Center Points in DOE Design
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September 19, 2005 at 2:34 pm #40736
Hi,
Does any one how many Center Points is recomended for a 2^3 Design , and Why?? (3 Replicates), no text variables.
Thank you vey much!!!0September 19, 2005 at 3:08 pm #127086Salvador,
6 Center Points0September 19, 2005 at 7:58 pm #127117
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.If you are going to run a 2^3 design with all continuous variables the most efficient use of your time would be to run two center points for a total of 10 experiments. Assuming the usual precautions of randomization you should analyze the results. The two center points give you replication as well as a test for possible curvilinear effects. You can throw in more if you wish (for better estimates of error) but the whole point of DOE is minimum work for maximum effort. Three full replicates of an entire design is a poor allocation of time and effort.
The two center points in addition to the usual terms from the basic 8 point design should give you a pretty good understanding of the behavior of the 3 variables of interest.0February 23, 2006 at 7:52 pm #134195
AnonymousParticipant@Anonymous Include @Anonymous in your post and this person will
be notified via email.Hi Robert,
Do you see any value in including a center point column in the model?
In Minitab you have the option of including or excluding the center point column in the model, with the default set to include. I cannot envision ever including this in the model. Minitab provides a report on curvature in ANOVA/Lack of Fit making the inclusion of the center point column to detect curvature unnecessary.
If the curvature is significant, keeping the center point column in the model will give you an inflated Rsquare value and the residuals may not clearly show the curvature.
Your opinion (and those of other DOE experts) would be greatly appreciated.0February 23, 2006 at 10:32 pm #134209
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.No I dont. The value of the replicated center points is to give you the ability to compute pure error and thus, by subtraction, lack of fit and to give you a visual indication, via the residual plots, of the need for investigating curvilinear effects. Since the center points will not allow you to identify the variable(s) contributing to the curvilinear behavior you can put in the square of any one of the model terms and have it enter the final regression as significant. Under these circumstances inclusion of the squared term does nothing more than make your residual plots look nice and, as you noted, inflate your R2.
0February 23, 2006 at 10:42 pm #134211
AnonymousParticipant@Anonymous Include @Anonymous in your post and this person will
be notified via email.Thanks Robert!
Could one argue that the inflated Rsquare is a “potential” Rsquare that may be achieved should you upgrade to an RSM design?0February 23, 2006 at 10:57 pm #134213Anonymous:Rats! Thwarted by Robert Butler again, I type too slowly.This extra feature of centre points makes it desirable to add them if you can afford a few more runs to your design.If you had a screening design using 8 runs with 7 factors, you can not get a good measure of the noise in the measurement because you have no replication, but adding only two to three centre points gets you a good measure of the noise without having to add a second replicate of eight additional runs. This gives you the SS(error) and, subsequently a way of measuring F for each factor.Weve done this successfully quite a few times where the experimental setup was very expensive and time consuming.Cheers, BTDT
0February 23, 2006 at 11:04 pm #134214
AnonymousParticipant@Anonymous Include @Anonymous in your post and this person will
be notified via email.Hi BTDT,
Thanks for the comment. My question was not “Why do we use center points?”, but Given that you have center points, what benefit is there in including the center point column (i.e. A*A) in the model? The default in Minitab is to include this term in the model.
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