In practice, 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.
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.
The statistical foundation here is well-established, which is why sampling plans from decades ago are still valid.
Published data on lot homogeneity from manufacturers who sample multiple vials consistently find variation below the published specifications, suggesting the sampling plans work.
The caveat is that sampling is a trade-off between cost and confidence, and neither test nor assumption is cost-free.
The practical summary: a lot number without a sampling statement is a lot number without meaning.
Any reason this would differ for a longer peptide? – lyoph_cake 7 months ago add a comment