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.