I would like to design a fractional factorial experiment that has 10 factors with 2 levels and 1 factor with 3 levels (a total of 11 factors). However, I am the only interested in 2 and 3-factor interactions involving only the factor that has 3 levels. Any recommendations on what type of design to use?
My intention is to use the design for a screening experiment.
Hi, maybe mixing a definitive screening design (10 factors @ 2 levels = 26 runs) with your 11th factor with 2 and 3-times interaction could solve that. Never did this, just an idea ;-)
Best regards, Andreas
FFD can be customized using any DoE software. If you have strong knowledge in statistics, you can do it in Microsoft Excel also.
Just test the 3 factor interaction on its own. You only need to include the 10 other factors if they possibly have a direct influence on the 3
A simple by hand solution is to start with a fractional factorial of the 2^10 in 16 then replicate with the 3 level varying each time. That's 48 treatments. This guarantees you'll be able to measure all main effects of the 3 as well as all interactions between the 3 with each 2 level factor but only get the main effects of the 2 level factors. Unfortunately the main effect of the three cost you 2df, each main effect of the 2 will require 10df and each interaction will require 10x2df=20df. That's a minimum of 32df plus one for error is min 33df. So a 48 is not bad but someone may have a better solution in 36 which I suspects may exist with some careful confounding. This is bc 36 is a 6^2 which caters nicely to 2 and 3 level attributes.
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