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Design of Experiments planning and analysis skill for factorial and response surface experiments.
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npx skills add https://github.com/a5c-ai/babysitter --skill doe-designer명령은 한 줄로 유지됩니다. 복사하기 전에 가로로 스크롤해 전체 내용을 확인하세요.
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Reference for querying the Atlas knowledge graph through its MCP tools — the SECONDARY enrichment/comparison layer that adds best-practice context to systems you have ALREADY scanned from your real sources (`az`, repos, dirs). Use when you need to look up nodes, edges, kinds, clusters, stats, or wiki pages in Atlas to compare against your real inventory. (atlas graph, query atlas, atlas mcp, search the graph, graph neighbors, atlas record, atlas kinds, enrichment layer)
Atlas turns your STATED NEED into a real systems atlas by SCANNING your actual sources (Azure via `az`, git repos, local dirs) and process/data mining them, THEN enriching against the Atlas knowledge graph. Use this skill when asked to inventory/map your real systems, scan your cloud + repos + directories, mine the real processes or data they contain, or collect their real constraints/gotchas. (atlas, scan my systems, inventory our azure account, map my repos, real systems atlas, process mining, data mining, collect nuances, system discovery)
This skill should be used when the user asks to "find skills in the wild", "assimilate popular workflows", "discover SKILL.md files in repos", "research external skills", "find workflow patterns", "survey the skill landscape", "what skills exist out there", or wants to investigate public repositories for extractable processes, babysitter plugins, and reusable procedural insights. Searches GitHub for SKILL.md files, classifies repos by archetype, and maintains structured research under docs/reference-repos/.
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SOC 직업 분류 기준
| name | doe-designer |
| description | Design of Experiments planning and analysis skill for factorial and response surface experiments. |
| allowed-tools | Bash(*) Read Write Edit Glob Grep WebFetch |
| metadata | {"author":"babysitter-sdk","version":"1.0.0","category":"quality-engineering","backlog-id":"SK-IE-017"} |
| graph | {"domains":["domain:industrial-engineering"],"skillAreas":["skill-area:statistical-analysis","skill-area:organizational-design","skill-area:data-analysis"],"roles":["role:operations-analyst","role:research-engineer"]} |
You are doe-designer - a specialized skill for designing, executing, and analyzing designed experiments for process optimization.
This skill enables AI-powered DOE including:
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"
}
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")
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"
}
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()
}
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
}
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}]"
}
This skill integrates with the following processes:
design-of-experiments-execution.jsroot-cause-analysis-investigation.jsstatistical-process-control-implementation.js{
"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]
}
}