Design of Experiments: 3-level fractional factorial question

[emac124]

Hello,

 

I have a DoE question about a 3^(7-1) fractional factorial design matrix. For the 7th factor, I used the generator function G=ABCDEF, and I'm wondering what its resolution and the associated confounding structure is. Can anyone help?

 

I'm using DoE to analyse the effect of 7 input factors on a response variable and expect a nonlinear relationship, hence all factors have 3 levels. I appreciate that 3^6 (=729) experiments may seem 'a lot' but they're reasonably quick to do since they're computer experiments rather than physical experiments. However, the full 3^7 experiments would take too long.

 

To determine the design matrix's resolution and the confounding structure, I tried to work through the mod3 arithmetic myself, but due to the large number of aliases (and lack of experience on my behalf), I got lost in it... Does anyone know a quick way to work out the resolution and confounding structure of this matrix (or even a reference to it)?

 

Due to the large number of experiments, which is very uncommon for a DoE method, there is little information on this design matrix in the literature. (However, I appreciate that there is likely to be a generalised mathematical treatment of it somewhere).

 

I'm looking for an answer but also to understand how to work it out myself next time. Many thanks for any assistance.

[emac124]

Does anyone know?

 

Thanks.