Why do I have replicate runs when adding constraints

Question

Hi,

when I do a simple DOE with 2 factors, discrete numeric (4 Levels) and use 12 runs leaving replicate runs as default at zero and just ME model, I get 3 replicates. Same happens with two continous variables.

// DOE - ME - 0 replicates but 3 each in generated design

DOE(

Custom Design,

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

Add Factor( Discrete Numeric, {1, 2, 3, 4}, "X1", 0 ),

Add Factor( Discrete Numeric, {1, 2, 3, 4}, "X2", 0 ),

Set Random Seed( 848947636 ), Number of Starts( 122330 ), Add Term( {1, 0} ),

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

Replicates( 0 ), Set Sample Size( 12 ), Optimality Criterion( 2 ),

Make Design, Make Table}

);

Current Data Table() << Summary(

Group( :X1, :X2 ),

Freq( "None" ),

Weight( "None" )

);

How can I avoid those replications? Is there a reason why I get replication even I set them to zero?

Or in other words - how can I force really no replicates?

Background, a customer plans a doe for gum tools with different cavities (based on levels for the discrete numeric parameters). In the generated tool layout there shouldn't be replication, they want to get in one shot all possible cavities and have then further process parameter set. (I believe with a block design we could do this nicely). However I wonder why I get replications when I do not want them to occur?

Thanks,

Martin

Phil_Kay · Answer

I think the bottom line is that you can only design the best experiment when you are clear about the objective. And you need to make sure that Custom Design is clear about the objective as well!

DonMcCormack · Answer

Martin,

I'm not getting similar results. Try this:

DOE(

Custom Design,

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

Add Factor( Discrete Numeric, {1, 2, 3, 4}, "X1", 0 ),

Add Factor( Discrete Numeric, {1, 2, 3, 4}, "X2", 0 ),

Set Random Seed( 1573553642 ), Number of Starts( 44161 ), Add Term( {1, 0} ),

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

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

Add Alias Term( {1, 1}, {2, 1} ), Set Sample Size( 10 ), Save X Matrix,

Make Design, Make Table}

);

I ran this on both my Mac and PC and got similar results whether I set the factors to If Possible or Necessary (i.e., no replicates). To Phil's point, you only need 7 observations to estimate the model parameters. Anything else will go into maximizing the optimality criterion. If your looking for something akin to a Latin Square (or BIB), you'll have to introduce additional criteria. Mark Bailey did something in the JMPer Cable newsletter years ago about generating a Latin Square in JMP.

Don

Phil_Kay · Answer

Hi Martin,

The 2 extremes of the factor levels will always give you the most power when testing a main effects model. Therefore Custom Design will always pick them as the runs, even when they have been picked already. Hence, replicate runs. This is best design if the objective is to test the main effects model. However, I don’t think this is the objective from what you describe.

You could avoid this happening by specifying a higher order model. Or by using another platform: the full factorial platform would give you all the possible combinations of factor settings. Or it sounds like space-filling is closer to what they want.

Hope this is helpful.

Phil