How to account for within-run response estimate variance in DOE evaluation?

Question

I am planning experiments on a process that produces parts in batches.

Let's say I have a 2 factor, 2 level full factorial. There will be a batch of each part produced under one of the 4 condition runs.

To determine the mean response for each run I will randomly select N parts from the batch for testing to determine mean and SD.

My mean response values will be used to evaluate effects but how does the SD (or variance) of my testing sample size N enter into the overall estimation of the effects, i.e. how does it affect prediction variance? It's not clear to me how this is worked into the Evaluate Design platform in JMP.

Note this particular instance expectation is that the variance will be relatively constant over the design region and can be estimated before hand. Testing of individual parts is destructive.

rpcanam · Answer

Thanks LouV. I realize I could use the SD as a response but I have prior knowledge that the factors will affect primarily the mean response and SD will remain approximately fixed. What I am trying to do is determine how my testing sample size (linked to budget) for estimating individual run means impacts the prediction variance of a model.

louv · Answer

You have an opportunity to capture standard deviation as a response column and minimize it as well as optimizing your mean.