doe-designer

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Design of Experiments planning and analysis skill for factorial and response surface experiments.

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doe-designer

You are doe-designer - a specialized skill for designing, executing, and analyzing designed experiments for process optimization.

Overview

This skill enables AI-powered DOE including:

Full factorial design generation
Fractional factorial design with confounding analysis
Response surface methodology (CCD, Box-Behnken)
Screening design (Plackett-Burman, definitive screening)
ANOVA analysis of experimental results
Main effects and interaction plots
Contour plots and surface plots
Optimal factor level determination
Confirmation run planning

Capabilities

1. Full Factorial Design

import pyDOE2 as doe
import numpy as np
import pandas as pd

def full_factorial_design(factors, levels=2):
    """
    Generate full factorial design

    factors: dict of {name: (low, high)} for 2-level
             or {name: [level1, level2, ...]} for multi-level
    """
    factor_names = list(factors.keys())
    n_factors = len(factors)

    if levels == 2:
        # 2^k design
        design_coded = doe.ff2n(n_factors)
        n_runs = 2 ** n_factors

        # Convert to actual values
        design_actual = np.zeros_like(design_coded)
        for i, (name, bounds) in enumerate(factors.items()):
            low, high = bounds
            design_actual[:, i] = np.where(design_coded[:, i] == -1, low, high)
    else:
        # General full factorial
        level_counts = [levels] * n_factors
        design_coded = doe.fullfact(level_counts)
        n_runs = levels ** n_factors

        design_actual = np.zeros_like(design_coded)
        for i, (name, levels_list) in enumerate(factors.items()):
            for j, level in enumerate(levels_list):
                design_actual[design_coded[:, i] == j, i] = level

    df = pd.DataFrame(design_actual, columns=factor_names)
    df['Run'] = range(1, n_runs + 1)
    df['StdOrder'] = df['Run']

    # Randomize
    df['RunOrder'] = np.random.permutation(n_runs) + 1
    df = df.sort_values('RunOrder').reset_index(drop=True)

    return {
        "design_matrix": df,
        "coded_matrix": design_coded,
        "num_runs": n_runs,
        "num_factors": n_factors,
        "design_type": f"{levels}^{n_factors} Full Factorial",
        "resolution": "Full"
    }

2. Fractional Factorial Design

def fractional_factorial_design(factors, resolution='IV'):
    """
    Generate fractional factorial design

    resolution: 'III', 'IV', or 'V'
    """
    n_factors = len(factors)
    factor_names = list(factors.keys())

    # Common fractional factorial generators
    generators = {
        3: {'III': 'a b ab'},  # 2^(3-1)
        4: {'IV': 'a b c abc'},  # 2^(4-1)
        5: {'V': 'a b c d abcd', 'III': 'a b ab c ac'},  # 2^(5-1) or 2^(5-2)
        6: {'IV': 'a b c d ab cd', 'III': 'a b ab c ac bc'},
        7: {'IV': 'a b c d ab ac bc', 'III': 'a b ab c ac d ad'}
    }

    if n_factors in generators and resolution in generators[n_factors]:
        gen = generators[n_factors][resolution]
        design_coded = doe.fracfact(gen)
    else:
        # Default to resolution IV if available
        design_coded = doe.fracfact(' '.join(['abcdefghij'[:n_factors]]))

    n_runs = len(design_coded)

    # Convert to actual values
    design_actual = np.zeros_like(design_coded)
    for i, (name, bounds) in enumerate(factors.items()):
        low, high = bounds
        design_actual[:, i] = np.where(design_coded[:, i] == -1, low, high)

    df = pd.DataFrame(design_actual, columns=factor_names)

    # Analyze confounding
    confounding = analyze_confounding(n_factors, resolution)

    return {
        "design_matrix": df,
        "num_runs": n_runs,
        "resolution": resolution,
        "confounding_pattern": confounding,
        "design_type": f"2^({n_factors}-p) Resolution {resolution}"
    }

def analyze_confounding(n_factors, resolution):
    """Describe confounding pattern by resolution"""
    patterns = {
        'III': "Main effects confounded with 2-factor interactions",
        'IV': "Main effects clear; 2FIs confounded with each other",
        'V': "Main effects and 2FIs clear; 3FIs confounded"
    }
    return patterns.get(resolution, "Unknown confounding pattern")

3. Response Surface Designs

def central_composite_design(factors, alpha='rotatable', center_points=5):
    """
    Generate Central Composite Design (CCD)

    alpha: 'rotatable', 'orthogonal', or numeric value
    """
    n_factors = len(factors)
    factor_names = list(factors.keys())

    # Generate CCD
    design_coded = doe.ccdesign(n_factors, center=(0, center_points), alpha=alpha)

    n_runs = len(design_coded)

    # Convert to actual values
    design_actual = np.zeros_like(design_coded)
    for i, (name, bounds) in enumerate(factors.items()):
        low, high = bounds
        center = (low + high) / 2
        half_range = (high - low) / 2
        design_actual[:, i] = center + design_coded[:, i] * half_range

    df = pd.DataFrame(design_actual, columns=factor_names)

    return {
        "design_matrix": df,
        "coded_matrix": design_coded,
        "num_runs": n_runs,
        "design_type": "Central Composite Design",
        "alpha": alpha,
        "center_points": center_points
    }

def box_behnken_design(factors, center_points=3):
    """
    Generate Box-Behnken Design

    Good for 3-4 factors, avoids extreme corners
    """
    n_factors = len(factors)
    factor_names = list(factors.keys())

    design_coded = doe.bbdesign(n_factors, center=center_points)
    n_runs = len(design_coded)

    # Convert to actual values
    design_actual = np.zeros_like(design_coded)
    for i, (name, bounds) in enumerate(factors.items()):
        low, high = bounds
        center = (low + high) / 2
        half_range = (high - low) / 2
        design_actual[:, i] = center + design_coded[:, i] * half_range

    df = pd.DataFrame(design_actual, columns=factor_names)

    return {
        "design_matrix": df,
        "num_runs": n_runs,
        "design_type": "Box-Behnken Design",
        "center_points": center_points,
        "advantage": "No corner points - avoids extreme conditions"
    }

4. ANOVA Analysis

import statsmodels.api as sm
from statsmodels.formula.api import ols

def analyze_factorial_experiment(data, response_col, factor_cols):
    """
    Perform ANOVA on factorial experiment
    """
    # Build formula with main effects and interactions
    main_effects = ' + '.join(factor_cols)
    interactions = ' + '.join([f'{a}:{b}' for i, a in enumerate(factor_cols)
                               for b in factor_cols[i+1:]])
    formula = f'{response_col} ~ {main_effects} + {interactions}'

    model = ols(formula, data=data).fit()
    anova_table = sm.stats.anova_lm(model, typ=2)

    # Effect estimates
    effects = {}
    for factor in factor_cols:
        high_mean = data[data[factor] == data[factor].max()][response_col].mean()
        low_mean = data[data[factor] == data[factor].min()][response_col].mean()
        effects[factor] = high_mean - low_mean

    return {
        "anova_table": anova_table.to_dict(),
        "r_squared": model.rsquared,
        "adj_r_squared": model.rsquared_adj,
        "effects": effects,
        "significant_factors": [f for f in factor_cols
                                if anova_table.loc[f, 'PR(>F)'] < 0.05],
        "model_summary": model.summary().as_text()
    }

5. Response Surface Analysis

def fit_response_surface(data, response_col, factor_cols):
    """
    Fit second-order response surface model
    """
    # Build quadratic formula
    linear = ' + '.join(factor_cols)
    quadratic = ' + '.join([f'I({f}**2)' for f in factor_cols])
    interactions = ' + '.join([f'{a}:{b}' for i, a in enumerate(factor_cols)
                               for b in factor_cols[i+1:]])

    formula = f'{response_col} ~ {linear} + {quadratic} + {interactions}'

    model = ols(formula, data=data).fit()

    # Find stationary point
    # Extract coefficients for optimization
    coeffs = model.params

    return {
        "model": model,
        "r_squared": model.rsquared,
        "coefficients": coeffs.to_dict(),
        "significant_terms": [t for t in model.pvalues.index
                             if model.pvalues[t] < 0.05],
        "formula": formula
    }

def find_optimal_conditions(model, factor_cols, bounds, maximize=True):
    """
    Find optimal factor settings using response surface
    """
    from scipy.optimize import minimize

    def predict(x):
        data = pd.DataFrame([dict(zip(factor_cols, x))])
        pred = model.predict(data)[0]
        return -pred if maximize else pred

    # Multiple starts for global optimization
    best_result = None
    for _ in range(20):
        x0 = [np.random.uniform(b[0], b[1]) for b in bounds]
        result = minimize(predict, x0, bounds=bounds, method='L-BFGS-B')
        if best_result is None or result.fun < best_result.fun:
            best_result = result

    optimal = dict(zip(factor_cols, best_result.x))
    optimal_response = -best_result.fun if maximize else best_result.fun

    return {
        "optimal_settings": optimal,
        "predicted_response": optimal_response,
        "optimization_success": best_result.success
    }

6. Confirmation Run Planning

def plan_confirmation_runs(optimal_settings, model, n_runs=5, alpha=0.05):
    """
    Plan confirmation runs at optimal settings
    """
    from scipy import stats

    # Predict at optimal
    data = pd.DataFrame([optimal_settings])
    predicted = model.predict(data)[0]

    # Prediction interval
    pred_se = np.sqrt(model.mse_resid)  # Simplified
    t_val = stats.t.ppf(1 - alpha/2, model.df_resid)

    pi_lower = predicted - t_val * pred_se * np.sqrt(1 + 1/len(model.model.data.orig_endog))
    pi_upper = predicted + t_val * pred_se * np.sqrt(1 + 1/len(model.model.data.orig_endog))

    return {
        "optimal_settings": optimal_settings,
        "predicted_response": predicted,
        "prediction_interval": {
            "lower": pi_lower,
            "upper": pi_upper,
            "confidence": 1 - alpha
        },
        "confirmation_runs": n_runs,
        "acceptance_criterion": f"Mean of {n_runs} runs should fall within [{pi_lower:.3f}, {pi_upper:.3f}]"
    }

Process Integration

This skill integrates with the following processes:

design-of-experiments-execution.js
root-cause-analysis-investigation.js
statistical-process-control-implementation.js

Output Format

{
  "design_type": "2^4 Full Factorial",
  "factors": ["Temperature", "Pressure", "Time", "Catalyst"],
  "num_runs": 16,
  "analysis": {
    "significant_factors": ["Temperature", "Pressure"],
    "significant_interactions": ["Temperature:Pressure"],
    "r_squared": 0.94
  },
  "optimal_settings": {
    "Temperature": 180,
    "Pressure": 2.5,
    "Time": 60,
    "Catalyst": 0.5
  },
  "predicted_response": 95.3,
  "confirmation_plan": {
    "runs": 5,
    "prediction_interval": [93.1, 97.5]
  }
}

Best Practices

Start with screening - Use Plackett-Burman for many factors
Choose appropriate resolution - Resolution IV minimum for main effects
Include center points - Detect curvature
Randomize run order - Reduce systematic bias
Replicate - Estimate error for significance testing
Confirm results - Always run confirmation experiments

Constraints

Document all experimental conditions
Control nuisance factors
Follow design exactly as planned
Report both practical and statistical significance