"Change Generating Rules" for custom design (is that option just only in screening design?)

[#1]

When I'm using Screening Design I can set the generators for the main effects by checking boxes in that menu and then click apply. I can't find how to do this in the Custom Design menu though.  That section isn't there. Is there a reason we can't specify the generating rules for a fractional factorial in custom design?

Trying to setup a WP/SP scenario. Otherwise I'd just use the screening design menu.

[#2 · Accepted solution]

Hi @awelsh,

The generation of optimal screening designs (through Custom design platform) and classical fractional factorial design is different.

• In the case of classical fractional factorial design, you specify the generator that will create complete confounded terms that you won't be able to differentiate (very often, main effects with high order effect, like 3/4/5-... factors interactions, assuming the Effect Hierarchy principle holds true). That result in designs where some terms are completely aliased/correlated, but since you have the flexibility to specify the generator, you can have some flexibility and try to estimate as precisely and unbiasedly as possible the terms of interest depending on the resolution of the design. It makes the design construction easy, so it's possible to create such design by hand. This design creation option is only available in platform Screening Designs.
• In the case of optimal screening designs, the generation of the design is done thanks to a coordinate exchange algorithm and an objective to achieve, named optimality criterion. Depending on your experimental objective, you can choose the most relevant optimality criterion : explainability through precise terms estimation and filtering (D- or A- optimality criterion) or predictivity through prediction variance minimisation (I- or G-optimality criterion). As the design is computed thanks to this algorithm and optimality target, you can't specify directly a generator : the algorithm will try, based on your assumed model, optimality criterion, experimental runs budget and any possible constraints, to minimize the correlations between terms in your model. So as much as possible, the resulting design will have partial correlations instead of complete confounding between terms like classical fractional factorial designs. However in some situations (for example generating a design with the minimum required number of runs and no constraints), the resulting optimal design can be a classical fractional factorial design. Optimal designs are a generalization of classical "textbook" designs like fractional factorial designs, able to handle constraints, with more flexibility on the model terms estimations thanks to the assumed model and the number of experimental runs.

Hope this answer will help you,

[#3]

Thank you for the detailed explanation with links. That was very helpful and I understand the difference now.

(context: I'm an experienced Lean Six Sigma Master Black Belt and Mechanical Engineer. However, I've been using Minitab for the last 10yrs and trying to learn advanced features of JMP. I was originally trained in JMP using basic features)

I was playing with the hard to change feature to make a Fractional Whole Plot / Split Plot design to learn how it works. I was following along with an example from Montgomery in his textbook. The algorithm was not generating the same design as the textbook, so I was just trying to set the generator so it would. I'm sure I could just have it make the full factorial and delete the non relevant rows.

However, after I made this post I realized that this custom design feature might not work anyway. It was a non-replicated example with no DoF for error and the fully saturated model does not produce a NPP or pareto since it's using REML. The Montgomery example just uses the graphical outputs for the analysis.

I'll just continue to analyze the WP/SP in the way that I used to with JMP 10yrs ago by analyzing two separate data tables. WP-summarize the table to the whole plots and fit the WP DoF. And then for the SP use the original full data table but only fit the SP DoF in the model. And then just do a practical / graphical analysis with NPP using the blue Lenth's PSE line and the Pareto.

I'm transitioning from Minitab which I'm familiar with on how to do WP/SP there and it will output a separate WP and SP analysis with NPP and Pareto and correct SS in the ANOVA. Which is pretty nice, but it's restrictive on what design's it'll let you pick. Very restrictive actually to usually just a few options. But from what I'm seeing JMP will not do this. However JMP can make much more complex and optimized designs.

The fancy stuff is fascinating to me intellectually, however in practice I tend to just run sequential classical fractional and full factorials. Sometimes those have lines of restrictions due to run order, materials, or setups. Hence my motivation to try out the hard to change stuff in the custom design.

[#4]

Hi @awelsh ,

It can indeed be a bit tricky to generate the exact same design than in a textbook or specific case study.
Depending on your needs (reproducing an analysis and/or creating a design), there might be several workaround helping you improve the reproducibility of your design generation and analysis :

• For teaching, the Custom design platform enables you to fix a random seed so that all students can obtain the same design. See Is it possible to make DOE generation reproducible? 
• I don't know about the specific example you mentioned, but it might still be possible to reproduce the design using a classical fractional factorial design for the split-plot part (to have full control over the generator and aliasing), and replicating this part into several whole plots. If you are interested, you can share the design so that I can try to reproduce it ?
• Another option is to copy-paste the design table from the source (textbook, Excel, ...) into JMP, and set up the correct column properties for Factors. This way, you can reproduce the analysis with the correct degrees of freedom for ANOVA between the whole plots and split-plots parts for example. You can check and test the examples provided here Example of a Split Plot Design Analysis and Example of a Split Plot Experiment. This direct analysis, once the factors are correctly set up, may help you and create a more straightforward analysis instead of two different tables and associated analysis.

Finally, if you are not limited to reproduce exactly a design from litterature, you can also let the Coordinate-Exchange algorithm work, and compare the resulting design with the design obtained in the textbook thanks to the platform Compare Designs. You'll see that design performances should be similar between the two designs.

Hope this complementary answer might help you,

[#5]

Thanks. I do teach, so the random seed fixing could be useful.

If you're curious I'm looking at 14.3 on page 639 of Design and Analysis of Experiments 8th Edition. Such a fantastic textbook. It's a 2^5-1 plasma etching scenario. I like how this one is a graphical analysis example as many of my students are just learning DOE and don't fully understand ANOVA tables. JMP was giving the foldover identify for the ABCDE. Textbook was 1 and JMP was giving the all -1.

[#6]

Hi @awelsh,

Indeed, excellent book and nice case study. To create the same design, you might need several steps (and some manual fine-tuning/specification) :

1. Create a replicated Full Factorial design for the Hard-to-change factors A, B and C, with Run order sorted "Right to Left" (16 experiments): 
   

   DOE(
   	Screening Design,
   	{Add Response( Maximize, "Y", ., ., . ), Add Factor( Continuous, -1, 1, "A", 0 ),
   	Add Factor( Continuous, -1, 1, "B", 0 ), Add Factor( Continuous, -1, 1, "C", 0 ),
   	Set Random Seed( 1751432727 ), Replicates( 1 ), Make Design( 2 ),
   	Simulate Responses( 0 ), Save X Matrix( 0 )}
   );

   It should create the "Whole plot part" of the design, and since the runs are all replicated once with a specific run order, it will create a whole plot structure (2 runs per whole plot) that you can further specify, by adding a column "Random Block" in your table with the right column properties set for the analysis : Design Role = Random Block and Value Order (to sort the value from 1 to 8). 
   You will also have to change the Factor Changes property of the factors A, B and C from "Easy" to "Hard" to be able to run the correct analysis once the complete design will be done.
2. Create the split plot part with a Full Factorial design for factors D and E, with Run Order sorted "Randomize". You might need some trials to have the same corresponding order than in the textbook :
   

   DOE(
   	Screening Design,
   	{Add Response( Maximize, "Y", ., ., . ),
   	Add Factor( Continuous, -1, 1, "D", 0 ),
   	Add Factor( Continuous, -1, 1, "E", 0 ), Set Random Seed( 1907388151 ),
   	Make Design( 1 ), Simulate Responses( 0 ), Save X Matrix( 0 )}
   );

   Once this 4-runs full factorial is done, you can replicate it with the same order using the platform Augment Designs, specifying a "Replicate" augmentation choice with 4 as the number of times to perform each run. You should then obtain the complete "split-plot part" of the design : 
   
3. Join datatables "Whole Plot part" and "Split plot part" by row number :
   

   // → Data Table( "Plasma Etching Tools Design" )
   Data Table( "1_Whole Plot part" ) << Join(
   	With( Data Table( "2_Split Plot part" ) ),
   	Select( :Pattern, :Whole Plots, :A, :B, :C ),
   	SelectWith( :D, :E, :Y ),
   	By Row Number,
   	Output Table( "Plasma Etching Tools Design" )
   );
   

   This last action should give you the same design as in the textbook. I have attached the different tables used and the last table with response values if you want to reproduce the design creation and/or analysis.

On a side note and "practical" consideration, using the Custom Design platform directly enables to create a design with same performances (in terms of power and prediction variance) :

But a different aliasing structure (avoiding complete confounding):

Here is how to generate it in JMP (datatable for Custom design is also attached):

DOE(
	Custom Design,
	{Add Response( Maximize, "Y", ., ., . ), Add Factor( Continuous, -1, 1, "A", 1 ),
	Add Factor( Continuous, -1, 1, "B", 1 ), Add Factor( Continuous, -1, 1, "C", 1 ),
	Add Factor( Continuous, -1, 1, "D", 0 ), Add Factor( Continuous, -1, 1, "E", 0 ),
	Set Random Seed( 1361270547 ), Number of Starts( 29927 ), Add Term( {1, 0} ),
	Add Term( {1, 1} ), Add Term( {2, 1} ), Add Term( {3, 1} ), Add Term( {4, 1} ),
	Add Term( {5, 1} ), Add Alias Term( {1, 1}, {2, 1} ),
	Add Alias Term( {1, 1}, {3, 1} ), Add Alias Term( {1, 1}, {4, 1} ),
	Add Alias Term( {1, 1}, {5, 1} ), Add Alias Term( {2, 1}, {3, 1} ),
	Add Alias Term( {2, 1}, {4, 1} ), Add Alias Term( {2, 1}, {5, 1} ),
	Add Alias Term( {3, 1}, {4, 1} ), Add Alias Term( {3, 1}, {5, 1} ),
	Add Alias Term( {4, 1}, {5, 1} ), Set N Whole Plots( 8 ), Set Sample Size( 16 ),
	Simulate Responses( 0 ), Save X Matrix( 0 ), Make Design}
);

Hope this response may help you,