How many vials from a QSC lot should I send for identity confirmation by mass spectrometry?

Setup, so nobody has to ask: QSC · identity confirmation by mass spectrometry.

I have worked this out and I would like someone to find the error, because I suspect there is one.

My working so far, for the record, is below, and I am fairly sure the error is in the unit conversion rather than the algebra.

Where is my error, and what is the correct working?

The failure mode here is publishing a result that applies to the tested vial alone while implying it applies to the entire lot.

Under AQL sampling plans, testing two vials from a fifty-vial lot gives you an operating characteristic curve that tells you what risks you are accepting.

In practice, if you have reason to suspect inhomogeneity — different appearance in different vials, or a long or warm shipment — testing more vials is the diagnostic move.

The practical summary: a lot number without a sampling statement is a lot number without meaning.

The single most misleading statement on a research-grade certificate is a lot number with no statement of how many vials from that lot were tested.

For a quantitative result like content, the acceptable range determines how many vials you need to test to establish the lot complies.

The underlying point is that 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.

Assume segregation is possible, and design your sampling to catch it if it exists.

edited 26 Jun 2025 by Dr_Elias_Weiss — added the method parameters

Worth being precise here: the honest statement is that unless you have tested multiple vials or have segregation data, you are making an assumption about lot homogeneity that may not hold.

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.

If testing multiple vials, state how many you tested and why you chose those vials.

edited 26 Jun 2025 by Dr_Bram_Verhoeven — reworded for clarity after a comment

The relevant detail is that if a lot has visibly segregated — some vials showing different appearance — then sampling the top and bottom of the shipment is worth doing.

Published segregation failures show that even modern automated processes sometimes produce lots with measurable vial-to-vial variation.

Published data on lot homogeneity from manufacturers who sample multiple vials consistently find variation below the published specifications, suggesting the sampling plans work.

The practical summary: a lot number without a sampling statement is a lot number without meaning.

edited 12 Jul 2025 by e_dziedzic — added the citation requested in comments