Requirements: Control of Components and Drug Product Containers and Closures, question 4, FDA, content current as of 16 November 2022. https:/
/ www. fda. gov/ drugs/ guidances- drugs/ questions- and- answers- current- good- manufacturing- practice- requirements- control- components- and- drug (read 6 November 2026) - 4Testing of Glycerin, Propylene Glycol, Maltitol Solution, Hydrogenated Starch Hydrolysate, Sorbitol Solution, and other High-Risk Drug Components for Diethylene Glycol and Ethylene Glycol, Guidance for Industry, Revision 1, FDA, May 2023. https:/
/ www. fda. gov/ media/ 167974/ download (read 6 November 2026) - 5EudraLex Volume 4, Annex 8, Sampling of Starting and Packaging Materials, European Commission. https:/
/ health. ec. europa. eu/ document/ download/ 22d03c04- 8512- 4336- 89dd- 556771fca388_ en?filename=anx08_ en. pdf (read 6 November 2026) - 6EudraLex Volume 4, Part I, Chapter 5, Production, section 5.35, European Commission, in operation from 1 March 2015. https:/
/ health. ec. europa. eu/ document/ download/ 4a1fdb4f- 6f6f- 49c4- b264- 8056e5bbe078_ en?filename=chapter_ 5. pdf (read 6 November 2026) - 7Guidance on good manufacturing practice and good distribution practice: questions and answers, Annex 8, EMA. https:/
/ www. ema. europa. eu/ en/ human- regulatory- overview/ research- development/ compliance- research- development/ good- manufacturing- practice/ guidance- good- manufacturing- practice- good- distribution- practice- questions- answers (read 6 November 2026) - 8ICH Q7, Good Manufacturing Practice Guide for Active Pharmaceutical Ingredients, section 7.3, ICH, 10 November 2000. https:/
/ database. ich. org/ sites/ default/ files/ Q7%20Guideline. pdf (read 6 November 2026)
AQuestions and answers
Does FDA require every container to be sampled for identity?
Not in general. FDA says the regulations don’t specify a number, but the plan must be scientifically sound, representative and give a high degree of confidence that each container holds what its label says. FDA notes that testing every container can be valuable, particularly for materials bought from distributors, and for glycerin, propylene glycol and other components at high risk of diethylene glycol and ethylene glycol contamination it recommends testing samples from every container.
Can identity be tested on a composite sample?
In the US, only if you can show that one wrong container would not be hidden by mixing, or another test on the composite confirms that every container held the same material. In the EU, Annex 8 expects an identity test on a sample from each container unless a validated procedure allows fewer; Annex 8 uses composite samples to assess the batch’s quality, with the number of samples that may be blended defined in the sampling plan.
Is √n+1 accepted in the EU?
Annex 8 does not use it. It expects identity testing of every container and allows a reduced number only with a validated procedure showing no single container can be mislabelled, which it calls improbable for material from unaudited brokers or for parenteral products. A √n+1 plan would need that validation behind it.
Can near-infrared spectroscopy be used to identify every container?
Yes, as an addition. EMA accepts the registered identity method performed on a statistically representative composite sample, supplemented by near-infrared identification of every container, for starting materials used in parenteral products. The near-infrared method must be validated, and using it in place of the registered method needs a variation.
How many samples are needed for packaging materials?
EU GMP asks for a statistically determined number, set in a sampling plan that considers the quantity received, the quality required, the type of material and what you know of the supplier. WHO points to defined sampling standards such as ISO 2859 and ANSI/ASQC Z1.4-1993. In the US, containers and closures can be released on a supplier’s certificate with at least a visual identification once the supplier’s results are validated.