Center point not in the center

joberi

I want to design an I-optimal response surface design with one factor having the center run not in the center. Normally one only sets -1 and 1 and the center is automatically defined in the middle. Is there a possibility to interfer at that point?

Thank you.

mpb

Several approaches come to mind.

1. If you have JMP 10 you can designate the special factor as Discrete Numeric Factor which allows you to specify the only allowable levels for that factor. I don't have access to JMP 10 at the moment but this should allow you to go ahead and generate your design without additional effort using Custom Design.

2. Using Custom Design you could generate your I-optimal design with all factors allowed to take true center values and then simply replace all 0's with whatever value you need for the special factor. You can evaluate the resulting design using DOE>Augment, adding 0 new rows. I did this using 0.5 instead of 0 and the diagnostics were not too much worse than the original design but you would have to evaluate your own situation.

3. Using Custom design you could set up a disallowed combination designed to only permit the special factor to take values near -1, 1, and the special value.  Again, using 0.5 I found the design evaluation to be similar to (2) above. The obvious difference is that in (2) the other factors continue to use -1, 0, 1 whereas this approach may cause other values between -1 and 1 to be generated. I'm including a sample script which demonstrates this approach.

DOE(

    Custom Design,

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

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

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

    Add Factor( Continuous, -1, 1, "X3", 0 ), Set Random Seed( 617282759 ),

    Number of Starts( 21 ), Add Term( {1, 0} ), Add Term( {1, 1} ),

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

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

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

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

    Set Sample Size( 16 ), Disallowed Combinations(

        -0.99 <= X2 <= 0.499 | 0.501 <= X2 <= 0.99

    ), Optimality Criterion( 2 ), Make Design}

);