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)

Attribute Data Charts (Counts/Categories)

X-bar/R Chart

Setup

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)

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)

Nelson Rules (Extended)

MNMUK Standard

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

Important: Western Electric Rule 2 triggers at 7 or more consecutive points on one side of the centerline (some references cite 8 or 9 — the broadly accepted standard is that 7+ points on one side constitutes an out-of-control signal requiring investigation). A run of 7 consecutive points on one side of the centerline IS an out-of-control condition.

Process Capability

Indices Overview

Key Difference: Cp/Cpk vs Pp/Ppk

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

Capability Targets

Automotive Industry Standards

Interpretation

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

1. Startup: 5 consecutive in Green = run production
2. 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
| Field | Value |
|-------|-------|
| **Characteristic** | [Description] |
| **Specification** | [LSL - USL] |
| **Target** | [Nominal] |
| **Chart Type** | [X-bar/R, I-MR, etc.] |

## Control Chart Data
| Subgroup | X̄ (or X) | R (or MR) |
|----------|----------|-----------|
| 1 | | |
| ... | | |

## Control Limits
| Chart | LCL | CL | UCL |
|-------|-----|----|----|
| X-bar | | | |
| R | | | |

## Process Capability
| Index | Value | Requirement | Status |
|-------|-------|-------------|--------|
| Cpk | | ≥1.33 | PASS/FAIL |
| Ppk | | ≥1.33 | PASS/FAIL |

## 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