Implement SPC charting, process capability analysis, and control chart interpretation. Covers control chart selection, capability indices, and out-of-control rules. USE WHEN user says 'SPC', 'Cpk', 'Ppk', 'control chart', 'process capability', 'X-bar R', 'statistical control', or 'out of control'. Integrates with ControlPlan, MSA, and AutomotiveManufacturing skills.
SPC uses statistical methods to monitor, control, and improve processes by distinguishing between:
Without SPC:
With SPC:
| 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 |
| 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 |
| 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 |
X-bar Chart:
UCL = X̄̄ + A₂ × R̄
CL = X̄̄
LCL = X̄̄ - A₂ × R̄
R Chart:
UCL = D₄ × R̄
CL = R̄
LCL = D₃ × R̄
| 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 |
I Chart:
UCL = X̄ + 2.66 × MR̄
CL = X̄
LCL = X̄ - 2.66 × MR̄
MR Chart:
UCL = 3.267 × MR̄
CL = MR̄
LCL = 0
| 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 |
| 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) |
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.
| 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) |
| 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 |
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)
| n | d₂ |
|---|---|
| 2 | 1.128 |
| 3 | 1.693 |
| 4 | 2.059 |
| 5 | 2.326 |
| 6 | 2.534 |
| Index | Minimum | Preferred | For CC |
|---|---|---|---|
| Cpk | 1.33 | 1.67 | 1.67 |
| Ppk | 1.33 | 1.67 | 1.67 |
| 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 |
┌─────────────────────────────────────────────┐
│ RED ZONE │ → Stop, adjust
├─────────────────────────────────────────────┤
│ YELLOW ZONE │ → Caution
├─────────────────────────────────────────────┤
│ GREEN ZONE (Middle 50%) │ → OK
├─────────────────────────────────────────────┤
│ YELLOW ZONE │ → Caution
├─────────────────────────────────────────────┤
│ RED ZONE │ → Stop, adjust
└─────────────────────────────────────────────┘
LSL Target USL
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]
Control Plan specifies SPC requirements:
Load: read ~/.claude/skills/Controlplan/SKILL.md
SPC validity requires adequate measurement system:
Load: read ~/.claude/skills/Msa/SKILL.md
Work instructions should include SPC procedures:
Load: read ~/.claude/skills/Automotivemanufacturing/SKILL.md
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