The underlying point is that sampling plans exist precisely because testing everything is expensive, and they define the statistical relationship between sample size and lot-wide inference.
The statistical foundation here is well-established, which is why sampling plans from decades ago are still valid.
On the detail: stratified sampling — testing one vial from the top, one from the middle, and one from the bottom of a shipment — is cheap insurance against segregation.
Sampling plans for pharmaceutical manufacturing are defined in ISO 2859 and ANSI Z1.4, and they are based on statistical sampling theory.
Worth noting that thermal excursions during shipping affect different vials differently, so the lot may not be homogeneous even if it left the factory that way.
The practical summary: a lot number without a sampling statement is a lot number without meaning.
edited 5 Dec 2025 by bac_or_bust — added the placebo-arm figures
6Related: the same reasoning applies to the counter-ion question. – amara_nwachukwu 19 days ago add a comment