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.
The statistical foundation here is well-established, which is why sampling plans from decades ago are still valid.
A statement that "lot 20260412 complies with specifications" is meaningless without stating which vials from the lot were tested and how many there were.
Lyophilised peptide homogeneity studies show that vial-to-vial variation is usually small but occasionally large, depending on the distribution in the freeze-dryer.
The caveat is that sampling is a trade-off between cost and confidence, and neither test nor assumption is cost-free.
If testing multiple vials, state how many you tested and why you chose those vials.
edited 20 Dec 2025 by Dr_Yusuf_Adeyemi — removed a claim I could not source