Forcing center points to be equally distributed across blocks custom design

Mittman

Operationally, it may be desirable to ensure a run at control condition ("center point") within each block of a DOE. How can I specify this when using the Custom Design platform?

 

Example (JMP Pro 17.2.0):

DOE(
	Custom Design,
	{Add Response( Maximize, "Y", ., ., . ), Add Factor( Blocking, 4, "X1" ),
	Add Factor( Continuous, -1, 1, "X2", 0 ),
	Add Factor( Continuous, -1, 1, "X3", 0 ), Set Random Seed( 259183913 ),
	Number of Starts( 189816 ), Add Term( {1, 0} ), Add Term( {2, 1} ),
	Add Term( {3, 1} ), Add Term( {1, 1} ), Add Alias Term( {2, 1}, {3, 1} ),
	Center Points( 3 ), Set Sample Size( 12 ), Simulate Responses( 0 ),
	Save X Matrix( 0 ), Make Design}
);

Victor_G

Hi @Mittman,

 

May I ask why did you create a blocking factor in your design ?

• Are the levels of this fixed blocking effect of interest, controllable (for example in the Profiler, you can choose the preferred level of the blocking factor to optimize the response), and expect to have an influence on the mean response (like choice between equipment A, B or C) ? This situation indeed requires a blocking factor in the design (fixed effect).
• Or are you more interested into evaluating the variance of your response regarding some levels of this random effect (like the variance of the measurement device for each day of experiment, to make sure there are no default/mis-calibration, ... between each day ?) ? This situation would require a random block effect, accessible through the Design Generation panel of Custom Design (option "Group new runs into random blocks of size :").

 

I tried to create designs using both options, either choosing fixed blocking effect by entering a blocking factor like you did, or choosing random blocking effect by specifying at the end of the Design Generation panel the grouping of runs into random blocks of size 4, and I was not able to generate a design where each of the three centre points are randomly distributed in the three blocks (one per block). By default the random design generation seems to favour other repartitions as they are more balanced than the one you expect.

As @statman mentioned, the random distribution of centre points in the Custom Design platform is done so that each block are the most similar between each other : the groups of experimental runs for each block are expected to be similar, so that the mean response is influenced mostly (hopefully) by the factors effects, and not the blocking factor effect. If you want to allocate one centre point per block, there are 3 remaining runs per block, so you might expect some imbalance of factors levels between blocks, which might compromise the similarity of blocks if any factor has a strong impact on the response.

 

If you really need to have one centre point per block for practical reasons, why not generating a design with 3 blocks and 9 runs, and add manually a centre point per block, before randomize runs inside each block ?

You can then compare this situation ("..._Force-centre-points" design) with a default Custom Design with same number of runs and 3 centre pojnts ("..._with-centre-points" design) using the Compare Designs platform.

• You can expect a slight decrease of power for main effects :
  

• You may also expect a slight increase of variance prediction over your experimental space due to this "forced" runs imbalance :
  
• Due to the different matrices generated, you will probably encounter different aliasing structure : 
  

   

So if you want to assign one centre point to each block for practical reasons, you will have to do it manually, as this situation is not optimal regarding the repartition of factors levels. It's a compromise between design performance & optimality, and the practical use of centre points you want to do.

 

Please find attached the two designs used for the comparative study,.
Hope this response will help you,

 

Custom Design_Force-centre-points.jmp

Custom Design_with-centre-points.jmp