How to create a fractional factorial design?

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Uwe Schumann 2019-6-12

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https://ww2.mathworks.cn/matlabcentral/answers/466632-how-to-create-a-fractional-factorial-design

评论： Uwe Schumann 2019-6-12

采纳的回答： James Browne

Hello MatLab team,

I want to create a fractional design.

I'm using <fracfact>.

This command allways generates full factorial design when using

gen=fracfactgen('a b c d e f',4,4) and then

[design, con]=fracfact(gen).

What am I doing wrong? I need the fractional factorial design.

Thank you for your help!

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Answer 1

James Browne 2019-6-12

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编辑：James Browne 2019-6-12

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Greetings,

I ran your code:

gen = fracfactgen('a b c d e f',4,4)  
[design, con] = fracfact(gen)

And, based on the output, I would say that you are not doing anything wrong, you are getting a fractional factoral design. First of all, if you have confounding, by definition, you are not running a full factorial experiment. Secondly, recall that full factorial designs have 2^k runs in them, where k is the number of factors. You have 6 factors in your design so a full factorial design would have 64 runs in it which translates to 64 rows in the design matrix.

The output of your code shows a design matrix with only 16 rows so you are definitely generating a fractional factorial design! It has been a long time since I studied design of experiments so I cant say much more than that without dusting off the ol' textbook.

Hope that helps~

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Uwe Schumann 2019-6-12

Hi James,

thank you for the quick answer.

My understanding of fracfactgen was a bit different: I believe that the commands that I used (gen=fracfactgen('a b c d e f',4,4 ) and [design, con]=fracfact(gen) ) create a matrix "design" which contains the variation of four parameters (so the length of 16 corresponds to a full factorial design). Two additional columns are shown in "design" which contain two versions of confounding.

In the mean time I think I have found out how to proceed with the result of fracfact(gen).

I think, now I have to choose one confounding column in the "design" matrix and filter out all lines which show the same value in that confounding column (it does not matter if I choose -1 or 1). Then the remaining lines are my fractional design of 2^k-1.

Could that be right?

Can you recommend some literature for me?

And (only if you want) can you tell what your application was for DoE? - Did you have a practical use for the method?

Did you use MatLab?

Thank's alot!

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