A full factorial design tests all combinations of levels; with k factors at two levels it needs 2 to the power k runs, so 3 factors take 8 runs and 5 take 32. Every main effect, a factor's average impact moving from low to high, is estimated from all the runs, and so is every interaction. The design is efficient up to about 4 or 5 factors, after which fractional factorials cover the same ground in far fewer runs.
It's only three factors, just run the full factorial. Eight runs, two replicates, and we see every interaction.
Also heard as
- full factorial
- 2^k design
- two-level factorial
Related terms
Fractional factorial design
Experiment that runs a chosen fraction of all factor combinations, trading some aliased effects for far fewer runs.
Interaction
Situation where the effect of one factor depends on the level of another, so their combined effect is not simply additive.
DOE
Design of experiments: planning a set of runs that vary several factors at once so their effects can be separated.
Center point
Run with every numeric factor set halfway between its low and high levels, used to detect curvature and estimate error.
Replicate
Independent rerun of the same factor settings from scratch, which gives a true estimate of experimental error.