Problem with Split-Split-Plot Design

Question

Dear JMPers! Currently I'm trying to set up a design for one of our customers. The right design is actually not that hard to find. We are interested in 3 factors: - X1: categorical 4 levels/ very-hard-to-change - X2: categorical 4 levels/ hard-to-change - X3: continuous with some restrictions depending on which level of B is used The model of interest is using the 2-factor-interactions and a quadratic effect for X3. Trying to do this in the custom designer the resulting design is quite strange to me. The hard-to-change- and very-hard-to-change-factors seem to be more or less randomized. In this case the first whole plot is ok for X1 the second one mixes multiple levels of X1. Same applies for most of the subplots and X2. Now I am wondering if I am doing it wrong or if the optimal algorithm has a problem with categorical data + the restrictions of the continuous variable or something like that? Here is what I am using: DOE( Custom Design, {Add Response( Maximize, "Y", ., ., . ), Add Factor( Categorical, {"L1", "L2", "L3", "L4"}, "X1", 2 ), Add Factor( Categorical, {"L1", "L2", "L3", "L4"}, "X2", 1 ), Add Factor( Continuous, -1, 1, "X3", 0 ), Set Random Seed( 243011 ), Number of Starts( 2 ), Add Term( {1, 0} ), Add Term( {1, 1} ), Add Term( {2, 1} ), Add Term( {3, 1} ), Add Term( {1, 1}, {2, 1} ), Add Term( {1, 1}, {3, 1} ), Add Term( {2, 1}, {3, 1} ), Add Term( {3, 2} ), Set N Whole Plots( 6 ), Set N Subplots( 17 ), Set Sample Size( 51 ), Disallowed Combinations( X2 == 1 & (X3 >= -1 & X3 <= 0.5) | X2 == 2 & (X3 >= 0 & X3 <= 1) | X2 == 3 & (X3 >= -0.25 & X3 <= 1) | X2 == 3 & (X3 >= -1 & X3 <= -0.5) ), Make Design} ); Thanks for any advice, Sebastian

Ryan_Lekivetz · Answer

Hi Sebastian,

Sorry you're running across this issue. There can be a problem with disallowed combinations and split-plots, which is why you’re getting the strange results. We're hoping to have this fixed in a future version of JMP.

I would highly recommend increasing the number of whole plots and subplots – even in the unconstrained case, there will likely be issues with fitting the model with the X1*X2 interaction. If you try a few simulate responses, you'll see the issue.

To get around the disallowed combinations issue, two possibilities you could try and compare the designs:

1) Create the unconstrained design, and create a formula that scales X3 based on the level of X2

2) Create the unconstrained design, keep the data table open and the active table

* go back to a new Custom Design, and enter X1 & X2 as covariates
* Add X3 as a continuous
* Add your model effects (if you didn't increase whole plots/sub plots, you'll probably need X1*X2 as "If Possible")
* Enter the disallowed combinations that you have above
* Pick the number of runs the same as your table
* Copy the X3 column (from Make Table if you wish) into the original data table.

Hope something there works for you!

Cheers,

Ryan

louv · Answer

Sebastian,

I ran it without the disallowed combinations based on your input about the desired model. All whole plots have one level X1. Perhaps the disallowed combinations are playing into it.

DOE(

Custom Design,

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

Add Factor( Categorical, {"L1", "L2", "L3", "L4"}, "X1", 2 ),

Add Factor( Categorical, {"L1", "L2", "L3", "L4"}, "X2", 1 ),

Add Factor( Continuous, -1, 1, "X3", 0 ), Set Random Seed( 280073349 ),

Number of Starts( 105 ), Add Term( {1, 0} ), Add Term( {1, 1} ),

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

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

Set N Whole Plots( 6 ), Set N Subplots( 17 ), Set Sample Size( 51 ), Make Design

}

)