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- How to add "center or axial point" to fractional factorial design?

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May 4, 2016 6:44 AM
(5782 views)

Hi all,

I am trying to create a fractional factorial design for seven factors and one response. But I would also like to add "center or axial point" to the design to account for quadratic effect. I use quotation mark for the "center or axial point" because I don't know what to call these points. Essential these points that I want to add are center of one or two factor instead of all the factors.

I've tried CCD and screening design option in jmp, but couldn't find the design list I need.

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A couple of approaches that you can use for this scenario.

1.) You could use the screening design platform if you are looking for a classical fractional factorial and generate that baseline design That experiment can then be augmented where you could specify the polynomial terms in the model of interest and thus drive the center point settings on those treatment combinations.

2.) You could use the custom design platform and drive the experiment you are looking for directly utilizing the model again to specify the polynomial terms of interest.

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You could also use the Definitive Screening Design found under DOE > Definitive Screening Design after JMP11. The axial points that you are after are generally part of the response surface type of model which would require a lot of resources to run on 7 factors. The DSD is probably a better choice for what you are doing as it would only take around 17-18 runs depending on the set up and has center points for the overall design and each factor built in. For a fractional factorial that would be the equivalent resource requirement to a resolution IV design with 1-2 center points, but the fractional factorial wouldn't provide any curvature information.

There is a nice webinar on the topic here: http://www.jmp.com/en_gb/events/ondemand/mastering-jmp/using-definitive-screening-designs-to-get-mor...

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A couple of approaches that you can use for this scenario.

1.) You could use the screening design platform if you are looking for a classical fractional factorial and generate that baseline design That experiment can then be augmented where you could specify the polynomial terms in the model of interest and thus drive the center point settings on those treatment combinations.

2.) You could use the custom design platform and drive the experiment you are looking for directly utilizing the model again to specify the polynomial terms of interest.

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You could also use the Definitive Screening Design found under DOE > Definitive Screening Design after JMP11. The axial points that you are after are generally part of the response surface type of model which would require a lot of resources to run on 7 factors. The DSD is probably a better choice for what you are doing as it would only take around 17-18 runs depending on the set up and has center points for the overall design and each factor built in. For a fractional factorial that would be the equivalent resource requirement to a resolution IV design with 1-2 center points, but the fractional factorial wouldn't provide any curvature information.

There is a nice webinar on the topic here: http://www.jmp.com/en_gb/events/ondemand/mastering-jmp/using-definitive-screening-designs-to-get-mor...

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Re: How to add "center or axial point" to fractional factorial design?

You are right, Michael. A fractional factorial design with a resolution of V will need 64 runs in my case. DSD is better in term of the time required.

One stupid question, why DSD doesn't allow me to add replicates?

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Re: How to add "center or axial point" to fractional factorial design?

That depends - there isn't anything that is stoping you from running the design platform twice (randomizing the order of each replicate separately) and then concatenating the data tables together. JMP will treat the data the same and you'd effectively have a replicate. You might want to add an additional center point as well, but I would check the design evaluation to be sure.

If you just wanted to add some additional center points to check repeatability, you can use the second option in the blocking part of the DSD work flow. Just treat the number of blocks as the number of additional center points you want. JMP will add an additional center point for each "block" you specify.

On why there isn't a formal "replicates" option like in the other design platform. I'm not sure. It may be that, since the DSD is a "screening design," the primary focus is screening and not predictive modeling and they didn't think it was necessary. Not to say you can't do some modeling with DSD's - See Brad Jones' paper from JMP Discovery 2015 - just that the primary goal is a thorough and efficient screen. But that's just a guess.

M

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Re: How to add "center or axial point" to fractional factorial design?

DSD is certainly an efficient approach and one I would certainly give serious consideration to. My response was directed toward the specific details in the question regarding polynomials on only 2 of the 7 variables (factors). This post hits the heart of the benefits of the JMP Custom Design platform which provides the most flexibility so the user can customize a design to fit the problem rather than be subject to forcing one's problem into a particular design type from a catalog.

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Re: How to add "center or axial point" to fractional factorial design?

Thanks for your further reply, Lou. I tried your 2nd solution for my problem. But I am new to JMP, so I am trying to be careful using custom design.

Here is what I did. I add one response to maximize it and seven continuous factors. In my model I add RSM to account for 1st and 2nd order interaction.

Because I want a modified fractional factorial design with a resolution of V, which should have 64 runs. So I specified here the runs to be 64 and get my design table.

Then my questions are

1) Will this design process solve my problem as a modified fractional factorial design with the "axial points" I want?

2) I don't need center points for my design, but I do get center points in this custom design table.

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Re: How to add "center or axial point" to fractional factorial design?

I guess my question back to you would be does your budget allow for running 64 experiments? If so, then the design approach that you shared is certainly a viable one. All of your main effects, two-way interactions and polynomial terms are well covered by specifying the RSM model that you chose. If you look at the design evaluation you will see that this design is very powerful. Having said that, most experimenters do not have a budget for that many experiments and rely on effect sparsity and effect heredity principles to try and delineate understanding by running fewer experiments. In fact the default number of runs for a RSM model with 7 continuous factors with the custom designer is 42 runs so 64 is only going to give you more power. A Definitive Screening Design only requires 17 runs and would be much more cost effective but may need to be augmented depending upon the number of active terms that surface. I never worry too much about this since I always know I can augment additional experiments to clarify any confusion. Most experimenters don't have the budget for 64 experiments, but if that is not an issue the design you propose would be quite effective.

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Re: How to add "center or axial point" to fractional factorial design?

Definitive screening design sounds a better option since I also want to add one replicate, which will make the design over my budget.

Do you have any comment on how to add replicate to definitive screening design in JMP? Thanks.

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Re: How to add "center or axial point" to fractional factorial design?

Replicate can be used to mean two different things. Would you like to replicate the entire experiment or just replicate a treatment combination (row).

If the latter is the case then I would just manually add a row at the end of the DSD generated of a replicate run at the end of the JMP table.