# central composite designs and Box-Behnken designs

Six Sigma – iSixSigma Forums Old Forums General central composite designs and Box-Behnken designs

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• #49838

vikranth
Member

Dear all,
When you are doing DOE using response surface methods, how do you chose between Central Composite designs and Box-Behnken designs?  Please eloberate.
Please advise if there is any good book which talks about DOE in detail.(something on the lines of DOE for dummies).
Best Regards,
Vikranth.

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#171074

George4
Participant

A good question for real experts

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#171086

Vallee
Participant

Clearly stated, I have not used these tools in DOE before; however it looks similar to matrix and vector rotation I did (many) years ago in factor analysis. The designs on which way to rotate your matrix takes a lot of practice and conceptual understanding. Below is a simple link with examples of your question but I can not validate its correctness. Post a question to Robert Butler and he may be able to help you.
http://www-rohan.sdsu.edu/doc/matlab/toolbox/stats/doe5.html
HF Chris Vallee

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#171089

Robert Butler
Participant

Box-Behnken designs are much more efficient that 3**k factorial designs.  They do not contain any corner points in the design space which may or may not be an advantage.  They are nearly orthogonal Res V designs and they estimate all linear effects, all quadratic effects, and all linear 2 way interactions.  The last is probably their biggest drawback  if you dont want all 2 ways there isnt any easy way to reduce the design to take this desire into account.  As with most designs the slight non-orthogonality isnt an issue.

Central composite designs are much more flexible with respect to the issue of 2 way interactions.  They are comprised of a standard 2**k factorial, center points, and axial points.  Because their core is a 2**k factorial you have the option of running a full factorial at the center or, if you dont desire information on some or all of the 2 way interactions you can run the core as a fractional factorial design.  What this means is that, if all of the 2way interactions are not of interest, the CCD will be more efficient than the Box-Behnken.

The axial (sometimes called star points) are outside of the bounds of the design space box defined by the factorial part of the design.  They are chosen to produce rotatability.  All this means is that the predicted response is capable of being estimated with equal variance regardless of the direction from the center of the design space.  From the standpoint of practice this means the axial points will correspond to your design space minimum and maximum and the min/max points of the factorial will be something greater or less than the overall minimum and maximum.  CCDs are also slightly non-orthogonal but again, it doesnt matter that much.

If you cant run factor levels at 5 distinct values (axial+, 1, 0, -1, axial-) then you can collapse the axial values to 1 and run a central composite face design.  This design wont have rotatability and will have a degree less orthogonality for the quadratic terms but, again, the issue is more of a theoretical concern than a practical one.

As for books, give the breadth of what you are asking there isnt any one single source of which Im aware.  One book which I think does a very good job of describing the various design options is Understanding Industrial Designed Experiments 4th edition  Schmidt and Launsby.  Chapter 3 in particular is probably the best general overview of the field Ive read.

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#171099

vikranth
Member

Thanks Mr.Butler.
It is very nice of you to answer the question.
Thanks for the rest of the people who have actively participated in the discussion..
Regards,
Vikranth.

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