Workflow 1: Process Capability Analysis¶

Process capability analysis evaluates whether your process can consistently meet specification limits. This is essential for Six Sigma DMAIC projects, quality control, and manufacturing validation.

When to Use This Workflow¶

✅ Quality verification: Check if process meets customer specifications
✅ Process validation: Demonstrate capability for new products or processes
✅ Continuous improvement: Benchmark performance over time
✅ Supplier qualification: Assess supplier quality capability

Quick Start (8 Lines)¶

import daspi as dsp

# Load your data
df = dsp.load_dataset("drop_card")
spec_limits = dsp.SpecLimits(0, float(df.loc[0, "usl"]))

# Run analysis
chart = dsp.ProcessCapabilityAnalysisCharts(
    source=df,
    target="distance",
    spec_limits=spec_limits,
    hue="method"
).plot().stripes().label(info=True)

chart.show()

Process Capability Analysis Example Example output: 5-panel capability analysis showing distribution, Cp/Cpk indices, Pp/Ppk indices, normal probability plot, and statistical summary

What You Get¶

The output includes 5 integrated panels:

Run chart: Shows data over observation order (detect trends/shifts)
Probability plot: Tests normality assumption (Q-Q plot)
Distribution histogram: Visualizes process spread vs spec limits
Cpk analysis: Short-term capability (accounts for centering)
Cp analysis: Long-term capability (assumes perfect centering)

Automatic interpretation includes: - Cp, Cpk, Pp, Ppk values with confidence intervals - Sigma level (Z-score) - Process performance assessment - Timestamp and analysis metadata

Understanding the Metrics¶

Cp (Process Capability)¶

Measures potential capability assuming perfect centering
Formula: Cp = (USL - LSL) / (6σ)
Target: ≥ 1.33 (manufacturing), ≥ 1.67 (critical processes)

Cpk (Adjusted Process Capability)¶

Measures actual capability considering process centering
Formula: Cpk = min(Cpu, Cpl) where:
Cpu = (USL - μ) / (3σ)
Cpl = (μ - LSL) / (3σ)
Target: ≥ 1.33 (manufacturing), ≥ 1.67 (critical processes)

Pp / Ppk (Process Performance)¶

Long-term capability indices using overall standard deviation
Similar interpretation as Cp/Cpk
Used for overall process assessment

Sigma Level¶

Six Sigma metric: higher is better
3-sigma: 99.73% within limits (2,700 DPMO)
6-sigma: 99.9997% within limits (3.4 DPMO)

Real-World Example: Manufacturing Validation¶

import daspi as dsp

# Load measurement data
df = dsp.load_dataset("drop_card")

# Define specification limits (from customer requirements)
spec_limits = dsp.SpecLimits(lower=0, upper=50)  # in cm

# Compare two manufacturing methods
chart = dsp.ProcessCapabilityAnalysisCharts(
    source=df,
    target="distance",
    spec_limits=spec_limits,
    hue="method",  # Compare methods side-by-side
    strategy='norm',  # Assume normal distribution
    agreement=6  # 6-sigma spread
).plot().stripes(
    mean=True,
    median=True,
    control_limits=True
).label(
    fig_title="Drop Card Manufacturing Capability",
    sub_title="Comparison of parallel vs perpendicular methods",
    target_label="Drop Distance (cm)",
    info=True
)

chart.save("capability_analysis.png")

# Extract capability metrics
processes = chart.processes()
for method, estimator in processes.items():
    desc = estimator.describe()
    print(f"\n{method}:")
    print(f"  Cp:  {desc.loc['cp'].iloc[0]:.3f}")
    print(f"  Cpk: {desc.loc['cpk'].iloc[0]:.3f}")
    print(f"  Sigma Level: {desc.loc['sigma_level'].iloc[0]:.2f}")

Advanced Options¶

Custom Distribution Strategy¶

# Auto-fit best distribution
chart = dsp.ProcessCapabilityAnalysisCharts(
    source=df,
    target="measurement",
    spec_limits=spec_limits,
    strategy='fit',  # Fit best distribution
    possible_dists=('norm', 'lognorm', 'weibull_min')
).plot().stripes().label(info=True)

One-Sided Specifications¶

# Only upper spec limit (e.g., defect rate, contamination)
spec_limits = dsp.SpecLimits(upper=100)

# Only lower spec limit (e.g., strength, yield)
spec_limits = dsp.SpecLimits(lower=500)

Subgroup Analysis¶

# Analyze by production shift, operator, or machine
chart = dsp.ProcessCapabilityAnalysisCharts(
    source=df,
    target="dimension",
    spec_limits=spec_limits,
    hue="shift",  # Compare day/night shifts
).plot().stripes().label(info=True)

Interpretation Guidelines¶

Cpk ≥ 1.67 (Excellent)¶

✅ Process is highly capable
✅ Very low defect rate expected
✅ Suitable for critical characteristics

1.33 ≤ Cpk < 1.67 (Acceptable)¶

✅ Process is capable
⚠️ Monitor regularly for shifts
⚠️ Consider improvement for critical features

1.00 ≤ Cpk < 1.33 (Marginal)¶

⚠️ Process barely meets requirements
⚠️ High defect risk with any process shift
👉 Improvement strongly recommended

Cpk < 1.00 (Inadequate)¶

❌ Process cannot meet specifications
❌ High defect rate expected
👉 Immediate improvement required

Common Issues & Solutions¶

Issue: Non-normal distribution¶

Solution: Use strategy='fit' to find best-fit distribution, or apply transformation.

Issue: Cpk << Cp¶

Cause: Process is not centered between spec limits
Solution: Adjust process target/mean

Issue: Cpk declining over time¶

Cause: Process drift, tool wear, or increased variation
Solution: Implement SPC monitoring (Workflow 3)

Next Steps¶

Workflow 2: Root Cause Analysis — Identify factors affecting capability
Workflow 3: SPC Charts — Monitor capability over time
Related: Gage R&R — Ensure measurement system is adequate