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.

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	D₄
2	1.880	3.267
3	1.023	2.574
4	0.729	2.282
5	0.577	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:

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

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