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Process capability analysis skill with Cp, Cpk, Pp, Ppk calculations and specification compliance assessment.
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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 | process-capability-calculator |
| description | Process capability analysis skill with Cp, Cpk, Pp, Ppk calculations and specification compliance assessment. |
| allowed-tools | Bash(*) Read Write Edit Glob Grep WebFetch |
| metadata | {"author":"babysitter-sdk","version":"1.0.0","category":"quality-engineering","backlog-id":"SK-IE-015"} |
| 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 process-capability-calculator - a specialized skill for analyzing process capability with respect to specifications.
This skill enables AI-powered capability analysis including:
import numpy as np
from scipy import stats
def calculate_capability_indices(data, usl, lsl, subgroup_size=None):
"""
Calculate Cp, Cpk capability indices
Uses within-subgroup variation (R-bar/d2 or S-bar/c4)
Requires stable process
"""
x = np.array(data)
# Process statistics
x_bar = np.mean(x)
specification_width = usl - lsl
# Estimate sigma within (short-term variation)
if subgroup_size and subgroup_size > 1:
# Use pooled standard deviation or R-bar method
# Simplified: using overall std with bias correction
d2 = {2: 1.128, 3: 1.693, 4: 2.059, 5: 2.326}
# In practice, calculate R-bar from subgroups
sigma_within = np.std(x, ddof=1) # Simplified
else:
# For individuals, use moving range
mr = np.abs(np.diff(x))
mr_bar = np.mean(mr)
sigma_within = mr_bar / 1.128 # d2 for n=2
# Capability indices
cp = specification_width / (6 * sigma_within)
cpu = (usl - x_bar) / (3 * sigma_within)
cpl = (x_bar - lsl) / (3 * sigma_within)
cpk = min(cpu, cpl)
return {
"Cp": round(cp, 3),
"Cpk": round(cpk, 3),
"Cpu": round(cpu, 3),
"Cpl": round(cpl, 3),
"sigma_within": round(sigma_within, 4),
"process_mean": round(x_bar, 4),
"usl": usl,
"lsl": lsl,
"interpretation": interpret_capability(cpk)
}
def interpret_capability(cpk):
if cpk >= 2.0:
return "World class (6 sigma)"
elif cpk >= 1.67:
return "Excellent (5 sigma)"
elif cpk >= 1.33:
return "Good (4 sigma)"
elif cpk >= 1.0:
return "Capable (3 sigma)"
elif cpk >= 0.67:
return "Poor (2 sigma)"
else:
return "Incapable (< 2 sigma)"
def calculate_performance_indices(data, usl, lsl):
"""
Calculate Pp, Ppk performance indices
Uses overall variation (long-term)
Does not require stable process
"""
x = np.array(data)
x_bar = np.mean(x)
sigma_overall = np.std(x, ddof=1) # Sample standard deviation
specification_width = usl - lsl
# Performance indices
pp = specification_width / (6 * sigma_overall)
ppu = (usl - x_bar) / (3 * sigma_overall)
ppl = (x_bar - lsl) / (3 * sigma_overall)
ppk = min(ppu, ppl)
return {
"Pp": round(pp, 3),
"Ppk": round(ppk, 3),
"Ppu": round(ppu, 3),
"Ppl": round(ppl, 3),
"sigma_overall": round(sigma_overall, 4),
"process_mean": round(x_bar, 4),
"interpretation": interpret_capability(ppk)
}
def test_normality(data):
"""
Test data for normality using multiple tests
"""
x = np.array(data)
n = len(x)
results = {}
# Shapiro-Wilk test (best for n < 50)
if n <= 5000:
stat, p_value = stats.shapiro(x)
results["shapiro_wilk"] = {
"statistic": round(stat, 4),
"p_value": round(p_value, 4),
"conclusion": "Normal" if p_value > 0.05 else "Non-normal"
}
# Anderson-Darling test
ad_result = stats.anderson(x, dist='norm')
results["anderson_darling"] = {
"statistic": round(ad_result.statistic, 4),
"critical_values": dict(zip(
['15%', '10%', '5%', '2.5%', '1%'],
[round(cv, 4) for cv in ad_result.critical_values]
)),
"conclusion": "Normal" if ad_result.statistic < ad_result.critical_values[2] else "Non-normal"
}
# D'Agostino-Pearson test (n > 20)
if n >= 20:
stat, p_value = stats.normaltest(x)
results["dagostino_pearson"] = {
"statistic": round(stat, 4),
"p_value": round(p_value, 4),
"conclusion": "Normal" if p_value > 0.05 else "Non-normal"
}
# Overall assessment
normal_count = sum(1 for r in results.values() if r.get("conclusion") == "Normal")
results["overall_assessment"] = "Normal" if normal_count >= 2 else "Non-normal"
# Descriptive statistics
results["descriptive"] = {
"skewness": round(stats.skew(x), 3),
"kurtosis": round(stats.kurtosis(x), 3),
"n": n
}
return results
from scipy.stats import boxcox
from scipy.optimize import brentq
def nonnormal_capability(data, usl, lsl, method='percentile'):
"""
Calculate capability for non-normal data
Methods:
- percentile: Use empirical percentiles
- boxcox: Transform to normal using Box-Cox
- weibull: Fit Weibull distribution
"""
x = np.array(data)
if method == 'percentile':
# Percentile method (distribution-free)
p0135 = np.percentile(x, 0.135) # Lower 0.135%
p99865 = np.percentile(x, 99.865) # Upper 99.865%
median = np.median(x)
# Equivalent Cp
spread = p99865 - p0135
cp_equiv = (usl - lsl) / spread if spread > 0 else np.inf
# Equivalent Cpk
cpu_equiv = (usl - median) / ((p99865 - median) * 2) if (p99865 - median) > 0 else np.inf
cpl_equiv = (median - lsl) / ((median - p0135) * 2) if (median - p0135) > 0 else np.inf
cpk_equiv = min(cpu_equiv, cpl_equiv)
return {
"method": "percentile",
"Cp_equivalent": round(cp_equiv, 3),
"Cpk_equivalent": round(cpk_equiv, 3),
"p0135": round(p0135, 4),
"p99865": round(p99865, 4),
"median": round(median, 4)
}
elif method == 'boxcox':
# Box-Cox transformation
# Shift data if necessary (must be positive)
shift = 0
if np.min(x) <= 0:
shift = abs(np.min(x)) + 1
x_shifted = x + shift
else:
x_shifted = x
# Find optimal lambda
transformed, lambda_opt = boxcox(x_shifted)
# Transform specification limits
if lambda_opt == 0:
usl_t = np.log(usl + shift)
lsl_t = np.log(lsl + shift)
else:
usl_t = ((usl + shift)**lambda_opt - 1) / lambda_opt
lsl_t = ((lsl + shift)**lambda_opt - 1) / lambda_opt
# Calculate capability on transformed data
result = calculate_capability_indices(transformed, usl_t, lsl_t)
result["method"] = "boxcox"
result["lambda"] = round(lambda_opt, 4)
result["shift"] = shift
return result
return None
def calculate_ppm_sigma(cpk, process_centered=True):
"""
Calculate expected PPM defect rate and sigma level
"""
if process_centered:
# Symmetric distribution around target
z = 3 * cpk
ppm_total = 2 * (1 - stats.norm.cdf(z)) * 1e6
ppm_upper = ppm_total / 2
ppm_lower = ppm_total / 2
else:
# Use Cpk for worst side
z = 3 * cpk
ppm_worst = (1 - stats.norm.cdf(z)) * 1e6
ppm_total = ppm_worst # Approximate
# Sigma level (with 1.5 sigma shift convention)
sigma_short_term = 3 * cpk
sigma_long_term = sigma_short_term + 1.5 # Industry convention
return {
"ppm_total": round(ppm_total, 1),
"ppm_percent": round(ppm_total / 1e4, 4),
"sigma_short_term": round(sigma_short_term, 2),
"sigma_long_term": round(sigma_long_term, 2),
"yield_percent": round((1 - ppm_total / 1e6) * 100, 4),
"dpmo": round(ppm_total, 0)
}
# Sigma level reference
SIGMA_REFERENCE = {
1: {"cpk": 0.33, "ppm": 691462, "yield": 30.85},
2: {"cpk": 0.67, "ppm": 308538, "yield": 69.15},
3: {"cpk": 1.00, "ppm": 66807, "yield": 93.32},
4: {"cpk": 1.33, "ppm": 6210, "yield": 99.38},
5: {"cpk": 1.67, "ppm": 233, "yield": 99.977},
6: {"cpk": 2.00, "ppm": 3.4, "yield": 99.99966}
}
def generate_capability_report(data, usl, lsl, target=None):
"""
Generate comprehensive capability analysis report
"""
x = np.array(data)
report = {
"summary": {
"n": len(x),
"usl": usl,
"lsl": lsl,
"target": target or (usl + lsl) / 2,
"specification_width": usl - lsl
},
"descriptive_statistics": {
"mean": round(np.mean(x), 4),
"std": round(np.std(x, ddof=1), 4),
"min": round(np.min(x), 4),
"max": round(np.max(x), 4),
"range": round(np.ptp(x), 4),
"median": round(np.median(x), 4)
}
}
# Normality test
normality = test_normality(x)
report["normality_test"] = normality
# Capability indices
if normality["overall_assessment"] == "Normal":
report["capability_indices"] = calculate_capability_indices(x, usl, lsl)
report["performance_indices"] = calculate_performance_indices(x, usl, lsl)
report["analysis_method"] = "Normal distribution"
else:
report["capability_indices"] = nonnormal_capability(x, usl, lsl, method='percentile')
report["performance_indices"] = nonnormal_capability(x, usl, lsl, method='boxcox')
report["analysis_method"] = "Non-normal - used percentile and Box-Cox methods"
# PPM and sigma
cpk = report["capability_indices"].get("Cpk") or report["capability_indices"].get("Cpk_equivalent", 0)
report["defect_prediction"] = calculate_ppm_sigma(cpk)
# Out of spec analysis
out_of_spec_high = np.sum(x > usl)
out_of_spec_low = np.sum(x < lsl)
report["observed_defects"] = {
"above_usl": int(out_of_spec_high),
"below_lsl": int(out_of_spec_low),
"total_out_of_spec": int(out_of_spec_high + out_of_spec_low),
"observed_ppm": round((out_of_spec_high + out_of_spec_low) / len(x) * 1e6, 1)
}
# Recommendations
report["recommendations"] = generate_recommendations(report)
return report
def generate_recommendations(report):
cpk = report["capability_indices"].get("Cpk") or report["capability_indices"].get("Cpk_equivalent", 0)
recommendations = []
if cpk < 1.0:
recommendations.append("Process is not capable - immediate improvement required")
recommendations.append("Reduce variation or widen specifications")
elif cpk < 1.33:
recommendations.append("Process marginally capable - continuous improvement recommended")
elif cpk < 1.67:
recommendations.append("Process capable - maintain monitoring")
else:
recommendations.append("Process highly capable - consider reducing inspection")
# Centering
mean = report["descriptive_statistics"]["mean"]
target = report["summary"]["target"]
if abs(mean - target) > (report["summary"]["specification_width"] * 0.1):
recommendations.append(f"Process off-center by {abs(mean - target):.3f} - consider centering adjustment")
return recommendations
This skill integrates with the following processes:
statistical-process-control-implementation.jsdesign-of-experiments-execution.jsroot-cause-analysis-investigation.js{
"summary": {
"n": 150,
"usl": 10.5,
"lsl": 9.5
},
"capability_indices": {
"Cp": 1.45,
"Cpk": 1.32,
"interpretation": "Good (4 sigma)"
},
"defect_prediction": {
"ppm_total": 966,
"sigma_long_term": 4.5,
"yield_percent": 99.903
},
"recommendations": [
"Process capable - maintain monitoring",
"Consider centering adjustment"
]
}