Optimizing a Mixture of maximum 3 Ingredients, with 5 ingredients to be Evaluated.

[#1]

I am fairly new to DOE and I have a classical mixture problem. I want to have a mixture of maximum 3 ingredients and optimize towards a specific response, but I have 5 ingredients which could possible fit. So my constraint would be that only 3 out of 5 should be used in one mix maximum. Which Design would work best? All can Carry from 0 to 1. is a D optimal Design needed because if my Special constraint?

Thanks for helping me out!

[#2 · Accepted solution]

Hi @LambdaCanary630,

Welcome in the Community !

I think of (at least) 2 options to get the Mixture design you want with the constraints on the number of ingredients. Here are the options (from easiest to most difficult) :

1. The repartition of points in any design is influenced by the model you assume in the Model panel. If your assumed model contains only effects up to 3rd order, you'll have only runs with up to 3 components in your Mixture design.
   Example here with a Custom D-Optimal design with 45 runs, assuming Scheffe Cubic model :
   

2. If you have supposed a more complex model and/or using a Space-Filling Design approach, one option is to use a Candidate Set approach : you generate a large list of different experiments through Custom Design, Simulator, or any other (DoE) platform, and you delete/filter the runs involving 4+ components.
   To do this filtering, you can add "binary" indicator formula columns for each of your mixture factors (if X1>0, then Indicator1=1, else 0) : 

   If(:X1 > 0, 1, 0)

   and use these indicator columns in a sum, where you can use a local data filter : Sum(Indicator1+Indicator2+...+Indicator5) ≤ 3 :

   Current Data Table() << Data Filter(
   	Location( {388, 388} ),
   	Add Filter(
   		columns( :"Indicator1+Indicator2+Indicator3+Indicator4+Indicator5"n ),
   		Where( :"Indicator1+Indicator2+Indicator3+Indicator4+Indicator5"n <= 3 )
   	)
   );

   The filtered remaining rows will respect your components number constraints.
   Then, you can use the Custom Design platform from your candidate runs table and click on the option "Select Covariate Factors", and then select the corresponding factors, to build a design only using possible runs from your candidate runs table : 

   

There might be other ways, but these 2 options look the most straightforward to me.
Hope this will help you,

[#3]

Thank you Victor!

I was Not sure if restricting the Model to the 3rd Order would precluce combination of more than 3. from a logical Point of view it totally makes Sense.

When I want to add a process Parameter, so either prepare a mixture in melt or in Solution, i would Need a combined Design, Right? But the Rest Stays the Same? So 3rd Order Model and d-optimal Design, but now combined? I also know That at least the pure components Are partly only possible to process in melt or solution, so this can be another constraint.

[#4]

Hi @LambdaCanary630,

Technically, any runs involving 3+ components could help in determining 3rd order effects. But the most informative runs will be the ones involving 3 components, hence the optimal design generated by the platform.

If you want to add a process parameter, I would recommend introducing this factor directly in the design with the mixture factors :

You could use the "Disallowed Combinations Filter" if you have some impossible combinations between mixture ratios and process parameter. For example here, I have specified that ratio for mixture components between 0,6 and 1 can't be used when process is "Solution" :

For explanations on factors constraints and how to use/apply them, I highly recommend the article Demystifying Factor Constraints by @Jed_Campbell. The Candidate Set approach can also be a solution if the previous constraints definitions are not possible or if the constraint is to complex to define with the previous options.

Hope this answer will help you, 

[#5]

Thank you for the clarification.

I tried to set the disallowed combination Filter, but it actually led to an error, because the Factor constraints Are Not usable with mixture factors. Is this because of my Academic license or in General?

[#6]

It's in general, blocking factors also prevent from using disallowed combinations.
It would be perhaps easier to use the Candidate Set approach in case of disallowed combinations for the mixture factors.