Statistical Process Control (SPC)

When to Activate This Skill

• "Set up SPC for [characteristic]"

• "Calculate Cpk for [process]"

• "What control chart should I use?"

• "Is this process in control?"

• "Interpret out-of-control pattern"

• "Conduct capability study"

• "What's the difference between Cp and Cpk?"

Purpose of SPC

SPC uses statistical methods to monitor, control, and improve processes by distinguishing between:

• Common cause variation - Normal, inherent process variation

• Special cause variation - Abnormal, assignable causes requiring action

Why SPC Matters

Without SPC:

• React only when defects occur

• Cannot predict process behavior

• May over-adjust stable processes

• Miss early warning signs

With SPC:

• Detect problems before defects

• Understand process capability

• Make data-driven decisions

• Continuously improve

Control Chart Selection

Variable Data Charts (Measurements)

Chart Data Type When to Use

X-bar/R Subgroups n=2-9 Standard variable control chart

X-bar/S Subgroups n≥10 Large subgroups

I-MR Individual measurements Low volume, long cycle, destructive test

Attribute Data Charts (Counts/Categories)

Chart Data Type When to Use

p chart Proportion defective Variable sample size, defective/not

np chart Count of defectives Fixed sample size, defective/not

c chart Defects per unit Fixed area/unit, count defects

u chart Defects per unit Variable area/unit, count defects

X-bar/R Chart

Setup

Parameter Guideline

Subgroup size (n) 3-5 typical, 5 preferred

Subgroup frequency Rational subgrouping - within-subgroup should be homogeneous

Minimum data points 20-25 subgroups before calculating limits

Control Limit Formulas

X-bar Chart:

UCL = X̄̄ + A₂ × R̄ CL = X̄̄ LCL = X̄̄ - A₂ × R̄

R Chart:

UCL = D₄ × R̄ CL = R̄ LCL = D₃ × R̄

Constants (A₂, D₃, D₄)

n A₂ D₃ D₄

2 1.880 0 3.267

3 1.023 0 2.575

4 0.729 0 2.282

5 0.577 0 2.115

6 0.483 0 2.004

Individual/Moving Range (I-MR) Chart

When to Use

• Long cycle time

• Destructive testing

• Expensive testing

• Batch processes

Control Limit Formulas

I Chart:

UCL = X̄ + 2.66 × MR̄ CL = X̄ LCL = X̄ - 2.66 × MR̄

MR Chart:

UCL = 3.267 × MR̄ CL = MR̄ LCL = 0

Out-of-Control Rules

Western Electric Rules (Standard)

Rule Pattern Indicates

Rule 1 1 point beyond 3σ Sudden shift

Rule 2 9 points in a row on same side of CL Process shift

Rule 3 6 points in a row trending (up or down) Trend/drift

Rule 4 14 points in a row alternating up/down Over-adjustment

Nelson Rules (Extended)

Rule Pattern

Rule 5 2 of 3 points beyond 2σ (same side)

Rule 6 4 of 5 points beyond 1σ (same side)

Rule 7 15 points in a row within 1σ of CL

Rule 8 8 points beyond 1σ (both sides)

MNMUK Standard

Use Rules 1-4 (Western Electric) as standard. Apply Nelson rules for critical characteristics or detailed analysis.

Process Capability

Indices Overview

Index Measures Formula

Cp Potential capability (spread) (USL - LSL) / 6σ

Cpk Actual capability (considers centering) Min(Cpu, Cpl)

Pp Process performance (spread) (USL - LSL) / 6s

Ppk Process performance (considers centering) Min(Ppu, Ppl)

Key Difference: Cp/Cpk vs Pp/Ppk

Aspect Cp/Cpk Pp/Ppk

Variation estimate Within-subgroup (R̄/d₂ or S̄/c₄) Overall (sample std dev)

Represents Process potential Process performance

Use when Process in control Initial assessment

Typically Higher Lower

Capability Formulas

Cp (Process Potential):

Cp = (USL - LSL) / 6σ

Where σ = R̄/d₂ (within-subgroup estimate)

Cpk (Process Capability):

Cpu = (USL - X̄̄) / 3σ Cpl = (X̄̄ - LSL) / 3σ Cpk = Min(Cpu, Cpl)

Pp (Process Performance):

Pp = (USL - LSL) / 6s

Where s = sample standard deviation

Ppk (Process Performance Index):

Ppu = (USL - X̄) / 3s Ppl = (X̄ - LSL) / 3s Ppk = Min(Ppu, Ppl)

d₂ Constants

n d₂

2 1.128

3 1.693

4 2.059

5 2.326

6 2.534

Capability Targets

Automotive Industry Standards

Index Minimum Preferred For CC

Cpk 1.33 1.67 1.67

Ppk 1.33 1.67 1.67

Interpretation

Cpk Value PPM (one tail) Interpretation

0.67 22,750 Poor, not capable

1.00 1,350 Barely capable

1.33 32 Capable (minimum automotive)

1.50 3.4 Good

1.67 0.3 Very good (CC target)

2.00 0.001 Excellent

Capability Study Process

Step 1: Plan the Study

• Identify characteristic

• Select measurement system (verify MSA)

• Determine sample size (minimum 30, prefer 50-100)

• Define sampling method

Step 2: Collect Data

• Collect samples under normal conditions

• Record in time order

• Document any special events

Step 3: Analyze Data

• Create histogram (check distribution)

• Check normality

• Calculate statistics

• Create control chart

• Check for statistical control

Step 4: Calculate Capability

• If in control: Calculate Cp, Cpk

• If not in control: Address special causes first, or report Pp, Ppk only

• Compare to requirements

Step 5: Interpret and Act

• Is capability adequate?

• What actions needed?

• Document results

Pre-Control (Alternative to SPC)

When to Use Pre-Control

• Very capable processes (Cpk >1.33)

• Short runs

• Quick setup verification

• Simpler than SPC

Pre-Control Zones

┌─────────────────────────────────────────────┐ │ RED ZONE │ → Stop, adjust ├─────────────────────────────────────────────┤ │ YELLOW ZONE │ → Caution ├─────────────────────────────────────────────┤ │ GREEN ZONE (Middle 50%) │ → OK ├─────────────────────────────────────────────┤ │ YELLOW ZONE │ → Caution ├─────────────────────────────────────────────┤ │ RED ZONE │ → Stop, adjust └─────────────────────────────────────────────┘ LSL Target USL

Pre-Control Rules

• Startup: 5 consecutive in Green = run production

• Running:

• Both in Green → Continue

• One Yellow → Check again immediately

• Both Yellow → Investigate/adjust

• Red → Stop, investigate

Output Format

When generating SPC content:

SPC Analysis

Characteristic Information

Control Chart Data

Control Limits

Process Capability

Assessment

• In Control: Yes / No
• Capable: Yes / No
• Actions Required: [List]

Integration with Related Skills

ControlPlan

Control Plan specifies SPC requirements:

• Which characteristics require SPC

• Sample size and frequency

• Reaction to out-of-control

Load: read ~/.claude/skills/Controlplan/SKILL.md

MSA

SPC validity requires adequate measurement system:

• ndc ≥5 for meaningful SPC

• Poor MSA = poor SPC decisions

• Verify MSA before starting SPC

Load: read ~/.claude/skills/Msa/SKILL.md

AutomotiveManufacturing

Work instructions should include SPC procedures:

• How to collect data

• How to plot points

• How to interpret charts

• What to do when out of control

Load: read ~/.claude/skills/Automotivemanufacturing/SKILL.md

Supplementary Resources

For detailed guidance: read ~/.claude/skills/Spc/CLAUDE.md

For capability study template: read ~/.claude/skills/Spc/templates/capability-study.md

For control chart selection: read ~/.claude/skills/Spc/reference/control-chart-selection.md

For capability indices: read ~/.claude/skills/Spc/reference/capability-indices.md

For out-of-control rules: read ~/.claude/skills/Spc/reference/out-of-control-rules.md