spc-control-charts

Statistical Process Control (SPC)

When to use

Use this skill when:

• Selecting the correct control chart type for a process characteristic
• Interpreting control chart signals — is this special cause or common cause?
• Calculating Cp, Cpk, Pp, Ppk and determining if the process is capable
• Responding to an out-of-control signal on a production line
• Setting up SPC for a new special characteristic (PPAP/APQP requirement)
• Auditing an SPC system for correctness and adequacy
• Explaining SPC results to a customer or during an audit

Prerequisites

• The characteristic to monitor (variable or attribute data)
• Production data (minimum 25 subgroups for control limits, 100+ pieces for capability)
• MSA study completed and %GRR < 30% for variable charts
• Process specification (nominal + tolerance) for capability calculations
• Subgroup size decided based on rational subgrouping principle

Workflow

Step 1 — Select the correct control chart

Variable data (measured values — length, weight, pressure, temperature)

| Chart | When to use |

|-------|------------|

| X̄-R (X-bar/Range) | Subgroup size 2–9; most common in manufacturing |

| X̄-S (X-bar/Sigma) | Subgroup size ≥ 10; better sensitivity to spread |

| I-MR (Individuals/Moving Range) | Subgroup size = 1; one measurement per inspection (slow processes, destructive tests) |

Attribute data (counts, pass/fail, defect rates)

| Chart | When to use |

|-------|------------|

| p-chart | Proportion defective; variable subgroup size |

| np-chart | Number defective; constant subgroup size |

| c-chart | Count of defects per unit; constant inspection area |

| u-chart | Defects per unit; variable inspection area |

Decision rule: If you can measure it with a number, use a variable chart. Variable charts are more sensitive and require smaller samples to detect process shifts.

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Step 2 — Calculate control limits

X̄-R chart

From at least 25 subgroups of size n:

• Centre line (X̄̄): Grand average of all subgroup means
• UCL_X̄ = X̄̄ + A₂ × R̄
• LCL_X̄ = X̄̄ − A₂ × R̄
• Centre line (R̄): Average of all subgroup ranges
• UCL_R = D₄ × R̄
• LCL_R = D₃ × R̄ (= 0 for n ≤ 6)

Constants for common subgroup sizes:

| n | A₂ | D₃ | D₄ |

|---|----|----|-----|

| 2 | 1.880 | 0 | 3.267 |

| 3 | 1.023 | 0 | 2.574 |

| 4 | 0.729 | 0 | 2.282 |

| 5 | 0.577 | 0 | 2.114 |

Important: Control limits are calculated FROM THE DATA — never set them to match the specification limits. Specification limits and control limits are completely separate concepts.

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Step 3 — Apply Western Electric Rules (out-of-control signals)

Divide the control chart into zones: Zone A (2–3σ from centre), Zone B (1–2σ), Zone C (0–1σ).

| Rule | Signal | Interpretation |

|------|--------|----------------|

| Rule 1 | 1 point beyond 3σ (outside control limits) | Large, immediate shift |

| Rule 2 | 9 consecutive points on same side of centre line | Process mean has shifted |

| Rule 3 | 6 consecutive points steadily increasing or decreasing | Trend — tool wear, drift |

| Rule 4 | 14 consecutive points alternating up and down | Systematic variation — two alternating distributions |

| Rule 5 | 2 of 3 consecutive points in Zone A or beyond (same side) | Large shift signal |

| Rule 6 | 4 of 5 consecutive points in Zone B or beyond (same side) | Moderate shift |

| Rule 7 | 15 consecutive points in Zone C (either side of centre line) | Stratification — data from two separate distributions |

| Rule 8 | 8 consecutive points beyond Zone C (either side) | Mixture — sampling from two processes |

Action required for ANY rule violation: Stop and investigate immediately. Do not reset control limits. Do not restart until root cause is identified.

Most commonly applied in automotive: Rules 1, 2, 3 minimum. Rules 1–8 for safety-critical characteristics.

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Step 4 — Calculate and interpret process capability

Capability data requirements: Process capability is only valid when calculated on a process that is in statistical control (no out-of-control signals) and with a minimum of 100 consecutive parts from that stable process. Fewer parts produce unreliable Cpk estimates — a Cpk calculated on 30 parts can vary by ±0.3 from the true value. Do not report Cpk based on fewer than 100 parts as a production capability figure; label it "preliminary" and state the sample size.

Short-term capability (within-subgroup variation):

• Cp = (USL − LSL) / (6σ̂) — capability — process spread vs. tolerance
• Cpk = min[(USL − X̄̄) / (3σ̂), (X̄̄ − LSL) / (3σ̂)] — centred capability — accounts for process mean location

σ̂ = R̄ / d₂ (for X̄-R chart)

Long-term performance (total variation including between-subgroup):

• Pp = (USL − LSL) / (6s) — same formula but uses overall standard deviation s
• Ppk = min[(USL − X̄̄) / (3s), (X̄̄ − LSL) / (3s)]

Acceptance criteria

| Index | Minimum | Target |

|-------|---------|--------|

| Cpk | 1.33 | 1.67 |

| Ppk | 1.33 | 1.67 |

| Cpk | Interpretation | PPAP action |

|-----|---------------|-------------|

| ≥ 1.67 | Excellent | ✅ Accepted |

| 1.33 – 1.67 | Acceptable | ✅ Accepted — monitor |

| 1.00 – 1.33 | Marginal | ⚠️ Customer approval required; add control measures |

| < 1.00 | Not capable | ❌ 100% inspection required; corrective action mandatory |

Cp vs. Cpk relationship

• Cp = Cpk: process is perfectly centred
• Cp > Cpk: process is off-centre — improve centering before widening control limits
• Never report only Cp without Cpk — a process can be off-centre and still show a good Cp

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Step 5 — Respond to an out-of-control condition

1. Stop the process (or place affected output on hold) — do not continue producing to an out-of-control process
2. Contain — identify affected output since last in-control point
3. Investigate — ask: what changed? (material lot, operator, shift, tooling, environment)
4. Identify root cause — use 5-Why or Fishbone (is-is-not to scope the problem first)
5. Correct — implement correction and verify the process returns to control
6. Document — note the signal, investigation, and action taken on the chart (or in the log)
7. Update PFMEA and Control Plan if the root cause reveals a new failure mode

Do NOT simply recalculate control limits after a shift to make the chart "look in control."

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Step 6 — Audit an SPC implementation

When reviewing SPC in production or at a supplier:

• [ ] Correct chart type selected for data type (variable vs. attribute)
• [ ] Minimum 25 subgroups used to calculate initial control limits
• [ ] Control limits calculated from process data — NOT set to specification limits
• [ ] Western Electric rules applied (minimum Rule 1, 2, 3)
• [ ] Out-of-control signals are annotated on the chart with the action taken
• [ ] Process capability calculated on stable (in-control) process only
• [ ] Cpk ≥ 1.33 minimum; 1.67 for special characteristics
• [ ] MSA study complete and %GRR < 30% for the gauge being used
• [ ] Control chart is used for decision-making — not filled in retroactively

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Validation criteria

An SPC implementation is adequate when:

• Chart type matches data type and subgroup size
• Control limits calculated from minimum 25 subgroups of production data
• Process in statistical control before capability is calculated
• Cpk ≥ 1.33 (minimum) for all monitored characteristics
• Out-of-control signals trigger documented investigation and corrective action

Common mistakes

• Setting control limits equal to specification limits (a fundamental SPC error — these are different concepts)
• Calculating capability on an out-of-control process (meaningless — must be stable first)
• Reporting Cp but not Cpk — hides off-centre processes
• Using only n=1 individual charts when subgrouping would reveal more
• Filling in control charts retroactively at end of shift — defeats the purpose of real-time monitoring
• Recalculating control limits to eliminate out-of-control points without identifying root cause
• Reporting Cpk = 1.45 based on 30 parts — too few; minimum 100 pieces for reliable capability

Output Format

At the start of each use, ask the user:

> "How would you like to receive the output?

> A — Structured Markdown (formatted tables and sections, ready to copy)

> B — Plain tables (simplified structure for Excel or Word)

> C — Narrative report (flowing text for a formal document or email)

>

> Default: A."

Adapt all output sections to the chosen format. If the platform or session context already defines a format preference, skip this question.

Changelog

| Version | Date | Author | Change |

|---------|------|--------|--------|

| 1.0 | 2026-06-06 | @RBraga01 | Initial release |

| 1.1 | 2026-06-06 | @migmcc | Added 100-part minimum requirement for valid capability study in Step 4; clarified in-control prerequisite before capability calculation |