# PQ Sample Size across multiple lots

#### Lauren1234

##### Registered
Hello,

Let's say that I'm doing a PQ and I've used confidence and reliability to determine my required samples size (e.g., 59), and I've determined that I will produce three lots for this qualification. When we're referring to a sample size of 59, does this mean I need to test 59 samples per lot? Or a minimum total of 59 samples across all three lots, meaning 20 samples per lot for a total of 60?

#### Bev D

##### Heretical Statistician
Super Moderator
The sample size calculation is intended for a single lot. This is because each lot will be produced under essentially different conditions. Sample sizes like what you have calculated are intended to be for a ‘population’ of material that is built under essentially the same conditions. Multiple lots provide replication which is necessary to prove that the process run under approved conditions is capable. PQ is intended to be multiple lots to prove the process is capable. So your sample size is for each lot and not to be spread out over multiple lots…does that help?

#### Lauren1234

##### Registered
The sample size calculation is intended for a single lot. This is because each lot will be produced under essentially different conditions. Sample sizes like what you have calculated are intended to be for a ‘population’ of material that is built under essentially the same conditions. Multiple lots provide replication which is necessary to prove that the process run under approved conditions is capable. PQ is intended to be multiple lots to prove the process is capable. So your sample size is for each lot and not to be spread out over multiple lots…does that help?
Thanks, Bev. I've traditionally done it this way, but I was recently challenged and it got me thinking whether there is any standard that I could point back to which outlines this?

#### Bev D

##### Heretical Statistician
Super Moderator
There is no “standard” that I am aware of. Most standards have very few references to statistics other than that they must be used. Probably because most standards are written to the lowest common Minimum.
Any good book on sampling statistics will reference what I have stated. Grant and Leavenworth is a good reference or Donald Wheeler. Mil std 105 might reference the lot or batch requirement as it derives almost directly from the original sources that derived the formulas.
discussing the fundamental requirement of sample size formulas applying to a single lot or batch is a bit (a lot) like discussing the proof of the power of gravity or that 2 + 2 = 4. Anyone who suggests that a sample size can be spread across multiple lots is completely ignorant of statistics. And probably physics.

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