topic Re: Mixture DOE Constraints in Discussions

Mixture DOE Constraints

Alpaca0920 — Thu, 08 Jun 2023 21:10:05 GMT

I am a new user for JMP, I am trying to create a design of experiment for a mixture. I have four factors in my experiment : resin, plasticizer, Modifier A, Modifier B. I do not want Modifier A to be in the same batch with Modifier B. I want Modifier A or Modifier B not both. How do I create a constraint to disallow these two ingredients to be together in the same run?

Re: Mixture DOE Constraints

Byron_JMP — Wed, 22 Jun 2022 14:17:46 GMT

This is a really good example that Tom Donnelly wrote up a while back.

7-Component Mixture Design with Additional Constraintshttps://community.jmp.com › us-gov-jug-tkb › J...

Re: Mixture DOE Constraints

Mark_Bailey — Wed, 22 Jun 2022 14:33:30 GMT

Here is a simple solution. Separate the proportion of the Modifier and the type of Modifier. Something like this:

Re: Mixture DOE Constraints

Alpaca0920 — Wed, 22 Jun 2022 14:39:39 GMT

I thought about doing this but Modifier A has a range of 0 to 0.09 and Modifier B has a different range of 0 to 0.3

Re: Mixture DOE Constraints

Phil_Kay — Thu, 23 Jun 2022 07:07:48 GMT

It would seem that it should be possible to set up the design as @Mark_Bailey suggests and then add

Modifier Type = A & Modifier > 0.09

as a disallowed combination.

However, you can't have disallowed combinations with Mixture factors in Custom Design :(.

I'm not sure why this is. I guess it is complex to implement constraints with optimal mixture designs. You might want to add that as a request in the JMP Wish List.

So I think you might need to use the Candidate Set Design approach as presented by @chris_gotwalt1 at JMP Discovery Europe 2021.

Following this approach I created a "Big Design" of 2000 runs that obeys the constraints that you have. Then used this as a candidate set for the smaller 40-run Custom Design. (Both designs attached). I think this approach would work for you?

You can see that it obeys the constraint you stated:

Re: Mixture DOE Constraints

Mark_Bailey — Thu, 23 Jun 2022 12:37:02 GMT

You could leave the default range -1 to +1 (coded levels) for Modifier. You can then interpret the results on the respective scales.

I generally advise against using a level of 0 for a continuous factor (mixture components are modelled as a continuous variable) because you essentially make it categorical (present, not present). I recommend using something close to 0, but far enough away to be meaningful. That advise, though, does not really apply to the proportion of a mixture component.

You are getting lots of ideas for solving your experiment design!