Western Electric run rules
A Shewhart control chart is out of control if any point exceeds the 3σ control limits—but that is only one of eight patterns that signal a process has changed. The Western Electric run rules (from the 1956 Statistical Quality Control Handbook) define seven additional patterns that are statistically unlikely if the process were stable. Each is compared against σ zones measured from the centerline.
Zone definitions
Divide each half of the control chart into three equal zones (each one standard deviation wide):
- Zone C: within ±1σ of the centerline
- Zone B: between 1σ and 2σ from the centerline
- Zone A: between 2σ and 3σ from the centerline (just inside the control limits)
The eight rules
| Rule | Pattern | Probability (if stable) |
|---|---|---|
| 1 | 1 point beyond 3σ (outside control limit) | 0.27 % |
| 2 | 2 of 3 consecutive points in Zone A or beyond (same side) | ≈ 0.39 % |
| 3 | 4 of 5 consecutive points in Zone B or beyond (same side) | ≈ 0.54 % |
| 4 | 8 consecutive points on the same side of the centerline (Zone C or beyond) | ≈ 0.39 % |
| 5 | 6 points in a row steadily increasing or decreasing (a trend) | ≈ 0.28 % |
| 6 | 15 consecutive points in Zone C (hugging the centerline) | Stratification signal |
| 7 | 14 points in a row alternating up and down | Systematic oscillation |
| 8 | 8 points in a row with none in Zone C (avoiding the center) | Mixture of two processes |
What each pattern means in practice
- Rules 1–4 indicate a shift in the mean. Look for operator changes, material lots, setups, or environmental changes.
- Rule 5 (trend) indicates drift: tool wear, machine warm-up, material creep, or a slow process change.
- Rule 6 (hugging) often means the chart was constructed from a mixture of subgroups from two different distributions. Each distribution individually is tight, making the combined chart “too stable.”
- Rule 7 (oscillation) suggests overadjustment: an operator is correcting a process that is actually in control, creating a pendulum effect.
- Rule 8 (bimodal) is characteristic of two streams mixed into one chart: two machines, two materials, or two shifts whose data are combined.
Common exam traps
- More rules = more false alarms. Each additional sensitizing rule increases the false-alarm rate. Many companies apply only rules 1–4 in production to keep false alarms manageable.
- The rules apply independently. Any single rule firing is sufficient to call the process out of control. You do not need all eight to trigger simultaneously.
- Rules apply to the same side of the centerline for runs rules 2–4. “2 of 3 in Zone A” means 2 of 3 on the same side. Points alternating above and below do not satisfy a run rule.
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