gh-lyndonkl-claude/skills/design-of-experiments/resources/template.md

Design of Experiments - Template

Workflow

Copy this checklist and track your progress:

DOE Template Progress:
- [ ] Step 1: Define experiment objective
- [ ] Step 2: List factors and levels
- [ ] Step 3: Select design type
- [ ] Step 4: Generate design matrix
- [ ] Step 5: Randomize and document protocol
- [ ] Step 6: Finalize experiment plan

Step 1: Define experiment objective

Specify what you're trying to learn (screening, optimization, response surface, robust design), primary response metric(s), and success criteria. See Objective Definition for examples.

Step 2: List factors and levels

Identify all factors (controllable inputs), specify levels for each (2-3 initially), distinguish control vs noise factors, and define measurable responses. See Factor Table Template for structure.

Step 3: Select design type

Based on objective:

• 2-5 factors, want all combinations → Full Factorial
• 5+ factors, limited runs → Fractional Factorial
• Screening 8+ factors → Plackett-Burman

Step 4: Generate design matrix

Create run-by-run table with factor settings for each experimental run. See Design Matrix Examples for format.

Step 5: Randomize and document protocol

Randomize run order, specify blocking if needed, detail measurement procedures, and plan replication strategy. See Execution Details for guidance.

Step 6: Finalize experiment plan

Create complete design-of-experiments.md document using Document Structure Template. Self-check with quality criteria in Quality Checklist.

---

Document Structure Template

Use this structure for the final design-of-experiments.md file:

# Design of Experiments: [Experiment Name]

## 1. Objective

**Goal**: [Screening | Optimization | Response Surface | Robust Design]

**Context**: [1-2 sentences describing the system/process being studied]

**Success Criteria**: [What constitutes a successful experiment? Measurable outcomes.]

**Constraints**:
- Budget: [Maximum number of runs allowed]
- Time: [Deadline or duration per run]
- Resources: [Equipment, personnel, materials]

## 2. Factors and Levels

| Factor | Type | Low Level (-1) | High Level (+1) | Center (0) | Units | Rationale |
|--------|------|----------------|-----------------|------------|-------|-----------|
| A: [Name] | Control | [value] | [value] | [value] | [units] | [Why this factor?] |
| B: [Name] | Control | [value] | [value] | [value] | [units] | [Why this factor?] |
| C: [Name] | Noise | [value] | [value] | - | [units] | [Uncontrollable variation] |

**Factor Selection Rationale**: [Why these factors? Any excluded? Assumptions?]

## 3. Response Variables

| Response | Description | Measurement Method | Target | Units |
|----------|-------------|-------------------|---------|-------|
| Y1: [Name] | [What it measures] | [How measured] | [Maximize/Minimize/Target value] | [units] |
| Y2: [Name] | [What it measures] | [How measured] | [Maximize/Minimize/Target value] | [units] |

**Response Selection Rationale**: [Why these responses? Any tradeoffs?]

## 4. Experimental Design

**Design Type**: [Full Factorial 2^k | Fractional Factorial 2^(k-p) | Plackett-Burman | Central Composite | Box-Behnken]

**Resolution**: [For fractional factorials: III, IV, or V]

**Runs**:
- Design points: [number]
- Center points: [number of replicates at center]
- Total runs: [design + center]

**Design Rationale**: [Why this design? What can/can't it detect?]

## 5. Design Matrix

| Run | Order | Block | A | B | C | Y1 | Y2 | Notes |
|-----|-------|-------|---|---|---|----|----|-------|
| 1 | 5 | 1 | -1 | -1 | -1 | | | |
| 2 | 12 | 1 | +1 | -1 | -1 | | | |
| 3 | 3 | 1 | -1 | +1 | -1 | | | |
| 4 | 8 | 1 | +1 | +1 | -1 | | | |
| 5 | 1 | 2 | -1 | -1 | +1 | | | |
| ... | ... | ... | ... | ... | ... | | | |

**Randomization**: Run order randomized using [method]. Original design point order preserved in "Run" column.

**Blocking**: [If used] Runs blocked by [day/batch/operator/etc.] to control for [nuisance variable].

## 6. Execution Protocol

**Preparation**:
- [ ] [Equipment setup/calibration steps]
- [ ] [Material preparation]
- [ ] [Personnel training]

**Run Procedure**:
1. [Step-by-step protocol for each run]
2. [Factor settings to apply]
3. [Wait/equilibration time]
4. [Response measurement procedure]
5. [Recording method]

**Quality Controls**:
- [Measurement calibration checks]
- [Process stability verification]
- [Outlier detection procedure]

**Timeline**: [Start date, duration per run, expected completion]

## 7. Analysis Plan

**Primary Analysis**:
- Calculate main effects for factors A, B, C
- Calculate 2-way interaction effects (AB, AC, BC)
- Fit linear model: Y = β0 + β1·A + β2·B + β3·C + β12·AB + ...
- ANOVA to test significance (α = 0.05)
- Residual diagnostics (normality, constant variance, independence)

**Graphical Analysis**:
- Main effects plot
- Interaction plot
- Pareto chart of standardized effects
- Residual plots (normal probability, vs fitted, vs order)

**Decision Criteria**:
- Effects significant at p < 0.05 are considered important
- Interaction present if p(interaction) < 0.05
- Optimal settings chosen to [maximize/minimize] Y1 while [constraint on Y2]

**Follow-up**:
- If curvature detected → Run [response surface design]
- If additional factors identified → Run [screening design]
- Confirmation runs: [Number] at predicted optimum settings

## 8. Assumptions and Limitations

**Assumptions**:
- [Linear relationship between factors and response]
- [No strong higher-order interactions]
- [Homogeneous variance across factor space]
- [Errors are independent and normally distributed]
- [Process is stable during experiment]

**Limitations**:
- [Design resolution limits – e.g., 2-way interactions confounded]
- [Factor range restrictions]
- [Measurement precision limits]
- [External validity – generalization beyond tested region]

**Risks**:
- [What could invalidate results?]
- [Mitigation strategies]

## 9. Expected Outcomes

**If screening design**:
- Pareto chart identifying 3-5 critical factors from [N] candidates
- Effect size estimates with confidence intervals
- Shortlist for follow-up optimization experiment

**If optimization design**:
- Optimal factor settings: A = [value], B = [value], C = [value]
- Predicted response at optimum: Y1 = [value] ± [CI]
- Interaction insights: [Which factors interact? How?]

**If response surface**:
- Response surface equation: Y = [polynomial model]
- Contour/surface plots showing optimal region
- Sensitivity analysis showing robustness

**Deliverables**:
- This experiment plan document
- Completed design matrix with results (after execution)
- Analysis report with plots and recommendations

---

Objective Definition

Screening: Screen 12 software config parameters to identify 3-5 affecting API response time. Success: Reduce candidates 60%+. Constraint: Max 16 runs.

Optimization: Optimize injection molding (temp, pressure, time) to minimize defect rate while cycle time < 45s. Success: < 2% defects (currently 8%). Constraint: Max 20 runs, 2 days.

Response Surface: Map yield vs temperature/pH, find maximum, model curvature. Success: R² > 0.90, optimal region. Constraint: Max 15 runs.

---

Factor Table Template

Factor	Type	Low (-1)	High (+1)	Center (0)	Units	Rationale
A: Temperature	Control	150°C	200°C	175°C	°C	Literature suggests 150-200 range optimal
B: Pressure	Control	50 psi	100 psi	75 psi	psi	Equipment operates 50-100, nonlinear expected
C: Time	Control	10 min	30 min	20 min	min	Longer times may improve but cost increases
D: Humidity	Noise	30%	70%	-	%RH	Uncontrollable environmental variation

Type definitions:

• Control: Factors you can set deliberately in the experiment
• Noise: Factors that vary but can't be controlled (for robust design)
• Held constant: Factors fixed at one level (not in design)

Level selection guidance:

• 2 levels: Start here for screening/optimization. Detects linear effects and interactions.
• 3 levels: Add center point to detect curvature. Required for response surface designs.
• Categorical: Use coded values (-1, +1) for categories (e.g., Supplier A = -1, Supplier B = +1)

---

Full Factorial Designs

When to use: 2-5 factors, want to estimate all main effects and interactions, budget allows 2^k runs.

Design structure: Test all combinations of factor levels.

Example: 2³ factorial (3 factors, 2 levels each = 8 runs)

Run	A	B	C
1	-	-	-
2	+	-	-
3	-	+	-
4	+	+	-
5	-	-	+
6	+	-	+
7	-	+	+
8	+	+	+

Advantages:

• Estimates all main effects and 2-way/3-way interactions
• No confounding
• Maximum precision for given number of factors

Limitations:

• Runs grow exponentially: 2³ = 8, 2⁴ = 16, 2⁵ = 32, 2⁶ = 64
• Inefficient for screening (wastes runs on unimportant factors)

Add center points: Replicate 3-5 runs at center (0, 0, 0) to detect curvature and estimate pure error.

---

Fractional Factorial Designs

When to use: 5+ factors, limited budget, willing to sacrifice some interaction information.

Design structure: Test a fraction (1/2, 1/4, 1/8) of full factorial, deliberately confounding higher-order interactions.

Example: 2⁵⁻¹ design (5 factors, 16 runs instead of 32)

Resolution IV: Main effects clear, 2-way interactions confounded with each other.

Run	A	B	C	D	E
1	-	-	-	-	+
2	+	-	-	-	-
3	-	+	-	-	-
4	+	+	-	-	+
5	-	-	+	-	-
...	...	...	...	...	...

Generator: E = ABCD (defining relation: I = ABCDE)

Confounding structure:

• A confounded with BCDE
• AB confounded with CDE
• ABC confounded with DE

Resolution levels:

• Resolution III: Main effects confounded with 2-way interactions. Use for screening only.
• Resolution IV: Main effects clear, 2-way confounded with 2-way. Good for screening + some optimization.
• Resolution V: Main effects and 2-way clear, 2-way confounded with 3-way. Preferred for optimization.

Choosing fraction: Use standard designs (tables available) or design software to ensure desired resolution.

---

Plackett-Burman Screening

When to use: Screen 8-15 factors with minimal runs, only care about main effects.

Design structure: Orthogonal design with runs = next multiple of 4 above number of factors.

Example: 12-run Plackett-Burman for up to 11 factors

Run	A	B	C	D	E	F	G	H	J	K	L
1	+	+	-	+	+	+	-	-	-	+	-
2	+	-	+	+	+	-	-	-	+	-	+
3	-	+	+	+	-	-	-	+	-	+	+
...	...	...	...	...	...	...	...	...	...	...	...

Advantages:

• Very efficient: Screen 11 factors in 12 runs (vs 2048 for full factorial)
• Main effects estimated independently

Limitations:

• 2-way interactions completely confounded with main effects
• Only use when interactions unlikely or unimportant
• Cannot estimate interactions

Use case: Early-stage screening to reduce 15 candidates to 4-5 for follow-up factorial design.

---

Design Matrix Examples

Format: Each row = one run. Columns: Run (design point #), Order (randomized sequence), Block (if used), Factors (coded -1/0/+1 or actual values), Responses (blank until execution), Notes (observations).

Run	Order	A: Temp (°C)	B: Press (psi)	C: Time (min)	Y1: Yield (%)	Y2: Cost ($)
1	3	150	50	10
2	7	200	50	10
3	1	150	100	10
4	5	200	100	10

---

Execution Details

Randomization: Eliminates bias from time trends/drift. Method: (1) List runs, (2) Assign random numbers, (3) Sort by random number = execution order, (4) Document both orders. Exception: Don't randomize hard-to-change factors (use split-plot design, see methodology.md).

Blocking: Use when runs span days/batches/operators. Method: Divide into 2-4 balanced blocks, randomize within each, analyze with block as factor. Example: 16 runs over 2 days → 2 blocks of 8.

Replication: True replication (repeat entire run), repeated measures (multiple measurements per run), or center points (3-5 replicates at center for pure error). Guidance: Always include 3-5 center points for continuous factors.

---

Quality Checklist

Before finalizing the experiment plan, verify:

Objective & Scope:

• Goal clearly stated (screening | optimization | response surface | robust)
• Success criteria are measurable and realistic
• Constraints documented (runs, time, cost)

Factors:

• All important factors included
• Levels span meaningful range (not too narrow, not outside feasible region)
• Factor types identified (control vs noise)
• Rationale for each factor documented

Responses:

• Responses are objective and quantitative
• Measurement method specified and validated
• Target direction clear (maximize | minimize | hit target)

Design:

• Design type appropriate for objective and budget
• Design resolution adequate (e.g., Resolution IV+ if interactions matter)
• Run count justified (power analysis or practical limit)
• Design matrix correct (orthogonal, balanced)

Execution:

• Randomization method specified
• Blocking used if runs span nuisance variable levels
• Replication plan documented (center points, full replicates)
• Protocol detailed enough for independent execution
• Timeline realistic

Analysis:

• Analysis plan specified before data collection
• Significance level (α) stated
• Decision criteria clear
• Residual diagnostics planned
• Follow-up strategy identified

Assumptions & Risks:

• Key assumptions stated explicitly
• Limitations acknowledged (resolution, range, measurement)
• Risks identified with mitigation plans