Mixture DoE with 6 ingredients, use maximum 3.

[#1]

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.

[#2]

Hi @DocBo,

Welcome in the Community !

Looking at the ratio between the water (solvent) and the additives, why not using a screening (optimal) design first ? Since water effect is of no interest in your additive screening, you could start with a D-Optimal design for your 5 additives, specify a model with main effects, 2-factor interactions (and quadratic effects if needed). See When not to run a mixture design.

Mixture designs are more optimization designs, so better suited if you want to find an optimum formula containing (almost) all your factors.

Is the cardinality constraint really a physical need (formulations are unstable or not possible to realize with more than 2 additives) ?

• If no, I would recommend exploring the additives influence on the response as freely as possible. You would still be able to add constraints a posteriori using your model and the Prediction Profiler.
• If yes, then you can use the Treatment cardinality constraint add-in soon available in JMP Marketplace : https://community.jmp.com/t5/Abstracts/Bridging-Theory-to-Clicks-Two-Level-Designs-with-Treatment/ev...

If you want to keep a mixture design for your topic, simply specifying a second order mixture model will provide a design with up to 2 additives in your formulations. See an example from this topic: Multiple > 3 component Mixture DOE allowing only ternary mixtures

Hope this answer will help you,

[#3]

Hi @Victor_G ,

thank you for your quick and the additional info / links. 

The restriction to max. 2 additives at a time is a request I have to meet, but there is no direct physical need. 

1) How can I implement the constraints posteriori using the model and the Prediction Profiler? But wouldn't this lead to unnescessary tests with to much additives?

2) I did set up a normal DoE with continous factors and 2-factor interaction. but it gives me tests with more than 3 additives in it. How do I get a design with maximum 2 at a time?

Thank you in advance.

[#4]

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,

[#5]

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 Commu....

I hope this helps.

Kind regards,

Laura