Quality Tools
Control Chart Generator
Plot process data against its centre line and control limits to see whether variation is common-cause or a signal to act on.
Process Control Chart
Control Limits
UCL: 10.6924
Center Line: 10.1900
LCL: 9.6876
σ (MR̄ ÷ 1.128): 0.1675
Process Status
Status:In Control
Out of Control: 0 points
Trending: 0 points
Data Summary
Sample Size: 10
Range: 0.4000
Mean: 10.1900 mm
Control Chart Rules & Interpretation
Out of Control Signals:
- Any point beyond control limits (±3σ)
- 9+ consecutive points on one side of center line
- 2 of 3 consecutive points beyond warning limits (±2σ), same side
- Unusual patterns or trends
Process Capability:
- Cpk ≥ 1.33: Excellent capability
- Cpk ≥ 1.0: Adequate capability
- Cpk < 1.0: Poor capability
- Cp: Potential capability (centered process)
What is a control chart?
Control charts are statistical tools used to monitor process performance over time and detect when a process goes “out of control” — when a special cause, rather than normal variation, is at work.
| Component | Meaning |
|---|---|
| Centre line (CL) | Process average |
| Upper control limit (UCL) | CL + 3σ |
| Lower control limit (LCL) | CL − 3σ |
| Warning limits | CL ± 2σ (optional) |
This tool draws an individuals (I) chart, so σ is estimated from the average moving range: σ = MR̄ ÷ 1.128.
Control limits come from the process itself, not from the specification — a process can be in control and still produce out-of-spec parts.
Control chart types
| Data | Chart | Plots |
|---|---|---|
| Variables | X̄-R | Subgroup average and range |
| Variables | X̄-S | Subgroup average and standard deviation |
| Variables | I-MR | Individual values and moving range |
| Attributes | p | Proportion defective |
| Attributes | np | Number defective |
| Attributes | c | Count of defects |
| Attributes | u | Defects per unit |
Out-of-control signals
| Rule | Pattern |
|---|---|
| 1 | Any point beyond the ±3σ limits |
| 2 | 9 or more consecutive points on one side of the centre line |
| 3 | 6 or more consecutive points steadily increasing or decreasing |
| 4 | 14 or more points alternating up and down |
| 5 | 2 of 3 consecutive points beyond ±2σ on the same side |
When a signal appears: investigate the cause immediately, correct it, document what was done, and confirm the chart returns to control.
Worked example: piston diameter
An illustrative line machining pistons to 85.00 mm ± 0.10 mm samples five pistons every hour and plots them on an X̄-R chart. Once the chart shows the process is stable, its mean is 85.02 mm and the within-subgroup standard deviation is 0.015 mm.
(85.10 − 84.90) ÷ (6 × 0.015) = 2.22min(0.08, 0.12) ÷ (3 × 0.015) = 1.78The process is capable, but sits 0.02 mm high. Re-centring it would lift Cpk towards Cp — and the chart is what tells you the adjustment worked rather than adding noise.