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Oct 18, 2017 9:57 AM
(1911 views)

I plan to run a DOE with 7 continuous factors, 1 categorical factor, 2 blocks.

The goal is both screening and optimization.

I want to use DSD, but encounter the following situations/questions:

1. Five of the continuous factors may have some sort of interactions. Will this limit the use of DSD?

2. Four of the five factor are three-level, but not equally apart (say 100, 120, 200). How to handle this?

3. One continuous factor has two levels only due to sample availability. How to handle it?

4. For all the continuous factors, I try to control the levels to be as far apart as possible, but it is impractical to get the max and min. Will this be a problem?

5. If I try to add a few center points (empty row), should I try to keep the original fall over nature of the design?

Thanks!

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Here are my thoughts on your three questions (your numbering scheme):

2. If you first design is a screening design, generally you are trying to find the required information for the least expenditure of resources. DSDs do pretty much rely on equally spaced levels so the design has the proper 'fold over' properties. With that many factors with this non-equally spaced characteristic have you considered running a 2 level (forget for now running the 'middle' level) D-optimal design with an emphasis on screening (that is keeping the number of runs minimal)? If you have specific knowledge of suspected two factor interactions that you would like to estimate, these can be included in the model specification window. Then the design will support their estimation.

3. If you go the D-optimal route suggested in 2. above, that solves this problem.

4. I'm not 100% sure what you mean here...my interpretation of your issue and reaction is just design the experiment at the levels you intend to actually conduct the experiment...not some arbitrarily chose wider levels.

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Re: Situations/questions in using DSD

For starters I think you are trying to force one single experiment to satisfy two very different goals...screening and optimization. These two goals generally lead to not ONE experiment but a minimum of two experiments using sequential experimental design.

DSD's are very much in the screening category, the idea being to efficiently identify active factors, relying on effect sparsity and effect heredity as key enablers. With a suspected 5 of your 7 continuous factors with active interactions this isn't exactly an effect sparse system if your suspicions are correct. My general recommendation would be to first establish active factors using a 'by the book' DSD, not bothering with replicates, center points, etc. Hopefully you are running JMP version 13 so you can take advantage of the new two stage model fitting workflow.

Then take what you learn about active factors and effects, and then running some sort of optimal design in JMP's custom design platform. This way you can specifiy exact model effects that are likely, based on what you learned in the DSD portion of your design. Interactions, quadratics, if needed, etc. From here use JMP's prediction profiler and simulator to find your optimal factor settings.

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Re: Situations/questions in using DSD

I like and will follow the "road map" you draw.

In the mean time could you address my question 2, 3 and 4 (below)? They have puzzled me for a while.

2. Four of the five factor are three-level, but not equally apart (say 100, 120, 200). How to handle this?

3. One continuous factor has two levels only due to sample availability. How to handle it?

4. For all the continuous factors, I try to control the levels to be as far apart as possible, but it is impractical to get the max and min. Will this be a problem?

Thanks!

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Here are my thoughts on your three questions (your numbering scheme):

2. If you first design is a screening design, generally you are trying to find the required information for the least expenditure of resources. DSDs do pretty much rely on equally spaced levels so the design has the proper 'fold over' properties. With that many factors with this non-equally spaced characteristic have you considered running a 2 level (forget for now running the 'middle' level) D-optimal design with an emphasis on screening (that is keeping the number of runs minimal)? If you have specific knowledge of suspected two factor interactions that you would like to estimate, these can be included in the model specification window. Then the design will support their estimation.

3. If you go the D-optimal route suggested in 2. above, that solves this problem.

4. I'm not 100% sure what you mean here...my interpretation of your issue and reaction is just design the experiment at the levels you intend to actually conduct the experiment...not some arbitrarily chose wider levels.

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Re: Situations/questions in using DSD

I assume you suggest I run a 2-level D-optimal custom design for screening to save resource and address problem 2 and 3, right?

What I mean in problem 4 is that for a continuous factor, often we can not practically test at the max and min values. Will this be a problem? For example, for a mechanical system, the input load ranges from -1000 Newton to +1000 Newton. But the test equipment can only generates min = 500 N and max = +500 N.

Thanks.

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Re: Situations/questions in using DSD

Yes, with my comments on 2. and 3. above, I'm suggesting considering a D - optimal, sequential design of experiments approach.

Often times we have constraints on the levels wrt to min and max that can be chosen for any given factor. Probably the biggest worry wrt to having to deal with level constraints is if the levels which are eventually run are far enough apart wrt to the response signal being able to rise above all the sources of noise and error that influence the response. If you have no idea...perhaps a small one factor at a time experiement for that single factor with a few replicates can give you some idea?

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