Blocking in DOE is the technique of grouping experimental runs to account for known nuisance variation (variation from sources that are not of primary interest but could obscure the effects of the factors being studied). By organizing runs into blocks, the nuisance variation is isolated and removed from the analysis.

Why Blocking Is Needed

• Real experiments take time and use resources that may change. If a DOE runs over multiple days, shifts, wafer lots, or chambers, these nuisance factors contribute variation that can mask the true factor effects.
• Without blocking, nuisance variation inflates the error term in statistical analysis, making it harder to detect real factor effects (reduced statistical power).
• Blocking separates nuisance variation from factor effects, sharpening the analysis.

How Blocking Works

• Identify the nuisance factor: What known source of variation could affect results? (e.g., different wafer lots, different days, different chambers).
• Divide runs into blocks: Each block contains a balanced set of experimental conditions. The nuisance factor changes between blocks but is constant within each block.
• Analyze: The block effect is estimated and removed, leaving a cleaner estimate of the factor effects.

Semiconductor DOE Blocking Examples

• Wafer Lot Blocking: If the DOE requires wafers from multiple lots and lots may differ, assign a complete replicate (or balanced subset) of the design to each lot.
• Day-to-Day Blocking: If the experiment runs over 2 days, block by day. Each day runs a balanced half of the design.
• Chamber Blocking: If testing involves multiple chambers, block by chamber to separate chamber-to-chamber variation from factor effects.

Blocking in a $2^k$ Factorial

• A $2^3$ factorial (8 runs) can be blocked into 2 blocks of 4 runs by confounding the highest-order interaction (ABC) with the block effect.
• Since the 3-way interaction is usually negligible, confounding it with blocks loses very little information while gaining clean estimation of all main effects and 2-factor interactions.

Blocking vs. Randomization

• Randomization averages out unknown nuisance effects — it doesn't remove them but prevents systematic bias.
• Blocking directly removes known nuisance effects — more powerful but requires identifying the nuisance factor in advance.
• Best practice: Block what you can, randomize what you cannot.

Blocking is a fundamental DOE technique that improves experimental efficiency — it ensures that the precision of factor effect estimates is not degraded by predictable sources of nuisance variation.