nested design

**Nested Design** is an **experimental design where levels of one factor are hierarchically contained within levels of another factor** — unlike crossed designs where every level of each factor appears with every level of every other factor, nested designs reflect natural hierarchies in the manufacturing process. **How Nested Designs Work** - **Hierarchy**: Factor B levels are unique within each level of Factor A (e.g., wafers within lots, dies within wafers). - **Random Effects**: Nested factors are typically random effects in the statistical model. - **Variance Components**: ANOVA decomposes total variance into between-lot, between-wafer, and between-die components. - **Notation**: B(A) means B is nested within A. **Why It Matters** - **Variance Decomposition**: Quantifies how much variation comes from lot-to-lot, wafer-to-wafer, within-wafer, and die-to-die sources. - **Natural Hierarchy**: Semiconductor manufacturing has inherent nesting (lot → cassette → wafer → die → site). - **Process Improvement**: Identifies the largest source of variation to target for improvement. **Nested Design** is **matching the experiment to the hierarchy** — analyzing the natural lot→wafer→die nesting structure of semiconductor manufacturing variation.