| name | spc-control-charts |
| description | Statistical Process Control (SPC) — select the correct control chart, interpret out-of-control signals using Western Electric rules, calculate and interpret Cp, Cpk, Pp, Ppk. Use when setting up SPC for a new characteristic, interpreting control chart signals, responding to special cause variation, or auditing SPC implementation. Covers AIAG SPC 2nd edition and IATF 16949 §8.3.3. |
| license | MIT |
| metadata | {"author":"RBraga01","version":"1.1","iso-9001":"9.1","iatf-16949":"8.3.3, 9.1.1","aiag-reference":"AIAG SPC 2nd Edition","domain":"quality-engineering","subdomain":"measurement","industries":"automotive,electronics,aerospace,medical,general","status":"approved","created":"2026-06-06","last_updated":"2026-06-06","updated_by":"migmcc","reviewed_by":"RBraga01","standard_edition":"AIAG SPC 2nd Edition (2005)"} |
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.
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.
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.
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
Step 5 — Respond to an out-of-control condition
- Stop the process (or place affected output on hold) — do not continue producing to an out-of-control process
- Contain — identify affected output since last in-control point
- Investigate — ask: what changed? (material lot, operator, shift, tooling, environment)
- Identify root cause — use 5-Why or Fishbone (is-is-not to scope the problem first)
- Correct — implement correction and verify the process returns to control
- Document — note the signal, investigation, and action taken on the chart (or in the log)
- 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."
Step 6 — Audit an SPC implementation
When reviewing SPC in production or at a supplier:
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 |
