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Categorical Mixture Design

Hi Folk,
I got some strange question from user.
There are 3 Mixture factors. She hopes to make mixture design in Custom DOE.
Factor A : 0.5 ~ 0.7(50% ~ 70%)
Factor B : 0.1 ~ 0.2(10% ~ 20%)
Factor C : 0.1 ~ 0.4(10% ~ 40%)
* Factor Constraints : A, B can have only specific values(categorical values)
  (A : 0.5, 0.6, 0.7     B : 0.1, 0.2)

I don't think Mixture Design could be done in this situation
Is Mixture Design possible ? If possible, how can we consider the constraints of factors A and B ?

Thanks

 

Re: Categorical Mixture Design

Hi @IkjuShin ,

Given your constraints, I think there are only 6 possible treatments.

A B C
0.5 0.1 0.4
0.7 0.1 0.2
0.7 0.2 0.1
0.5 0.2 0.3
0.6 0.1 0.3
0.6 0.2 0.2

I think that is the design. The only choice is how many repeats of each treatment.

You can use Custom Design with the attached table as a covariate table. Allow covariate runs to be repeated.

Select the model that you want to estimate. (i think you will only be able to estimate a main effects or 2nd order model, not cubic or higher order)

i think that should work. Let me know.

Cheers!
Phil

 

 

Re: Categorical Mixture Design

Hi Phil,
Thanks for your idea. 
Since factor c don't have any constraint, there might be another way.
Thanks

Re: Categorical Mixture Design

I think Phil is correct. There are no constraints on C, but A and B do have the constraints. Since this is a mixture, you can't vary C on it's own.  Fixing A and B determines C. Phil has specified every possible combination of A and B. C then just makes up the rest of the mixture.

The covariates approach is probably best. Another way to make this, is to have A and B be 3-level categorical factors. Create a full factorial design. Then add column C as a formula. You would have to add column properties and such to analyze as a mixture design if that approach is taken.