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Pharmaceutical Sampling Plan Calculator

Compare WHO n, p and r sampling-plan counts for pharmaceutical starting-material consignments.

Pharmaceutical sampling plan calculator

Compare WHO n, p and r plan counts for a consignment of starting-material sampling units. The calculations do not select the plan for you.

Calculate n, p and r

Enter the number of containers or other sampling units in the consignment. No value is prefilled.

In short: Enter the number of sampling units in a consignment to calculate the WHO n, p and r plan counts. The plans have different purposes and assumptions; the calculator does not decide which plan to use.

Formulas

For a consignment with N sampling units, WHO Technical Report Series No. 929, Annex 4 (2005), §§5.1.1–5.1.3 describes:

n = 1 + √N
p = 0.4 × √N
r = 1.5 × √N

WHO says to use simple rounding for n, and rounding up to the next whole number for p and r. The guidance says that when N is 4 or less, every container is sampled under the n plan. The calculator also caps the p and r counts at N, so an output cannot exceed the number of sampling units entered. WHO Technical Report Series No. 929, Annex 4 (2005), §§5.1.1–5.1.3.

What each plan is for

  • n plan: WHO describes this as a guiding principle, not a statistically based plan. It should be used cautiously only when the material is considered uniform and comes from a recognized source. WHO says it is not recommended for manufacturers’ control laboratories that must analyse and release or reject each received consignment of starting materials.
  • p plan: WHO describes this for uniform material from a recognized source when the main purpose is identity testing. Samples are taken from every sampling unit; after concordant identity results, the original samples are pooled into p final samples.
  • r plan: WHO describes this for material suspected to be non-uniform or received from a source that is not well known. WHO also identifies herbal medicinal products used as starting materials as a possible use. Samples are initially taken from each unit for identity testing; if results are concordant, r samples are selected and tested individually.

These are descriptions of the plans in WHO Technical Report Series No. 929, Annex 4 (2005). Sampling choices depend on the material, purpose, risk and applicable procedure. The calculator provides counts only; it does not establish material uniformity, source reliability, identity results, release decisions or acceptance criteria. WHO TRS 929, Annex 4 (2005), §§5.1.1–5.1.3.

Assumptions and limitations

  • N means the number of sampling units in one consignment, such as containers; it is not the number of individual tablets, test portions or laboratory replicates.
  • The WHO n, p and r plans concern starting-material sampling. They are not interchangeable and are not general acceptance-sampling plans for finished products or packaging materials.
  • WHO TRS 929 Annex 4 (2005) says the n plan is not statistically based and should serve only as a guiding principle.
  • The tool does not generate random unit identifiers, create a sampling procedure, test samples or choose a plan for a site.

Use your approved sampling procedure and risk assessment.

References

  • World Health Organization, WHO Expert Committee on Specifications for Pharmaceutical Preparations: Thirty-ninth report, WHO Technical Report Series No. 929 (2005), Annex 4, “WHO guidelines for sampling of pharmaceutical products and related materials,” §§5.1.1–5.1.3 and Table 1. Official WHO publication.