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3 way interactions in mixture DOE with process variables

william_zhou

Hi all,

Recently I want to creat a mixture DOE with 2 process variables under the platform of Custom Design.

Suppose all the 3 way interactions are possible, so the design script is as below:

DOE(

Custom Design,

{Add Response( Maximize, "Y", ., ., . ),

Add Factor( Continuous, -1, 1, "X1", 0 ),

Add Factor( Continuous, -1, 1, "X2", 0 ), Add Factor( Mixture, 0, 1, "X3", 0 ),

Add Factor( Mixture, 0, 1, "X4", 0 ), Add Factor( Mixture, 0, 1, "X5", 0 ),

Set Random Seed( 335544 ), Number of Starts( 200 ), Add Term( {3, 1} ),

Add Term( {4, 1} ), Add Term( {5, 1} ), Add Term( {1, 1}, {2, 1} ),

Add Term( {1, 1}, {3, 1} ), Add Term( {1, 1}, {4, 1} ),

Add Term( {1, 1}, {5, 1} ), Add Term( {2, 1}, {3, 1} ),

Add Term( {2, 1}, {4, 1} ), Add Term( {2, 1}, {5, 1} ),

Add Term( {3, 1}, {4, 1} ), Add Term( {3, 1}, {5, 1} ),

Add Term( {4, 1}, {5, 1} ), Add Term( {1, 1}, {2, 1}, {3, 1} ),

Add Term( {1, 1}, {2, 1}, {4, 1} ), Add Term( {1, 1}, {2, 1}, {5, 1} ),

Add Term( {1, 1}, {3, 1}, {4, 1} ), Add Term( {1, 1}, {3, 1}, {5, 1} ),

Add Term( {1, 1}, {4, 1}, {5, 1} ), Add Term( {2, 1}, {3, 1}, {4, 1} ),

Add Term( {2, 1}, {3, 1}, {5, 1} ), Add Term( {2, 1}, {4, 1}, {5, 1} ),

Add Term( {3, 1}, {4, 1}, {5, 1} ), Set Sample Size( 24 )}

);

But when I press the button of "Make Design", a JMP alert window appears which says "Optimal designer failed to converge."

How can I handle this kind of mixture DOE?

Thank you.

William

Accepted answers

louv

William,

Agree with Don's input except I would consider i-optimal.

DOE(

Custom Design,

{Add Response( Maximize, "Y", ., ., . ),

Add Factor( Continuous, -1, 1, "X1", 0 ),

Add Factor( Continuous, -1, 1, "X2", 0 ), Add Factor( Mixture, 0, 1, "X3", 0 ),

Add Factor( Mixture, 0, 1, "X4", 0 ), Add Factor( Mixture, 0, 1, "X5", 0 ),

Set Random Seed( 1103215951 ), Number of Starts( 100 ), Add Term( {1, 1} ),

Add Term( {2, 1} ), Add Term( {3, 1} ), Add Term( {4, 1} ), Add Term( {5, 1} ),

Add Term( {1, 1}, {2, 1} ), Add Term( {3, 1}, {4, 1} ),

Add Term( {4, 1}, {5, 1} ), Add Term( {3, 1}, {5, 1} ),

Add Term( {3, 1}, {4, 1}, {5, 1} ), Add Alias Term( {1, 1}, {3, 1} ),

Add Alias Term( {1, 1}, {4, 1} ), Add Alias Term( {1, 1}, {5, 1} ),

Add Alias Term( {2, 1}, {3, 1} ), Add Alias Term( {2, 1}, {4, 1} ),

Add Alias Term( {2, 1}, {5, 1} ), Set Sample Size( 12 ),

Optimality Criterion( 2 ), Make Design}

);

Blue = d-optimal

Green = i-optimal

Number of runs = 12

Model terms = X1, X2, X3, X4, X5, (X1*X2), (X3*X4), (X3*X5), (X4*X5), (X3*X4*X5)

7137_Screen Shot 2014-08-25 at 7.42.01 PM.png

Lou

All comments

Jeff_Perkinson


William Zhou wrote:

Hi all,
Recently I want to creat a mixture DOE with 2 process variables under the platform of Custom Design.
Suppose all the 3 way interactions are possible, so the design script is as below:

DOE(
 Custom Design,
 {Add Response( Maximize, "Y", ., ., . ),
 Add Factor( Continuous, -1, 1, "X1", 0 ),
 Add Factor( Continuous, -1, 1, "X2", 0 ), Add Factor( Mixture, 0, 1, "X3", 0 ),
 Add Factor( Mixture, 0, 1, "X4", 0 ), Add Factor( Mixture, 0, 1, "X5", 0 ),
 Set Random Seed( 335544 ), Number of Starts( 200 ), Add Term( {3, 1} ),
 Add Term( {4, 1} ), Add Term( {5, 1} ), Add Term( {1, 1}, {2, 1} ),
 Add Term( {1, 1}, {3, 1} ), Add Term( {1, 1}, {4, 1} ),
 Add Term( {1, 1}, {5, 1} ), Add Term( {2, 1}, {3, 1} ),
 Add Term( {2, 1}, {4, 1} ), Add Term( {2, 1}, {5, 1} ),
 Add Term( {3, 1}, {4, 1} ), Add Term( {3, 1}, {5, 1} ),
 Add Term( {4, 1}, {5, 1} ), Add Term( {1, 1}, {2, 1}, {3, 1} ),
 Add Term( {1, 1}, {2, 1}, {4, 1} ), Add Term( {1, 1}, {2, 1}, {5, 1} ),
 Add Term( {1, 1}, {3, 1}, {4, 1} ), Add Term( {1, 1}, {3, 1}, {5, 1} ),
 Add Term( {1, 1}, {4, 1}, {5, 1} ), Add Term( {2, 1}, {3, 1}, {4, 1} ),
 Add Term( {2, 1}, {3, 1}, {5, 1} ), Add Term( {2, 1}, {4, 1}, {5, 1} ),
 Add Term( {3, 1}, {4, 1}, {5, 1} ), Set Sample Size( 24 )}
);

But when I press the button of "Make Design", a JMP alert window appears which says "Optimal designer failed to converge."
How can I handle this kind of mixture DOE?
Thank you.

William

William posted his question in his personal space. I'm replying after moving it to the SE Discussion to get his question sent to the community.

-Jeff

louv

William,

Have you considered the Scheffe Model?

Optimality = i-optimal

7148_Screen Shot 2014-08-25 at 10.06.09 AM.png

louv

William,

For some reason the X1*X2 interaction was not included but if I amend the model using the cross feature to include the X1*X2 interaction all proceeds fine.

7149_Screen Shot 2014-08-25 at 10.18.02 AM.png

William Mixture DOE.jmp

william_zhou

Lou,

Thank you for your feedback!

Your answer inspired me to remove the term of X1*X2 from the model, then it works!

DonMcCormack

William,

I'd recheck your design. When I ran your code, the X1 and X2 main effect terms were missing from the model. I don't think you want to do that. The problem with higher order mixture terms and interactions between process variables and mixture variables is that there is because of the linear dependency between mixture terms. In your example, X3 + X4 + X5 must add to a fixed value (usually 1). So, for something like the X1*X3 interaction, you can substitute X3 = (1 - X4 - X5) and see that X1*X3 = X1 - X1*X4 - X1*X5. This is why you are getting the non convergence message when you try to fit your original model. There are terms in the model that shouldn't be there because they are confounded. Not sure why the Custom Designer let them slip past, but I believe that's the original problem. As long as you keep the process variables and mixture variables separated, you shouldn't have a problem. For example, this model works:

DOE(

Custom Design,

{Add Response( Maximize, "Y", ., ., . ), Add Factor( Continuous, -1, 1, "X1", 0 ),

Add Factor( Continuous, -1, 1, "X2", 0 ), Add Factor( Mixture, 0, 1, "X3", 0 ),

Add Factor( Mixture, 0, 1, "X4", 0 ), Add Factor( Mixture, 0, 1, "X5", 0 ),

Set Random Seed( 911276116 ), Number of Starts( 800 ), Add Term( {1, 1} ),

Add Term( {2, 1} ), Add Term( {3, 1} ), Add Term( {4, 1} ), Add Term( {5, 1} ),

Add Term( {1, 1}, {2, 1} ), Add Term( {3, 1}, {4, 1} ),

Add Term( {3, 1}, {5, 1} ), Add Term( {4, 1}, {5, 1} ),

Add Term( {3, 1}, {4, 1}, {5, 1} ), Add Alias Term( {1, 1}, {3, 1} ),

Add Alias Term( {1, 1}, {4, 1} ), Add Alias Term( {1, 1}, {5, 1} ),

Add Alias Term( {2, 1}, {3, 1} ), Add Alias Term( {2, 1}, {4, 1} ),

Add Alias Term( {2, 1}, {5, 1} ), Set Sample Size( 12 ), Make Design}

);

Don