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
Workflow Routing
| Trigger | What to do |
|---|---|
| "what control chart should I use for [data]" | Use Control Chart Selection tables (Variable vs Attribute) to pick X-bar/R, X-bar/S, I-MR, p/np/c/u based on data type and subgroup size |
| "set up SPC / calculate control limits for [characteristic]" | Follow Capability Study Process Steps 1-3, then calculate limits via X-bar/R Chart or Individual/Moving Range (I-MR) Chart formulas |
| "is this process in control?" / "interpret this pattern" | Check plotted points against Out-of-Control Rules (Western Electric Rules 1-4 standard; Nelson Rules 5-8 for detailed analysis) |
| "calculate Cpk/Ppk" / "is this process capable?" | Apply Process Capability formulas, compare to Capability Targets (Cpk/Ppk ≥1.33 minimum, ≥1.67 for CC), interpret PPM via the Interpretation table |
| "what's the difference between Cp and Cpk" / "Cpk vs Ppk" | Explain via the Key Difference: Cp/Cpk vs Pp/Ppk table (within-subgroup vs overall variation) |
| "conduct a capability study" | Walk through Capability Study Process Steps 1-5 |
| "is pre-control appropriate here" | Use Pre-Control (Alternative to SPC) criteria and zone rules |
| "generate SPC report/analysis" | Emit using the Output Format template below |
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 | 8 points in a row on same side of CL (some sources: 9) | Process shift/mean 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.
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
| 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
| 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]
Examples
Example 1 — Selecting and setting up a control chart
User: "We're machining a bore diameter on a CNC lathe, subgroup of 5 parts every hour. What chart should we use and what are the control limits?"
Output: Recommends an X-bar/R chart per Control Chart Selection (subgroups n=2-9), calculates UCL/CL/LCL using the A₂/D₃/D₄ constants for n=5, and flags the minimum 20-25 subgroups needed before finalizing limits per the X-bar/R Chart Setup guidance.
Example 2 — Interpreting an out-of-control signal
User: "Our control chart shows 8 consecutive points above the centerline. Is this out of control, and what should we do?"
Output: Identifies this as a Rule 2 violation (run of 7+ points on one side of centerline) per Out-of-Control Rules, explains it indicates a process/mean shift (special cause variation), and recommends investigation per the MNMUK standard (Western Electric Rules 1-4).
Example 3 — Capability assessment for PPAP
User: "Customer wants Ppk for PPAP submission on a critical characteristic. We measured Cpk = 1.45 in production but haven't calculated Ppk yet."
Output: Distinguishes Cpk (within-subgroup, process potential) from Ppk (overall variation, process performance) per the Key Difference: Cp/Cpk vs Pp/Ppk table, calculates Ppk from the overall sample standard deviation, and compares to the CC target of ≥1.67 per Capability Targets, flagging if Ppk falls short of Cpk (indicating between-subgroup variation exists).
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