Hmmmmmm. I think understand your concerns

@Dan_Obermiller.

Ok so here's a thought. And this is delving into stuff I'm really not familliar with so let me know if this is absurd. Even though the Experimental Design using PCs results in a model in terms of PCs, the y vector is still in real units. So could one do what

@Thierry_S suggested, generating the PCs. This way you are able to generate a design that at least tries to pick points that are along directions of maximum variance. Load those into the DoE platform as covariates. And then, I was just looking through the PLS platform

@Victor_G shared, maybe instead of making a model in terms of the PCs, do a PLS regression of the final data against the original data set.

That way you are just using the PCs to make sure the usage of the original column space is maximized in your design, but you're using a regression model that prioritizes the original, physically grounded column space.

Is this reasonable? My first worry is that this just relegates the optimality criterion to the proverbial back room, but from what I gather, PLS is designed to handle highly correlated variables, so the need for optimality criterion is lessened? There might be other issues as well.

I'm just a lowly chemical engineer, so let me know if I'm not treating the statistics well here.

Edward Hamer Chandler, Jr.