Mixture DoE with 6 ingredients, use maximum 3.

Question

Dear Community,

I'd like to set up a mixture DoE comprised of:

* Polymer: 80%
* Water: 18,4% - 20%
* Additive1: 0-0,8%
* Additive2: 0-0,8%
* Additive3: 0-0,8%
* Additive4: 0-0,8%
* Additive5: 0-0,2%

Since Polymer ist constant, I removed it. Hence I get:

* Water: 92% - 100%
* Additive1: 0-4%
* Additive2: 0-4%
* Additive3: 0-4%
* Additive4: 0-4%
* Additive5: 0-1%

Now I want to screen Additive performance, but have only 1 or 2 Additives present in the mixture at the same time.

By this in the model, I want to consider only the main effects and the interaction between two additives. Since water acts only as a filler, but has no effect on the response, I neglet effects between Add *water and only want to consider Add(A)*Add(B) effects.

May anyone could explain please, how do I make sure JMP selects only mixtures with 1 or 2 different Additives and water?

Any ideas welcome.

Thank you in advance.

Factors.png

Model_Design.png

DoE_w_5Additives - Factors.jmp

RikkiTikkiTavi · Answer

Hi Laura, is it only suitable for bayes opt auto mode ? I was hoping to enforce all my constraints using a candidate data set in bayes opt custom mode but it seems that profiler is disabled. Is that expected behavior ?

Laura_Lancaster · Answer

Hi,

If you have access to JMP 19.1 you can access some new functionality in a JSL function that allows you to generate random samples (candidate sets) that can be subject to linear constraints, variable bound constraints, and cardinality constraints on specified component group variables.  The function is called Random Linearly Constrained Uniform.  It is an extension of the function, Polytope Uniform Random, that has existed in JMP for a long time.  (You can find the details of how to use it and some examples in the JMP object scripting index.)  For your example, I can call the function with the following JSL:

Names Default To Here( 1 );

A = [1 1 1 1 1 1];
b = [1];
L = [.92 0 0 0 0 0 ];
U = [1 .04 .04 .04 .04 .01];
nwarm = 100;
nstride = 100;
tol = 1e-8;
// Index the constrained subgroups.  Index = 0 is not in a constrained subgroup.
G = [0 1 1 1 1 1];
// Lower cardinality constraints for the constrained subgroups
LC = [1];
// Upper cardinality constraints for the constrained subgroups
UC = [2];
points = Random Linearly Constrained Uniform(
	100,
	A,
	b,
	L,
	U,
	1,
	0,
	0,
	nwarm,
	nstride,
	tol,
	G,
	LC,
	UC
);
dt = As Table( points );

This produces a candidate set of 100 runs that is saved to a table that looks like the following:

The Bayesian Optimization platform that is in JMP Pro 19 is really ideal for these types of problems.  Check out the presentation that I gave with Kasia and Chris at Discovery to learn more:  Bayesian Optimization for Formulations Involving Complex Constraints with JMP 19... - JMP User Community.

I hope this helps.

Kind regards,

Laura

Victor_G · Answer

Hi @DocBo,

1) Testing the additives without constraints would help you determine more easily and precisely the main effects and interaction effects between the additives in the design. When using the Prediction Profiler linked to your model, you can set the value of factor to any value (like 0) with CTRL+click, set the value to the corresponding factor, and check lock factor setting to optimize your formula without the less promising factors (identified thanks to your model).

2) You can use the candidate set approach, creating a table with only 2 factors at a time, and use this table to select the runs in your design using Custom Design platform and the option Select Covariate Factors. Balanced Incomplete Block designs could also be an option (example here). Or wait for the add-in mentioned before that would provide better design options.

Best,