Custom DOE platform

Question

I have 5 factors and after selecting 2 factor interactions of interest it seems I need 16 runs.   My questions are as follows:

How can I quickly see the resolution in the custom platform..?  I can see the alias table but not sure how to interpret the top line of effects.  I am only interested main effects + 2 factor interactions.

Now the tricky bit.  I have a budget of 25 runs not 16.  So I want to know the best way to add runs in the most efficient way.  I could add replicates or replicates with wider factor set points, as well as a 2 to 3 centrepoints.  When I tried the augment design option I only got 32 runs with 2 replicates (i.e. not a lot of help ).

If in the custom platform I choose user defined 25 runs instead of the default 16 runs, how is JMP determining the remaining runs..?  Also if I select D or I-optimal from the custom platform is this then changing these additional runs in some way.?

outlier · Answer

Thanks Jeff.  Finally I upgraded to JMP 10 and ran the experiment.

bradleyjones · Answer

The 16 run D-optimal design for fitting the main effects are all the 2 factor interactions is the Resolution V fractional factorial design. You can convince yourself of this by adding the 3 factor interactions to the Alias Terms. Then you will see that each two-factor interaction is confounded with a three-factor interaction. In this case there is only one strength 4 orthogonal array (Resolution V design) and the custom designer finds this design. However, in general, there may be many designs that are orthogonal for the main effects but have other statistical properties that are different.

To your question about what to do with 25 runs. I would suggest that you create a 24 run design for the 5 main effects and 10 two-factor interactions saving one run for verificaiton of your model. I would ask the Custom Designer to create 4 replicate runs. These runs will be chosen to maximize the D-efficiency of the design subject to the restriction that there are 4 replicates. This will give you 4 degrees of freedom for pure error. You will also have 4 lack-of-fit degrees of freedom. These will prove useful if it turns out that some three factor interaction happens to be large. JMP's Fit Model will automatically do a Lack of Fit test. If that test is significant, then you can use Stepwise to find a higher order interaction that may be causative.

The resulting design I found on doing this is 94.29% D-efficient for the model with all the two-factor interactions. The VIFs are all 1.125. For the main effects model the design is 98% D-efficient and the maximum VIF is 1.05.

This design is not the most D-efficient design possible for 24 runs and a two-factor interactions model but it has two other capabilities that the most D-efficient design does not have. Those are the 4 replicates and the ability to do a Lack-of-Fit test.

Here is the URL for a blog that I wrote on individual run replication:

New in JMP 10 for experiment design

Here is the script to generate the design I described.

DOE(Custom Design,{Add Response(Maximize,"y",.,.,.),

Add Factor(Continuous,-1,1,"X1",0),

Add Factor(Continuous,-1,1,"X2",0),

Add Factor(Continuous,-1,1,"X3",0),

Add Factor(Continuous,-1,1,"X4",0),

Add Factor(Continuous,-1,1,"X5",0),Set Random Seed(5735943),

Number of Starts(10000), 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 Term({1,1},{2,1}),Add Term({1,1},{3,1}),

Add Term({1,1},{4,1}),Add Term({1,1},{5,1}),

Add Term({2,1},{3,1}),Add Term({2,1},{4,1}),

Add Term({2,1},{5,1}),Add Term({3,1},{4,1}),

Add Term({3,1},{5,1}),Add Term({4,1},{5,1}),Replicates(4),

Set Sample Size(24)}

);

outlier · Answer

Thanks for the inputs.  I actually have 5 continuous factors and plan to do 1 screening experiment (25 runs) and then probably 1 RSM (the 2 biggest factors 5 levels).

If I use the screening design platform I can choose fractional factorial resolution V design with 16 runs.  If I use the custom design platform and select all 2nd order interactions it is suggesting 32 runs as default and 16 runs as minimum.  The 16 minimum runs from the custom design platform also appear to have no aliaising (I am interpreting the alias matrix = resolution V but it is not explicit).  As the custom design is defaulting to D optimal (100% D efficient), should I expect the same design as given by the screening design platform (i.e. the 16 minimum run design in the custom design equal to the 16 run resolution V design in the screening design platform).  ?

Assuming this is true, if I use the custom design platform and select "user defined" 25 runs instead of 16 (minimum) I get D efficiency 94.5%.  As the main objective is screening, is this the most likely optimal design?  The alternative is for me to stick with 16 runs (which I think is already resolution V) and add other runs ad hoc.  In the past (when I had less factors) I have typically replicated the corners and centrepoints (to confirm robustness, and I worry that if responses are small compared to the noise it might be hard to estimate sensitivity of the factors).  That could equate to >~5 replicates to estimate the error (assuming the error is the same for each run).   But with 5 factors it is still hard for me to choose replicates in an optimal way.  I guess the question is whether D optimal is what I really want, or is optimal in only one dimension.