How many vials from a TFC lot should I send for an HPLC purity test?

Concretely: TFC · an HPLC purity test.

I want the working, not the result — I need to be able to redo it with different numbers.

I care about the precision as well as the value — I want to know how many figures are real.

How many significant figures are actually justified here?

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.

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.

If the lot was manufactured in multiple batches, testing vials from each batch separately establishes whether batch-to-batch variation is acceptable.

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

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

A certificate that reports one test result on one vial extrapolates to claim that all two hundred vials in the lot are identical, which is an assumption worth questioning.

A statement that "lot 20260412 complies with specifications" is meaningless without stating which vials from the lot were tested and how many there were.

Stated carefully, 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.

One qualification: testing more vials gives better confidence, but at some point the cost outweighs the benefit.

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

If a lot has visibly segregated — some vials showing different appearance — then sampling the top and bottom of the shipment is worth doing.

If the entire lot failed qualification, a retest on a different vial is sometimes done, but reporting a retest result under the same lot number is misleading.

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

The limitation is that you cannot know for certain without testing every vial, and you almost never can afford to do that.

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

edited 26 Oct 2024 by Dr_Malik_Osei — expanded the table to cover the lower concentration

Concretely, 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.

The sample size determination requires choosing a confidence level and an acceptable error rate, and the smaller the error rate you want, the larger your sample must be.

Sampling plans for pharmaceutical manufacturing are defined in ISO 2859 and ANSI Z1.4, and they are based on statistical sampling theory.

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

In practice, two vials tested from a lot of ten is very different from two vials tested from a lot of ten thousand, and most certificates do not state the lot size.

Acceptance Sampling by Attributes defines the number of samples you need from a lot to claim a specified quality level at a specified risk — it is in ANSI standard Z1.4.

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