Unit content
Factorial experiments and interaction effects
When several process factors may matter, changing one factor at a time can miss interactions and use experiments inefficiently.
A factorial experiment tests combinations of factor levels. In a two-level design with factors $A$ and $B$, four conditions are used:
$$(-,-),\quad (+,-),\quad (-,+),\quad (+,+).$$
A main effect describes the average response change associated with changing one factor. An interaction occurs when the effect of one factor depends on the level of another.
Suppose average measured response is
| $A$ | $B$ | response |
|---|---|---|
| low | low | 10 |
| high | low | 14 |
| low | high | 11 |
| high | high | 20 |
At low $B$, raising $A$ changes the response by $14-10=4$. At high $B$, the same change in $A$ gives $20-11=9$. The effect of $A$ therefore depends strongly on $B$; there is an interaction.
A one-factor-at-a-time experiment could easily miss that structure.
Factorial designs become especially valuable in manufacturing because temperature, speed, pressure, feed, material condition and tooling often interact physically. The goal is not merely to rank knobs independently, but to identify a model of how combinations of settings influence the response.