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Interesting Mixture Design Setup

A customer asked me about how to set up a mixture design.  The design itself is fairly straightforward:

• 4 ingredients
• First 3 ingredients need to sum to ~30% with the 4th being a filler.

 

The wrinkle that's got me stumped is that they want to choose from 7 potential ingredients (i.e. 7 choose 3) for a given treatment combination.  While this seems somewhat odd, my gut tells me there should be a way to do it.  And they are okay with this being a big design... 

 

Thoughts?

Re: Interesting Mixture Design SetupSorry, my mistake - you're 100% correct on the interactions statement. I'll chalk it up to this cold my daughter gave me - I've been foggy for days!

I think you're on to something with the BIDB idea (or the Custom Design). Use each of the treatment blocks as a set of experiments where the ingredients are constant and the mixture is tested. Basically a DOE within a DOE. Just as part of the discussion I'll dummy something up and post it.

Thanks!

MRe: Interesting Mixture Design Setup

I suspect they are interested in how combinations of mixture components interact. Not sure if you could quantify the effect of one component independent of the other 2 in the mixture. If they were independent, it wouldn't matter which three components were used in a given experiment. You could run 3 mixture experiments, each with a different set of components (e.g., ABC, DEF, GAD). As long as you used all seven, you'd be OK.

Two more ideas, create the combination blocks using Custom Designer or BIBD. Here's the code for each of these.

 

DOE(
 Balanced Incomplete Block Design,
 {Treatments( "Treatment", 7, {"A", "B", "C", "D", "E", "F", "G"} ),
 Blocks( "Block", 3, 1, 7 ), Make Design}
);

DOE(
 Custom Design,
 {Add Response( Maximize, "Y", ., ., . ),
 Add Factor( Categorical, {"A", "B", "C", "D", "E", "F", "G"}, "Treatment", 0 ),
 Set Random Seed( 776273344 ), Number of Starts( 21362 ), Add Term( {1, 0} ),
 Add Term( {1, 1} ), Set Runs Per Random Block( 3 ), Set Sample Size( 14 ),
 Simulate Responses( 0 ), Save X Matrix( 0 ), Make Design}
);

Re: Interesting Mixture Design SetupPretty sure this is the combinatorial equivalent to a fishing expedition… so I’m guessing all 35. It’s also probably a reasonable assumption at this point that they won’t be considering interactions – just a screening design.

Best,

M
Re: Interesting Mixture Design Setup

Do they want to examine all 35 combinations or only a subset. If the later, how will they decide which combos?