Three levels, three factors-RSM

[#1]

Can I use Response surface method to design an experiment with three factors of three levels for each factor?

[#2 · Accepted solution]

Hi, asaalsaadi10!

There are several ways, each with several variations on a theme.  Here are a couple:

• Make a Face-centered Central Composite design

DOE(

  Response Surface Design,

  {Add Response( Maximize, "Y", ., ., . ), Change Factor Settings( 1, -1, 1, "X1" ),

  Change Factor Settings( 2, -1, 1, "X2" ),

  Add Factor( Continuous, -1, 1, "X3", 0 ), Set Random Seed( 657142714 ),

  Make Design( 2 ), Set Axial Choice( 3 ), Center Points( 2 ), Simulate Responses,

  Make Table}

);

• Make a Custom Design

DOE(

  Custom Design,

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

  Add Factor( Discrete Numeric, {1, 2, 3}, "X1", 0 ),

  Add Factor( Discrete Numeric, {1, 2, 3}, "X2", 0 ),

  Add Factor( Discrete Numeric, {1, 2, 3}, "X3", 0 ), Set Random Seed( 37214 ),

  Number of Starts( 4754 ), Add Term( {1, 0} ), Add Term( {1, 1} ),

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

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

  Add Term( {2, 1}, {3, 1} ), Set Sample Size( 16 ), Optimality Criterion( 2 ),

  Simulate Responses, Make Design}

);

Good luck!

[#3]

asaalsaadi10: Generally speaking the optimal DOE approach is more flexible than the classical Box Behnken or face centered CCD approach. You are locked into the number of runs for the BB or CCD...not so with the optimal approach...deployed in JMP in the Custom Design platform. Exact model specification is another. Maybe you don't really need all possible quadratic effects? Other considerations might arise too...suppose you have constraints on the factor space? Again BB and CCD don't play well in that sand box. Made for optimal DOE. So just as Kevin Anderson shared, lots of things to consider before you settle on one design family or series of mouse clicks in JMP.

And the one thing you probably DON'T want to do is a 3**3 full factorial. Still technically an RSM style experiment...with lots interactions and polynomial effects that may not be of particular interest.