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Aug 10, 2013 8:38 AM
(1720 views)

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.?

4 REPLIES

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Aug 13, 2013 4:04 PM
(1351 views)

Hi,

I posed your question to Bradley Jones who developed the Custom Design platform and this is his response:

There many questions here but I cannot be quite sure of an answer unless I know whether you have categorical factors with more than two levels. I suspect you do because otherwise with 5 factors each at two-level, the Custom Designer would not have 16 runs as the default.

If you do have factors with more than two levels then the question of resolution is not relevant because resolution is a concept that only applies to designs having all factors at two-levels. So, resolution is an idea with limited applicability.

What is more generally useful is knowing how many effects you can estimate with a given number of runs and whether these effects may be biased by the presence of active effects that are not in your model.

If you have 25 runs, you may well have enough runs to estimate all the two-factor interactions even though you are only interested in two of them. This would make your design like a resolution V design even if you have categorical factors with more than two levels. I would recommend adding all the two factor interactions to your original model to see if 25 runs is sufficient to fit them all.

It is always useful to have replicate observations because that allows you to estimate the error variance without having the correct model. It also can allow you to do a test of lack of fit.

My personal preference is to add terms to my model before replicating observations because I feel comfortable estimating the error variance using the extra runs not being used to estimate the model terms. Also, you need to have at least 5 or more replicates before you can get a decent pure error estimate of the variance. I view this as a substantial investment just to estimate one parameter.

If all your factors are continuous, then 25 runs is enough to estimate the full quadratic model. That is, you can estimate all the main effects, two factor interactions and quadratic effects. With that budget, I would run an I-optimal RSM design that you can get by clicking the RSM button.

-Jeff

-Jeff

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Aug 15, 2013 5:25 AM
(1351 views)

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.

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Aug 15, 2013 8:32 AM
(1351 views)

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)}

);

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Sep 29, 2013 7:17 AM
(1351 views)

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