Spc

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

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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

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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

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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

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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

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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.

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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

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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

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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

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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

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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]

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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.

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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).

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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).

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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

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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