Run Chart

Run Chart

A run chart shows a data series in time order and tests whether that order looks random. Unlike a control chart it has no control limits — only a median line. Four formal runs tests detect typical non-random patterns.

Median line: The median of the values. With random variation about half the points fall above, half below. Points exactly on the median are excluded from the tests.

Run about the median: A consecutive sequence of points all on the same side of the median. For purely random data the expected number of such runs follows from the counts above/below.

Run up/down: A sequence of consecutively increasing or decreasing values. Random series typically produce many short changes — extremely few (long monotone streaks) or extremely many (zigzag) are suspicious.

Run charts are used in the Measure phase to get a first feel for the process before setting up a control chart. They are less formal than Shewhart charts because they need no spread assumption — the median works for non-normal data too.

The Four Runs Tests

• Clustering — too few runs about the median (points cluster on one side). Indicates a level shift or mixed population.
• Mixtures — too many runs about the median (points cross too often). Indicates two superimposed sources, e.g. two machines.
• Trends — too few runs up/down (long monotone runs). Indicates drift, wear, warm-up/cool-down effects.
• Oscillation — too many runs up/down (zigzag). Indicates systematic over-correction, e.g. controller overshoot.

Each test produces a p-value. If p < α (default 0.05), the pattern is significant — the hypothesis of pure random order is rejected. More than one simultaneously-flagged test usually points to a real special cause.

Reading and Reacting

• First inspect the shape — trends, cycles, jumps are often visible by eye.
• Then check the p-values. A single small p can be chance (multiple comparisons!), two or more clearly indicate structure.
• If patterns are significant: investigate the cause before setting up a control chart. Special causes will bias the baseline.
• If all tests pass and the picture looks random: data is ready for a control chart (I-MR, X̄-R, …).

Pitfalls

Run chart as a control chart substitute: A run chart shows patterns but no control limits. It does not replace a control chart for ongoing monitoring — only the pre-analysis.

Unclear data order: Runs tests assume the order of values matches the time of collection. Sorted or regrouped data produces garbage results.

Too few data points: With fewer than ~10 points the runs tests carry almost no power. At least 15–25 points for meaningful p-values; on small samples interpret roughly.

Multiple comparisons: Four simultaneous tests inflate the false-alarm rate. A single p < 0.05 is weak evidence; the picture becomes significant when several tests fire at once or one is very small.

Examples

This module ships with the following example datasets — load any of them in the app with a single click.