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.

Does anyone know?

 

Thanks.