Run charts and trend rules
A run chart plots data points in time order with a center line at the median (not the mean). It is simpler than a control chart — no control limits — but it can detect non-random patterns that signal a process change. Run charts are often used early in the Measure phase to visualize baseline behavior before control charts are set up.
Run chart vs. control chart
| Run chart | Control chart | |
|---|---|---|
| Center line | Median | Mean (X̅) |
| Limits | None | UCL and LCL at ±3σ |
| Use | Simple trend detection; early baseline | Full SPC; detecting special causes |
| Data needed | Any time-ordered data | Enough to establish stable σ̂ estimate |
What is a "run"?
A run is one or more consecutive data points on the same side of the median. Points exactly on the median do not count — skip them when counting runs.
Non-random pattern rules (run rules)
These patterns indicate a non-random process — a special cause is likely present:
| Rule | Pattern | Signal |
|---|---|---|
| Too few runs | Fewer runs than expected for the number of data points (lower critical value in run chart table) | Clustering or shift |
| Too many runs | More runs than expected (upper critical value) | Oscillation (e.g., alternating high/low) |
| Shift | 6 or more consecutive points all above or all below the median (some sources use 8) | Shift in process level |
| Trend | 5 or more consecutive points all going up or all going down (some sources use 6 or 7) | Trend in process |
| Astronomical point | A single extreme outlier | Special cause event |
25 consecutive batches of Examplorphine Line 2 fill weight measurements plotted in time order. Median = 250.1 mg.
Observation: Batches 14–22 are all above the median — nine consecutive points on one side. That meets the shift rule whether your reference uses 6 or 8 points, signaling a shift in the process level starting around batch 14.
Follow-up: Check what changed before batch 14 — materials lot, operator, equipment maintenance, environmental change.
Common run chart signals and causes
| Pattern seen | Possible cause |
|---|---|
| Upward trend | Tool or equipment wear; gradual material drift; operator fatigue late in shift |
| Sudden shift above median | Material lot change; equipment repair or replacement; shift change |
| Oscillation (high-low-high) | Two alternating sources (e.g., two lines, two operators, two suppliers) |
| Random scatter, no pattern | Process is stable; variation is common cause |
Interpreting run charts vs. reacting to individual points
A key Six Sigma principle is that not every point above or below average is significant. Common cause variation is the natural, expected noise in a process. Special cause variation is a signal that something has changed. Run rules help distinguish the two without over-reacting to normal variation (tampering).
- Tampering: adjusting a process in response to common cause variation makes things worse — this is one of Deming’s key insights.
- Correct response to special cause: find and fix the assignable cause (a changed input, a broken gage, an untrained operator).
- Correct response to common cause: improve the process system, not individual data points.
Common exam traps
- Run chart uses the median, not the mean, for its center line. A few outliers can skew the mean but not the median.
- Points on the median don’t count for run counting. Skip them.
- A run chart cannot identify control limits or calculate Cp/Cpk. Use a control chart for that.
- The shift rule is usually 6 or more points on the same side of the median, and the trend rule 5 or more consecutive points in one direction. The numbers vary by source — read what the question states.
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