Interesting Mixture Design Setup

MikeD_Anderson

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?

DonMcCormack

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}
);