majiayu000 Design of Experiments
Table of Contents
Purpose
Design of Experiments (DOE) helps you systematically discover how multiple factors affect an outcome while minimizing the number of experimental runs. Instead of testing one variable at a time (inefficient) or guessing randomly (unreliable), DOE uses structured experimental designs to:
- Screen many factors to find the critical few
- Optimize factor settings to maximize/minimize a response
- Discover interactions where factors affect each other
- Map response surfaces to understand the full factor space
- Validate robustness against noise and environmental variation
When to Use
Use this skill when:
- Limited experimental budget: You have constraints on time, cost, or resources for testing
- Multiple factors: 3+ controllable variables that could affect the outcome
- Interaction suspicion: Factors may interact (effect of A depends on level of B)
- Optimization needed: Finding best settings, not just "better than baseline"
- Screening required: Many candidate factors (10+), need to identify vital few
- Response surface: Need to map curvature, find peaks/valleys, understand tradeoffs
- Robust design: Must work well despite noise factors or environmental variation
- Process improvement: Manufacturing, chemical processes, software performance tuning
- Product development: Formulations, recipes, configurations with multiple parameters
- A/B/n testing: Web/app features with multiple variants and combinations
- Machine learning: Hyperparameter tuning for models with many parameters
Trigger phrases: "optimize", "tune parameters", "factorial test", "interaction effects", "response surface", "efficient experiments", "minimize runs", "robustness", "sensitivity analysis"
What Is It?
Design of Experiments is a statistical framework for planning, executing, and analyzing experiments where you deliberately vary multiple input factors to observe effects on output responses.
Quick example:
You're optimizing a web signup flow with 3 factors:
- Factor A: Form layout (single-page vs multi-step)
- Factor B: CTA button color (blue vs green)
- Factor C: Social proof (testimonials vs user count)
Naive approach: Test one at a time = 6 runs (2 levels each × 3 factors)
- But you miss interactions! Maybe blue works better for single-page, green for multi-step.
DOE approach: 2³ factorial design = 8 runs
- Tests all combinations: (single/blue/testimonials), (single/blue/count), (single/green/testimonials), etc.
- Reveals main effects AND interactions
- Statistical power to detect differences
Result: You discover that layout and CTA color interact strongly—multi-step + green outperforms everything, but single-page + blue is close second. Social proof has minimal effect. Make data-driven decision with confidence.
Workflow
Copy this checklist and track your progress:
Design of Experiments Progress:
- [ ] Step 1: Define objectives and constraints
- [ ] Step 2: Identify factors, levels, and responses
- [ ] Step 3: Choose experimental design
- [ ] Step 4: Plan execution details
- [ ] Step 5: Create experiment plan document
- [ ] Step 6: Validate quality
Step 1: Define objectives and constraints
Clarify the experiment goal (screening vs optimization), response metric(s), experimental budget (max runs), time/cost constraints, and success criteria. See Common Patterns for typical objectives.
Step 2: Identify factors, levels, and responses
List all candidate factors (controllable inputs), specify levels for each factor (low/high or discrete values), categorize factors (control vs noise), and define response variables (measurable outputs). For screening many factors (8+), see resources/methodology.md for Plackett-Burman and fractional factorial approaches.
Step 3: Choose experimental design
Based on objective and constraints:
- For screening 5+ factors with limited runs → Use resources/methodology.md for fractional factorial or Plackett-Burman
- For optimizing 2-5 factors → Use resources/template.md for full or fractional factorial
- For response surface mapping → Use resources/methodology.md for central composite or Box-Behnken
- For robust design against noise → Use resources/methodology.md for parameter vs noise factor arrays
Step 4: Plan execution details
Specify randomization order (eliminate time trends), blocking strategy (control nuisance variables), replication plan (estimate error), sample size justification (power analysis), and measurement protocols. See Guardrails for critical requirements.
Step 5: Create experiment plan document
Create design-of-experiments.md with sections: objective, factors table, design matrix (run order with factor settings), response variables, execution protocol, and analysis plan. Use resources/template.md for structure.
Step 6: Validate quality
Self-assess using resources/evaluators/rubric_design_of_experiments.json. Check: objective clarity, factor completeness, design appropriateness, randomization plan, measurement protocol, statistical power, analysis plan, and deliverable quality. Minimum standard: Average score ≥ 3.5 before delivering.
Common Patterns
Pattern 1: Screening (many factors → vital few)
- Context: 10-30 candidate factors, limited budget, want to identify 3-5 critical factors
- Approach: Plackett-Burman or fractional factorial (Resolution III/IV)
- Output: Pareto chart of effect sizes, shortlist for follow-up optimization
- Example: Software performance tuning with 15 configuration parameters
Pattern 2: Optimization (find best settings)
- Context: 2-5 factors already identified as important, want to find optimal levels
- Approach: Full factorial (2^k) or fractional factorial + steepest ascent
- Output: Main effects plot, interaction plots, recommended settings
- Example: Manufacturing process with temperature, pressure, time factors
Pattern 3: Response Surface (map the landscape)
- Context: Need to understand curvature, find maximum/minimum, quantify tradeoffs
- Approach: Central Composite Design (CCD) or Box-Behnken
- Output: Response surface equation, contour plots, optimal region
- Example: Chemical formulation with ingredient ratios
Pattern 4: Robust Design (work despite noise)
- Context: Product/process must perform well despite uncontrollable variation
- Approach: Taguchi inner-outer array (control × noise factors)
- Output: Settings that minimize sensitivity to noise factors
- Example: Consumer product that must work across temperature/humidity ranges
Pattern 5: Sequential Experimentation (learn then refine)
- Context: High uncertainty, want to learn iteratively with minimal waste
- Approach: Screening → Steepest ascent → Response surface → Confirmation
- Output: Progressively refined understanding and settings
- Example: New product development with unknown factor relationships
Guardrails
Critical requirements:
Randomize run order: Eliminates time-order bias and confounding with lurking variables. Use random number generator, not "convenient" sequences.
Replicate center points: For designs with continuous factors, replicate center point runs (3-5 times) to estimate pure error and detect curvature.
Avoid confounding critical interactions: In fractional factorials, don't confound important 2-way interactions with main effects. Choose Resolution ≥ IV if interactions matter.
Check design balance: Ensure orthogonality (factors are uncorrelated in design matrix). Correlation > 0.3 reduces precision and interpretability.
Define response precisely: Use objective, quantitative, repeatable measurements. Avoid subjective scoring unless calibrated with multiple raters.
Justify sample size: Run power analysis to ensure design can detect meaningful effect sizes with acceptable Type II error risk (β ≤ 0.20).
Document assumptions: State expected effect magnitudes, interaction assumptions, noise variance estimates. Design validity depends on these.
Plan for analysis before running: Specify statistical tests, significance level (α), effect size metrics before data collection. Prevents p-hacking.
Common pitfalls:
- ❌ One-factor-at-a-time (OFAT): Misses interactions, requires more runs than factorial designs
- ❌ Ignoring blocking: If runs span days/batches/operators, block accordingly or confound results with time trends
- ❌ Too many levels: Use 2-3 levels initially. More levels increase runs exponentially.
- ❌ Unmeasured factors: If an important factor isn't controlled/measured, it becomes noise
- ❌ Changing protocols mid-experiment: Breaks design structure. If necessary, restart or analyze separately.
Quick Reference
Key resources:
- resources/template.md: Quick-start templates for common designs (factorial, screening, response surface)
- resources/methodology.md: Advanced techniques (optimal designs, Taguchi, mixture experiments, sequential strategies)
- resources/evaluators/rubric_design_of_experiments.json: Quality criteria for experiment plans
Typical workflow time:
- Simple factorial (2-4 factors): 15-30 minutes
- Screening design (8+ factors): 30-45 minutes
- Response surface design: 45-60 minutes
- Robust design (Taguchi): 60-90 minutes
When to escalate:
- User needs mixture experiments (factors must sum to 100%)
- Split-plot designs required (hard-to-change factors)
- Optimal designs for irregular constraints
- Bayesian adaptive designs → Use resources/methodology.md for these advanced cases
Inputs required:
- Process/System: What you're experimenting on
- Factors: List of controllable inputs with candidate levels
- Responses: Measurable outputs (KPIs, metrics)
- Constraints: Budget (max runs), time, resources
- Objective: Screening, optimization, response surface, or robust design
Outputs produced:
design-of-experiments.md: Complete experiment plan with design matrix, randomization, protocols, analysis approach