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.