Forcing center points to be equally distributed across blocks custom design

[#1]

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}
);

[#2]

Excuse my ignorance, but don't you want your center points to be run randomly across the blocks?  I don't understand what you mean by "control condition".  This is not necessary for experimentation.  Once the design is made in JMP, you can easily specify the appropriate run order. 

How many blocks are you running?

[#3]

I'm purely speculating regarding @Mittman 's use of the phrase '...control condition ("center point")...'. Occasionally the engineers I worked with would include supplemental treatment combinations in a designed experiment as a kind of 'check' for nuisance or noise factors being present during experimental execution. Not necessarily in the center of the experimental space. We rarely included the responses for these treatment combinations in the analysis. It was just to give the engineers a warm fuzzy feeling about the unknown creeping into the execution of the experiment. Maybe this is what @Mittman is contemplating doing and they are trying to force the runs into specific blocks?

[#4]

The number of blocks is variable. I am considering a class of multifactor experiments where the center point represents the current working condition. The blocks represent batches of material and the number of units in a batch is fixed. For operational reasons, there is a policy that at least one unit within each batch must get the standard processing.

[#5]

OK, keep track of the run order for the CP's.  Use a MR chart to look at those .  If they show consistency, then (MR-bar/1.128)^2 will provide an estimate of the variance over the course of the experiment.  Compare this to the current variability in the process.  This may be a good estimate of the MSE for statistical tests.

I prefer using blocks as fixed effects when you know what is confounded with the block (in your case, batches).  Make sure you add block-by-factor interactions to your model.  These are terms that quantify the robustness of your design factors to the batch effect.

[#6 · Accepted solution]

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,

[#7]

Thanks for the suggestion. I think I will manually add the centerpoints after generating the design without centerpoints (recognizing that this is not mathematically optimal.) The blocking is necessary to account for differences in incoming batches of material. (These could be modeled as random or fixed; I am opting to model as a fixed effect.)

[#8]

Any update?