Fractional Factorial Design

Method

Run only a chosen subset of all possible combinations of factor levels. We only focus on main effects and two-factor interactions. Higher order interactions $>2$ are usually negligible.

Aliasing

When running a fraction of the full design, some effects are confounded (cannot separate based on data alone).

Resolution

The Resolution will tall you how to estimate effects.

Example

Suppose we have factors $A,B,C,D$. A full run will have $2^4=16$ total runs (In this case, our factors are $\in \{-1,1\}$. We can run a half-fractional design resulting in $8$ runs.

We set $D=A\times B\times C$

Thus, we will only need 8 runs for $A,B,C$