Assumption of negligible interaction
All three main effects are confounded with 2-factor interactions in a 23-1 fractional factorial experiment defined by
C = AB
Therefore in order to use the estimated main effects to rank the importance of the factors,
It must be assumed that the interactions are zero (or at least negligible compared to the main effects).
Tests
The main effects of all three factors can be estimated, but with only four runs there are no residual degrees of freedom. As a result,
It is impossible to test the significance of the main effects.
Using this design for screening would therefore be an exploratory technique and should be followed by an experiment with more runs (and fewer factors) to estimate interactions and assess the significance of the effects.