## I would like to set a mixture design (DOE) with one factor being discrete in JMP. How is that possible?

Community Trekker

Joined:

Aug 29, 2016

I would like to set a mixture design (DOE) with one factor being discrete in JMP. How is that possible? Thank you very much for feedback on this.

1 ACCEPTED SOLUTION

Accepted Solutions

Joined:

Nov 1, 2013

Solution

If I understand your response, the discrete numeric is actually a mixture, but the issue is that you cannot specify it as mixture?

If so, there are two ways to go about it. Let's say we have a 5-level discrete numeric mixture (X1), and 2 other mixture factors (X2 & X3). The cleanest way is to create the design for just X1 (as discrete numeric) & X2 (continuous for the purposes of creating the design), since X3 will just be 1 - X1 - X2. We need to use disallowed combination to make sure X1 + X2 doesn't go below 0 or above 1. If you run the first piece of jsl in the attached as an example, it should give you an idea.

The other option is to have all 3 factors, X1 as discrete numeric, and X2 & X3 as continuous, but use the disallowed combinations to have their sum "close to 1". The numbers won't look as nice, since the custom designer has to work much harder to optimize it, and you would have to "X2" or "X3" after to make sure the sum is 1 (since the sum will be not quite 1). This is the second example of code, but please note that in this case, you'll want to manually remove the intercept from the model terms.

In either case, you'll need to change the type to mixture afterwards. Sometimes for myself, I just create a separate design with mixture factors, and copy the new design into it, so it has the right column properties.

Hope this helps,

Ryan

6 REPLIES

Staff

Joined:

Jul 2, 2014

Hello,

Here is one option for you.  You can use the Custom Design platform under DOE to designate the factor types you want for your Mixture Design.  Below is an example of a 3 level discrete factor and two mixture factors.  You can have upwards of 8 different levels for your discrete factor.

If on the the other hand you want keep one factor as a constant amount in the mixture and vary the others from low to high you can use a mixture sum to limit the mixture components to specified percentage and use the constant amount to make up the difference.

Hope this helps.

Community Trekker

Joined:

Aug 29, 2016

Hello billw,

thank you very much for your instant help. However, I did try this solution before but when doing it like this, I can't add constraints of mixture for all three factors. Since one factore is not flagged as "mixture" but as "discrete numeric" it will not be considered in the mixing rules by jmp. Do you have an idea, what my mistake might be?

Super User

Joined:

Feb 10, 2013

How many mixture factors do you have? It sounds like maybe you only have 2? If that is the case then if one is X the other is 100% - X so you only need one in your design.  The JMP documentation for a mixture design with a process variable (i.e., non-mixture factors) is found in the DOE book.  From your Help menu: Help > Books > Design of Experiments Guide and then go to Chapter 5 around page 164.

Joined:

Nov 1, 2013

Solution

If I understand your response, the discrete numeric is actually a mixture, but the issue is that you cannot specify it as mixture?

If so, there are two ways to go about it. Let's say we have a 5-level discrete numeric mixture (X1), and 2 other mixture factors (X2 & X3). The cleanest way is to create the design for just X1 (as discrete numeric) & X2 (continuous for the purposes of creating the design), since X3 will just be 1 - X1 - X2. We need to use disallowed combination to make sure X1 + X2 doesn't go below 0 or above 1. If you run the first piece of jsl in the attached as an example, it should give you an idea.

The other option is to have all 3 factors, X1 as discrete numeric, and X2 & X3 as continuous, but use the disallowed combinations to have their sum "close to 1". The numbers won't look as nice, since the custom designer has to work much harder to optimize it, and you would have to "X2" or "X3" after to make sure the sum is 1 (since the sum will be not quite 1). This is the second example of code, but please note that in this case, you'll want to manually remove the intercept from the model terms.

In either case, you'll need to change the type to mixture afterwards. Sometimes for myself, I just create a separate design with mixture factors, and copy the new design into it, so it has the right column properties.

Hope this helps,

Ryan

Community Trekker

Joined:

Aug 29, 2016

Thank you Ryan.lekivetz for your feedback.

From my current point of view, your first recommendation seems to fit my demands the most. I guess I will need more time to think about that, but as I said, this looks promising to me. Thanks again!

Joined:

Apr 3, 2013

Ryan's approach is a great way to approach this problem as the optimal designs give you the most flexibility, but you may have some difficulties specifying the model in terms of the continuous variables. That can lead to problems getting interior points of your design space (if desired).

Another possible option, if you have an unconstrained mixture design OR the constrained space is a smaller simplex, is to go with a "classic" mixture design: the simplex lattice. When choosing that design in JMP, just remember to state that the number of levels is 4 rather than 5. That will put EVERY component at 5 levels and gives you a grid over the entire design space.

Dan Obermiller