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Spc skill

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This skill helps you implement SPC charting and capability analysis to monitor processes and drive data-driven improvements.

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SKILL.md

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---
name: Spc
description: 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.
---

# 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
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:

```markdown
# 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`

Overview

This skill implements Statistical Process Control (SPC) functionality including control chart creation, process capability analysis, and interpretation of out-of-control signals. It guides chart selection (X-bar/R, X-bar/S, I-MR, p/np/c/u), computes Cp/Cpk and Pp/Ppk, and recommends actions based on standard rules and automotive targets. The skill integrates MSA checks and Control Plan requirements for robust studies.

How this skill works

Provide characteristic details, sample data, subgroup size and spec limits; the skill chooses an appropriate chart, computes control limits using standard constants, and plots X̄, R, S, or MR as applicable. It applies Western Electric and optional Nelson rules to flag out-of-control patterns and calculates capability indices using within-subgroup or overall variation depending on control status. Results include control limits, capability indices, assessment (in control / capable), and recommended next steps.

When to use it

When you say 'SPC', 'control chart', 'statistical control', or 'out of control'.
To calculate Cpk, Ppk, Cp, or Pp for a process or characteristic.
When selecting the correct chart (X-bar/R, I-MR, p/np/c/u) for measurement or attribute data.
To verify process stability before running a capability study or reporting Cpk.
When interpreting special-cause patterns (Western Electric / Nelson rules).
To incorporate SPC requirements from a Control Plan or validate measurement system adequacy with MSA.

Best practices

Use rational subgrouping and typical subgroup sizes (n=3–5 for X-bar/R; n≥10 for X-bar/S).
Collect time-ordered data and at least 20–25 subgroups before fixing limits for X-bar/R charts.
Verify measurement system (MSA) before relying on SPC; ndc should be ≥5 for meaningful results.
If process is not in control, address special causes before reporting Cp/Cpk; otherwise report Pp/Ppk.
Follow Western Electric rules as default; apply Nelson rules for critical characteristics.
Document sampling plan, special events, and any adjustments in the capability study report.

Example use cases

Set up an X-bar/R chart for a machining dimension with subgroup size 4 and determine if the process is in control.
Calculate Cpk and Ppk for an assembly torque characteristic and compare against automotive targets (≥1.33 preferred).
Choose between I-MR and X-bar/R when measurements are individual or subgrouped.
Interpret a run of 6 points trending upward and recommend investigation actions.
Run a capability study: plan, collect 50 samples, check control, then compute Cp/Cpk if stable.
Use pre-control zones for quick setup verification on a very capable short-run process.

FAQ

When should I use Cp/Cpk versus Pp/Ppk?

Use Cp/Cpk when the process is in statistical control and within-subgroup variation represents true process variation. Use Pp/Ppk for initial assessments or when the process is not in control, since they use overall variation.

How many subgroups or samples do I need for a capability study?

Plan for a minimum of 30 samples, preferably 50–100. For control charts, have at least 20–25 subgroups before calculating stable control limits for X-bar/R.