I have done a screening experiment for 8 factors. I have used a fractional factorial with 12 runs(sorry I didn't know about definitive screeing yet). I am repeating the same design in several runs, each on a different instrument, and I'm treating these runs act as blocks since they represent instrument-to-instrument variation. My intent is to treat the instrument factor as a random effect so I can extent my inferences to a larger population. Is there a name for this design I can latch onto. It is not a blocked fractional factorial since I'm not dividing a single replicate over several blocks (instruments). I'm replicating the design. Now I can do the analysis and know how to construct the model, but I can't figure out what the statistical community calls this.
I suppose I could have used different aliasing for each block and maybe cleared the main effects entirely from the 2-level interactions. But for the simplicity of the execution it was easier to replicate the same design over several instruments.