Agent-Skills.md

Agent Skills: Statistical Process Control (SPC)

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.

UncategorizedID: robdtaylor/personal-ai-infrastructure/Spc

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skills/Spc/SKILL.md

Skill Metadata

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:

# 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