On the detail: the failure mode here is publishing a result that applies to the tested vial alone while implying it applies to the entire lot.
The statistical foundation here is well-established, which is why sampling plans from decades ago are still valid.
Testing a vial that has been open in the lab for three months is testing aged material, not the fresh lot, and the result should be explicitly noted as a retest.
Sampling plans for pharmaceutical manufacturing are defined in ISO 2859 and ANSI Z1.4, and they are based on statistical sampling theory.
The limitation is that you cannot know for certain without testing every vial, and you almost never can afford to do that.
Assume segregation is possible, and design your sampling to catch it if it exists.
edited 19 Jul 2024 by nadia_kowalczyk — expanded the table to cover the lower concentration