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A_Huber
Level I

Add levels to an augmented design

Hi, I would like to adopt an existing design. The current design has four factors with two levels. Now I would like to add at least one or two levels to two factors.
Is it possible to use augment design or is there another way? Until now I found no answer to adopt the design.
Best regards, Andre!

 

 

 

3 REPLIES 3
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statman
Level VII

Re: Add levels to an augmented design

Andre, pardon me, but I am confused by your wording.  Do you mean adapt or adopt?

 

I have some questions/comments:

1. What was the 4 factor design?  A full factorial or a fraction?

2. Are the factors continuous or categorical?

3. Assuming you analyzed the first experiment, it seems you learned 2 of those factors were "most interesting" and the remainder of the terms were insignificant (So no interactions were significant)?

4. For the 2 factors that were "most interesting" you want to experiment at levels different from the first experiment.  Do you want to move the experiment space or do you want to quantify quadratic and cubic terms in the model?

 

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A_Huber
Level I

Re: Add levels to an augmented design

Hi Steatman
 
sorry, I mean adapt.
 

Regarding to your questions:
I have some questions/comments:
1. What was the 4 factor design?  A full factorial or a fraction?
fraction design
2. Are the factors continuous or categorical?
The factors are continuous
3. Assuming you analyzed the first experiment, it seems you learned 2 of those factors were "most interesting" and the remainder of the terms were insignificant (So no interactions were significant)?
Yes I 2 factors are "most interesting"
4. For the 2 factors that were "most interesting" you want to experiment at levels different from the first

For the 2 factors that were "most interesting" you want to experiment at levels different from the first experiment.  Do you want to move the experiment space or do you want to quantify quadratic and cubic terms in the model?

For the factors I used the max. and min. value. Now I would like to add some factors in between. So I want to quantify quadratic and cubic terms in the model. 

 

An additional question:

What if, I assume that all four factors (with two levels) seem to be important (interaction) after the evaluation of the fraction design. What would be the best approach to quantify quadratic and cubs terms? It is not possible to set the levels at any value. There is a list with possible values. 

Highlighted
statman
Level VII

Re: Add levels to an augmented design

"For the factors I used the max. and min. value. Now I would like to add some factors in between. So I want to quantify quadratic and cubic terms in the model."

 

I assume you mean levels?  Are you really wanting to fit a quadratic or cubic model or are you looking for the best level within the extremes of the first experiment?  If the factors were significant at the extremes, this implies there is a linear relationship.  You can certainly add levels inside the space.  Thoughts about your sequence of experiments:

You used a 2-level, fractional factorial (you did not provide the resolution of this design) and found 2 factors that are most interesting.  There is certainly some aliasing, but I will assume the results "make sense" or are similar to your predicted results.  But, you did not anticipate non-linear relationships?  Now you do?  Why? If you had anticipated non-linear relationships, adding center points to the design would have been useful, and still may be an interesting test.  I don't recall you discussing any strategy to handle noise?  Adding points to the existing data set would confound block effect with the additional treatments.

 

Regarding:

"What if, I assume that all four factors (with two levels) seem to be important (interaction) after the evaluation of the fraction design. What would be the best approach to quantify quadratic and cubs terms? It is not possible to set the levels at any value. There is a list with possible values."

I'm not sure I understand.  If all 4 factors were deemed important, this does not mean the interactions are?  But, you can certainly restrict the design space using JMP's custom design platform.  Your strategy of using a fractional factorial to create a large design space and then iterating to understand more complex relationships inside this space is sound.

Again, I'm not sure you really want the non-linear terms (especially cubic) or you just want to find optimum levels?

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