"algo-mfg-doe"

Design of Experiments (DOE)

Overview

DOE systematically varies process factors to identify their effects on responses. Full factorial tests all combinations; fractional factorial tests a strategic subset. Identifies main effects and interactions. More efficient than one-factor-at-a-time (OFAT) which misses interactions. Uses ANOVA for analysis.

When to Use

Trigger conditions:

• Identifying which process factors significantly affect quality/yield
• Optimizing process settings for target performance
• Screening many factors to find the vital few

When NOT to use:

• When the process is not stable (stabilize with SPC first)
• For observational data with no ability to manipulate factors

Algorithm

IRON LAW: One-Factor-At-A-Time (OFAT) MISSES Interactions
Changing one factor while holding others fixed cannot detect
interactions (where the effect of A depends on the level of B).
Full factorial or fractional factorial designs test ALL main effects
AND interactions in fewer runs than OFAT. A 2³ factorial (8 runs)
gives more information than 6 OFAT runs at lower cost.

Phase 1: Input Validation

Define: response variable(s), factors (2-7 practical), levels per factor (usually 2 for screening, 3 for optimization), constraints, noise factors. Gate: Factors and levels defined, practical to run all experimental conditions.

Phase 2: Core Algorithm

Screening (many factors): 2^(k-p) fractional factorial. Choose resolution III+ (main effects not confounded with each other).

Optimization (few factors): 2^k full factorial or central composite design (CCD) for response surface.

1. Generate design matrix (run order, factor level assignments)
2. Randomize run order (critical for validity)
3. Execute experiments, record responses
4. Analyze: ANOVA for factor significance, effect plots, interaction plots
5. If optimizing: fit response surface model, find optimal settings

Phase 3: Verification

Check: R² of model is adequate, residuals are normally distributed and random. Confirmation runs at predicted optimal settings match prediction. Gate: Model is significant, residuals OK, confirmation runs pass.