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I'd like to know the name of the method in the picture below. It's the same category as full - and factorial fractional design. It's quite difficult to search the net for this equation - I've tried wolfram etc but to no avail. If I remember correctly it's a response design of some kind(?) but I might be wrong.

enter image description here


Thanks for your help. I've read up on central composite design but I'm not sure if I understand it completely.

So I've my variables x1,x2,x3 represented as a cube and I add the center point to see if the variables are linear - what if they are not? Then I add the star points from the center point to see what variable affect the response the most. Is this an accurate description of the essence of the methodology or have I misunderstood/missed something?

Is the number of "experiments" or runs I need to do >= 9? Because 2³ (yellow dots) + 1 center point are 9 runs? I'm trying to compare central composite design with full fractional design (2³=8 runs) and fractional factorial design (with 1/2 fraction: 4 runs).

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It's a central composite design. You start with the yellow runs to be able to do screening on the effects. You usually add several of the blue points so that you can estimate variance in terms of pure error, and also test for lack of fit. When lack of fit is detected you can follow up with the red axial runs to fit a quadratic model as your response surface and use that for process optimization or what have you.

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  • $\begingroup$ Apologies for off-topic ping: there is a suggestion on Meta to make [randomized-experiment] a synonym of [random-allocation] tag (stats.meta.stackexchange.com/a/4651). You have enough reputation in this tag in order to vote for this suggestion here: stats.stackexchange.com/tags/random-allocation/synonyms - it now needs 4 upvotes to go through. If you disagree with the proposal, consider commenting on Meta to explain why. I will delete this comment soon. Cheers. $\endgroup$
    – amoeba
    May 3, 2017 at 11:04
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You are close: try response surface methodology/regression. A similar pic is the second cover slide here, and provides a reference for the method. The equation is a second order polynomial, which would be a more general term to search for, should the former prove insufficient.

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