Creating a Mixture DoE

[#1]

Hi,

I hope you are well. I want to perform a screening experiment to understand which materials in the formulation are impacting the response. There are a number of materials I want to study the impact of (10 in total), however, in any given formulation there are combinations of materials that we can't accept. I've expressed this below, as we only want only one from the following A, B, C, D, E, and F in any formulation test. When the materials are in total, 1A or 2A, 1B or 2B, 1C or 2C, 1D or 2D, 1E or 2E. Note each material described as 1A, 1B or 2B etc... is unique and has varying concentration limits.

How do I create the DoE using custom screen or definitive screen (whichevers best) to measure the impact of these materials?

Thank you very much  

[#2]

I don't think I'm understanding your question properly. Specifically, this sentence:

When the materials are in total, 1A or 2A, 1B or 2B, 1C or 2C, 1D or 2D, 1E or 2E. Note each material described as 1A, 1B or 2B etc... is unique and has varying concentration limits.

a) could you add more clarity to this?

b) this page might be helpful

[#3]

Hi Jed,

Thanks for your response. Simply put all the materials are factors we wish to study, however, there are combinations of materials/factors that we simply don't want to test in any given run. How do I set up my design so specified material/factor combinations don't show up in any given run? 

Hope this makes more sense? The link provided for demystifying factor constraints was helpful, although I'm still trying to make it work. 

Thanks

[#4]

Is there a way you could post the design and explain the combinations you'd like to avoid? You could do this with anonymized responses/factors. This could help the community be more specific with help.

[#5]

Hi Jed,

I've included an example excluding sensitive information but shows what we are trying to do.

I've figured we can group the materials we want only one of to appear in any given run as 2 level categorical/blocking variables and have a continuous factor to scale quantity for each categorical factor created. Your information has helped me learn that you can use the disallowed combinations filter to constrain the varying factor limits for each materials to get round this challenge.

This could work but you can't express the materials as mixture variables, so it is better as an approach to run 2x separate DoE's (Set A and B respectively) expressing the materials as mixture variables or using the above approach which combines both?

Thanks very much for your help

[#6]

Hi @Fox_782199,

Before going into details, is the total quantity of your formulation fixed ? Meaning the total amount of your components should reach a certain value/percentage (like 80g or 100%, 80%, ...) ?

• If yes, this is probably a Mixture design indeed. But depending on the relative scales of the ingredients involved, it may be sometimes possible to use a factorial design.
• If no, this is probably more a factorial design, and you may have a lot of options to choose the most relevant design depending on your objective(s), factors specifications and types, number of factors, number of runs and model supposed. As you describe, you can use Optimal design and specify for each ingredient a categorical factor with 2 levels (Option 1 or 2 for each raw material) as well as a continuous factor (concentration min / concentration max) and exclude with "disallowed combination" some parts of your experimental space if some options for ingredients don't have the same overlapping concentration ranges. There are several ressources and use cases on this topic in the JMP Community.

I hope this first question will help you,

[#7]

Hi Victor,

Thanks you, this clarifying question is helpful. 

For this particular study, I would say the total formulation is not fixed to a certain value (the total formulation amount is similar, however, some material quantities are expressed in slightly different units and therefore will not be fixed) so it sounds like doing a factorial experiment similar to the described earlier is the way to go. 

This is more for my general learning now, if I were to say the formulation was fixed and therefore a mixture design, what would you advise? Run the Set A and B in 2 respective mixture DoE's, or is there another way? 

Thanks

[#8 · Accepted solution]

Hi @Fox_782199,

Thanks for your response.
Now it seems that you're indeed not in a Mixture design scenario, but more a factorial design, where you have a lot of options to choose from. If you need more guidance on the Custom design (or other relevant designs for your study), don't hesitate to ask specific and follow-up questions.

As a general response, if you were in a Mixture design scenario (so all ingredients are added to reach a fixed quantity/value/percentage, meaning you're more interested in ratios than in absolute quantity value), I would try to include all factors in one DoE and specify a relevant model (with the help of Custom design platform to be handle mixture and categorical factors). 

This may represent a big number of experiments to run, but may be more "accurate", as you're directly taking into account the possible interactions between the choice of a raw material and its concentration, and seeing its impact on the rest of the formulation. Creating two separate designs on set A and B won't give you the information about the interactions between choice of the raw mterial, its concentration, and the other factors : you'll have two separate mixture designs, with two optimima, but they may not be related to each other. You won't be able to assess if the right combination of ingredients is a mixture from sets A and B, only see optimized ratio for set A and for set B independently.

I hope this answer will help you,