How to add a group of center points to a 2-level data set

[#1]

Hi all.

I have an existing data set that needs to be analyzed, but the existing set is comprised of a 2-level matrix and a set of three "centerpoints". I'd like to take advantage of the reproducibility information from the three centerpoints, but just throwing them in with the experimental matrix unbalances the analysis (there are a couple categorical factors in the original matrix).

Is there a valid way to do this?

Thanks

[#2]

Although unbalanced designs are not ideal, they can still be analyzed. Just put the data with the experimental results and analyze. 

Other possible options:

Ignore the replicates, reducing the sample size. But sample size is actually more important than balance. So this is not a good option.

Perform additional experiments to get a balanced design. This route makes sense, if it is possible and the process has not changed from the first set of trials to the new set. You can add the additional runs by using the Augment Design option in JMP.

[#3]

The experiments were done a few years back, so it's not really possible to do more to fill out the matrix to get a nice, balanced design. If I just dump the 3 center point runs in I still get a decipherable analysis, but the inclusion of a center point setting on the categorical factors creates a 3rd level in the analysis that doesn't have sufficient information around it (i.e. the only runs with the center point categorical has everything else at the center setting too).

I was hoping I could take the reproducibility information from the group of 3 center point runs and feed that into the analysis of the 2-level matrix design in an effort to improve the results of the analysis.

[#4]

My comments.  There isn't enough information on your experiment provided, but here are some thoughts. How can you have center points with categorical factors?  AFAIK, center points require all factors be continuous and for the test for curvature the all quadratic terms are confounded.  (Note: I have seen folks create surrogate center points with a couple of categorical factors, but that usually is just setting the categorical factors to one of the 2 levels). You can use the replicates of the center points as an estimate of the mean square error.  In fact, if center point is the current conditions, replicates of this as an estimate of current process variance is an interesting test of significance (ANOVA) for the other factor effects.

[#5]

@statmanGenerally we think of center points as being relevant to only continuous factors as you point out. But one can create a design which has continuous AND categorical factors AND center points. The usual convention, if you have the budget and resources, is to add treatment combinations to the experiment such that each center point combination of continuous factors is run at least twice for EACH level of the continuous factors. This arrangement maintains balance and estimation of all possible effects if running say a full factorial design...but as one finds out pretty quickly, the size of the design balloons pretty quickly.

A more prudent, economical and efficient approach would almost always be take advantage of optimal design techniques and build out the design to fit the problem vs. the method I cite above....which basically shoe horns the problem into the design because, 'well it's in the Classic catalog as the only way to do it'. 

[#6]

The organization is enamored of having replicate runs at the current target conditions as a part of the experiment, but they balk at expanding the design space to accommodate a 3-level factor to be incorporated in there and to do multiple runs at the edge conditions. I was hoping to take advantage of the triplicate center condition to make up for the lack of replicates at the edge conditions. Anyways, that ship has sailed and I need to deal with what I've got..!

¯\_(ツ)_/¯

[#7]

Ahh, good observation! What happened was a pair of continuous characteristics were grouped together and then varied in concert to push the system toward two extremes. In this case, the two continuous parameters that were lumped together were salt content and pH. The system being characterized was an ion exchange resin bed, so increasing the salt content and decreasing the pH would encourage lower levels of binding. Decreasing the salt and increasing the pH would encourage higher levels of binding. Curvature isn't really expected in this system.

Maybe I could break out the individual components that make up each of the categoricals and analyze it that way...

Your statement:
"You can use the replicates of the center points as an estimate of the mean square error. In fact, if center point is the current conditions, replicates of this as an estimate of current process variance is an interesting test of significance (ANOVA) for the other factor effects."
Sounds like it would apply here. The center points are center points of the conditions for the step.