Center Points in DOE Design

 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.

  No I don’t. 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.

Anonymous: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.We’ve done this successfully quite a few times where the experimental setup was very expensive and time consuming.Cheers, BTDT