Is a Sample Size of 1 Enough for Unbiased and Objective Results?

I’m sure you didn’t mean to create a theoretical discussion but think of this. Statistics are used to make conclusions about populations based on sampling. If you have a sample of one, how do you propose understanding if the variation or central tendency is what you’d expect?

A homogeneous powder? I’d be skeptical with that assumption with my experience. Especially if you imply the homogeneity wouldn’t impact the measurement but I’d assume you have particle size variation at a MINIMUM but of course as my good friend @mike-carnell would state–get a sampling plan to confirm your business understanding.

Yes, I read how the testing is expensive but SOMEONE must have done sample random sampling in the bulk of powder to conclude homogeneity and that must have been justified?

Just a few thoughts.

A sample size of one can be sufficient in some circumstances. That’s the way water and food products are tested for bacteria and other contaminants. My father outlaw worked in the metallurgy lab in a steel mill and he’d get one sample from the furnace. If it wasn’t up to spec he’d tell them what they needed to add and then he’d get another sample. Over time you can do statistical analysis for additional insight but it would be wasteful to take multiple samples from the same homogeneous batch. But there’s a caveat (isn’t there always?) How much variation (R&R) is in your gauges and methods? If this variation exceeds your desired confidence level you might need multiple samples even if you reasonably expect them to be the same.