# Number of centerpoints

Six Sigma – iSixSigma Forums Old Forums General Number of centerpoints

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• #30613

Stefan Szemkus
Participant

A question which always accures when teaching or applying a design with centerpoints is: How often do I have to repeat the centerpoint?
I tried to find some books or articles about how to chose the right number of Centerpoints in a 2^k factorial design – without success.
Any ideas how to approach?
Thanks!
Stefan

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#79907

mcleod
Member

Stefan,
What I do during experimental design is to get the right mix between the number of replicates and the number of center points to improve the power of my design.  I use a good DOE program to help me play that “what-if” game.  The center points help determine if the relationship when going from your low setting to your high setting is linear or not.  Evaluation using center points may in fact show that this relationship exhibits curvature and whether or not the curvature is siginificant.
Design and Analysis of Experiments by Montgomery (5th edition p. 275) has an excellent list that sums up the use of center points but does not address the # of points to use.
If you are interested in the DOE program I referred to, you can email me at [email protected] and I will share that information with you.
I know I didn’t exactly answer your question, but I hope I least got you headed in the right direction.
Scott

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#79908

mcleod
Member

Correction, my email address is [email protected].
Scott

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#79918

Robert Butler
Participant

The purpose of any replication in a design is to develop an estimate of the error.  The purpose of a centerpoint in an otherwise two level design is to permit the detection of curvilinear behavior.  Relpication of the centerpoint allows the investigator to address both of these questions at once.
If you are severely constrained with respect to resources and time, a simple replication of the center point ( i.e. the center point is run twice) will permit an investigation of curvilinear behavior (via residual analysis) and an estimate of error.  If you wish to improve your estimate of error you may increase the number of replicates run on the center, however, you need to understand the assumption that you are making if you take this course of action.
Concentrating all of your replicates at the center means that you are assuming that the variance across the experimental space is constant.  If it isn’t constant, the estimate of error that you will get from running only multiple replicates on the center will probably be an underestimate of the variance of the space and you will wind up declaring effects significant when they really are not.
Thus, the choice of the number of replicates of the centerpoint is driven by the aims of your experimental effort and there is really no such thing as the right number of centerpoint replicates.  If you are looking to conserve resources and time then one or more replicates on only the centerpoint makes sense.  If you have a little more latitude with respect to your investigation ,centerpoint replication complimented with replication of other points in the design space will provide you with the same check of curvilinear behavior and a more realistic estimate of experimental error.

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#79919

Erik L
Participant

An additional piece of insight would be through integrating the use of center points with blocking techniques.  Plots of the center points across the blocking factor could help with increasing the degree of belief in either the estimate of variability within the design space and repeatability of the average response across a temporal spectrum (e.g. insurance that there were not ‘lurking variables’ influencing the results of any one particular set of runs).
Regards,
Erik

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