Negative values of Central Composite Design

[#1]

Hi!

I want to investigate doses of 6 factors at 3 levels - 0, 1, 2 pieces. Without 2 factor interactions confounded with main effects.

So I have chosen Central Composite Design - Orthogonal with 9 center points and 53 runs, axial value rotatable - 2.78. Is this the right choice?

What confuses me is that the generated design (besides values 0, 1, 2) has values: -1,37841423 and 3,37841423.

3,3 is ok, but how to implement the negative value -1,37841423 ? Do I need to use 0 pieces in such a case?

The last question is that in a Design Evaluation section in Alias Matrix and Color Map there are such effects as X1*X1*X1 and X1*X1. Interaction with itself? What do they mean and why do we need them?

Thank you very much! 

[#2]

There are several design methods what would produce a good design for your case of six factors and the quadratic model for effects. Why did you choose a central composite design?

Your choice of the rotatable and orthogonal properties forced the axial points to extend beyond the specified factor range. You could select 'on face' instead.

Orthogonal and rotatable designs can be expensive and are not necessary to estimate such a model. The presence of correlation of the estimates will inflate the variance of the estimates but this increase can be tolerable if the correlation is small, the response variance is small, and the effects are large.

The alias matrix and color map on correlations provide information about the bias in your estimates by terms that are not in the model but might represent active effects.

[#3]

Thank you, Mark! I chose CCD because it had a better results in Color Map on correlation and Alias Matrix.

I considered 3-level design with 6 Discrete Numeric factors using Custom Design feature. Here is its Color Map:

The other option was Taguchi L24 design:

And Rototable CCD-Orthogonal:

And when I use "On face" there are red squares:

The cost is not very high so it is ok to have up to 60-70 runs.