Mixture DOE - how to limit number of ingredients in final formula?

[#1]

Dear All,

I am using JMP for the first time and I'm trying to run a DOE with 6 mixture factors (A, B1, B2, B3, B4, B5) and 1 categorical factor. This is a chemical formulation and I only can use a maximum of 2 ingredients of type B, i.e., the final formula must have just 2 or a maximum of 3 ingredients (A + 1 type of B or A + 2 types of B).
Sum of all type B must make up between 1% and 40% of the final blend.
Can you help me to set up this in JMP?
Thank you,

Sofia

[#2]

Dan is giving you excellent advice.  I will only add, if you are appropriately at the point of running mixture designs (or any optimization design), you should already know the effects of noise (which will have a potentially large effect on consistency and predictability).  If not, you will find the contours of the mixture profiler will possibly change with changing noise.  Provided you have truly characterized the effects of noise, your analysis of mixtures is interpreting the surface/contour plots from the mixture profiler.  If you are missing data, the plots will be less precise and can be misleading.  We're less interested in statistical significance as the factors in the mixture have already been determined to be significant.  You are just looking for the appropriate proportions of each component.

[#3]

Ok, thank you @Dan_Obermiller 

Should I add some replicate run(s) to the design?

[#4]

Replicate runs are always nice to have. More importantly in this case would be to change the objective to an I-optimal design. I forgot to do that before including it. That seems to have more of an impact on this situation than a replicate would. Remember, I am not endorsing this design. I am endorsing the design approach. You should explore the proper number of runs for your needs. Including replicates is a good idea, but it will depend on how many runs you can perform.

[#5]

Oh, one more thing. Can you open the design dialog to see what was done? Yes. There is a DOE Dialog script that you can run. Although it will recreate the design, just close the data table. You will have the DOE Dialog available to make changes. But please completely understand the WHY behind each of the steps that I did. If you make changes, my steps will likely need to be changed so that you can obtain a valid design. That will require an understanding of the underlying approach.

[#6]

I see this problem just a bit different.

I think you have two, maybe three components that are being blended together. We just don't know the names of the last two.

So, I think this design approach might work:

DOE(
Custom Design,
{Add Response( Maximize, "Y", ., ., . ),
Add Factor( Mixture, 0.6, 0.99, "A", 0 ),
Add Factor( Categorical, {"B1", "B2", "B3", "B4", "B5"}, "First B Type", 0 ),
Add Factor( Categorical, {"B1", "B2", "B3", "B4", "B5"}, "Second B Type", 0 ),
Add Factor( Mixture, 0.01, 0.4, "First B Proportion", 0 ),
Add Factor( Mixture, 0, 0.4, "Second B Proportion", 0 ),
Set Random Seed( 187611 ), Number of Starts( 351 ), Add Term( {1, 1} ),
Add Term( {4, 1} ), Add Term( {5, 1} ), Add Term( {1, 1}, {2, 1} ),
Add Term( {1, 1}, {3, 1} ), Add Term( {1, 1}, {4, 1} ),
Add Term( {1, 1}, {5, 1} ), Add Term( {2, 1}, {3, 1} ),
Add Term( {2, 1}, {4, 1} ), Add Term( {2, 1}, {5, 1} ),
Add Term( {3, 1}, {4, 1} ), Add Term( {3, 1}, {5, 1} ),
Add Term( {4, 1}, {5, 1} ), Set Sample Size( 48 ), Simulate Responses( 0 ),
Save X Matrix( 0 ), Make Design}
);

This does have a drawback of possibly having the same B component for part 1 and part 2. However, I considered that to be just looking at blends with just one of the B components.

Would this work?

[#7]

Thank you @Dan_Obermiller.

It is a very interesting approach. The issue is that I need to define different upper limits for the different B types: B1, B2 and B3 would be maximum 0.2 while B4 maximum 0.03 and B5 maximum 0.05.

Is there any solution?