nested experiments

**Nested experiments** are the **DOE structures that organize factors in hierarchical levels when some variables are harder or slower to change than others** - they preserve statistical power while making fab experimentation operationally feasible under real tool and schedule constraints. **What Is Nested experiments?** - **Definition**: Experimental design where one factor level exists inside another, such as runs nested within chamber or lot nested within tool. - **Typical Use**: Split-plot and split-split-plot studies where temperature may change daily but gas flow can change per run. - **Statistical Model**: Mixed-effects analysis separates between-group and within-group variability correctly. - **Output**: Reliable estimates for main effects and interactions without violating practical run constraints. **Why Nested experiments Matters** - **Operational Realism**: Hard-to-change factors can be tested without unrealistic run sequencing. - **Data Integrity**: Prevents incorrect ANOVA conclusions caused by ignoring hierarchical error structure. - **Cycle-Time Control**: Reduces costly recipe changeovers while still extracting meaningful cause-effect insight. - **Scale-Up Value**: Nested designs map better to real production logistics than idealized full randomization. - **Decision Confidence**: Teams can quantify which variability source is tool-level versus run-level. **How It Is Used in Practice** - **Hierarchy Planning**: Classify each factor as hard-to-change or easy-to-change before matrix construction. - **Run Execution**: Sequence experiments by whole-plot groups, then randomize sub-plot settings within each group. - **Model Fitting**: Use mixed-model software to estimate effects and confidence intervals with correct error terms. Nested experiments are **the practical DOE framework for complex manufacturing realities** - they deliver valid statistical conclusions without breaking fab execution constraints.