Central Composite Design - Orthogonal Axial Values

[#1]

All - 

I'm creating a Response Surface Design, Central Composite Design for 3 Continuous Factors. 

If you select Central Composite Design under Design Type, it starts with 16 runs, 2 center points. You can then choose the axial value and the default for the Orthogonal design is an axial value of 1.287. With 2 center points and 2 replicates, this creates an experimental design with 48 runs.

However, if you choose CCD-Orthogonal under Design type, you actually start with 23 runs, 9 center points and the default axial value is 1.668. With the default of 9 center points and 2 replicates, you have an experimental design with 69 runs. This ends up with 27 center points - which seems excessive.

Why is there a difference in the default axial value when both are central composite orthogonal designs? What is the reason for so many center points in the second scenario?

Thanks

Shannon

[#2]

There are different 'flavors' of the central composite design. They are explained in the JMP Help, the Design of Experiments Guide in particular. These flavors offer different benefits. It is necessary to constrain the axial distance and the number of center points to achieve the benefit. Nothing will break, however, if you don't follow the design. For example, if you change the axial distance or number of center points, then the CCD is no longer a particular flavor, but it will still work.

If you want more flexibility and control over your design, for example, the number of runs, then I strongly recommend using the JMP Custom Design. You can use the same response and factor definitions. You can click the RSM button in the Model section to add all the tradition terms and to change the optimality criterion to I-optimal. So the custom design can reproduce the classic design when it is optimal, but it can also do lots of things that a classic design can't.

[#3]

 Thank you for the information. I've read through the documentation I could find but I do not see an explanation for why the CCD-Orthogonal has a default of 9 centerpoints but the standard Central Composite Design only has 2 centerpoints. Is there somewhere I can look to specifically understand that?

[#4]

Did you see this page about the central composite design choices? (I just want to be sure.)

Also, this information is documented in popular textbooks that cover the old design methods that started the response surface methodology. There are constraints on the axial length and the number of center points in order to achieve the property of these designs (i.e., on-face, rotatable, orthogonal). Literature sources led to this table in the JMP training course about these design methods.

[#5]

To add just a bit more detail to the information that Mark provided, the labeling that JMP provides does not make it clear what type of design you are using. The default axial scaling is Rotatable. The labeling that appears in the design choices is based on that axial choice. So when you see a CCD with 2 cp's, that is a rotatable CCD. The CCD that is Uniform Precision is a Rotatable Uniform Precision. So when you see the CCD that says orthogonal, you are getting both Rotatable AND Orthogonal. Please note that if you change the axial distance, the labeling in the design choice box does not update for that change.