Plackett-Burman Design

Plackett-Burman (PB) Design is a two-level fractional factorial screening design with $N = 4n$ runs (8, 12, 16, 20, ...) — capable of screening up to $N-1$ factors in $N$ runs, providing the most economical estimate of main effects when interactions are assumed negligible.

How PB Designs Work

• Construction: Based on Hadamard matrices — each row is a circular shift of the first row.
• Resolution III: Main effects are confounded with two-factor interactions (not estimable separately).
• Fold-Over: Adding a mirror image of the design (fold-over) de-aliases main effects from interactions.
• Assumption: Two-factor and higher interactions are negligible (effect sparsity principle).

Why It Matters

• Most Economical: 12-run PB screens 11 factors — the minimum possible for that many factors.
• Standard Tool: The go-to screening design in semiconductor process development.
• Limitation: Cannot estimate interactions — follow up with factorial or response surface designs.

Plackett-Burman is the bare minimum experiment — the most economical way to screen many factors when only main effects need to be estimated.