Learn · updated 2026-10-22
Run chart rules: how to spot a real shift
A run chart is your data in time order with a line at the median. No control limits, no assumptions about the distribution, and it works with as few as 10 points. Two simple counts tell you whether the process has shifted.
The two rules. Count only the points that aren't exactly on the median; call that N.
Shift: the longest run on one side of the median is more thanround(log2(N) + 3)Too few crossings: the line crosses the median fewer times thanthe 5% limit of Binomial(N − 1, ½)
Either one is a signal that something changed. For 20 points: a run of 8 or more, or fewer than 6 crossings.
The limits
| Points off the median (N) | Shift if longest run is more than | Shift if crossings are fewer than |
|---|---|---|
| 10 | 6 | 2 |
| 12 | 7 | 3 |
| 14 | 7 | 4 |
| 16 | 7 | 4 |
| 18 | 7 | 5 |
| 20 | 7 | 6 |
| 22 | 7 | 7 |
| 24 | 8 | 8 |
| 26 | 8 | 8 |
| 28 | 8 | 9 |
| 30 | 8 | 10 |
| 35 | 8 | 12 |
| 40 | 8 | 14 |
| 45 | 8 | 17 |
| 50 | 9 | 19 |
| 60 | 9 | 23 |
| 70 | 9 | 28 |
| 80 | 9 | 32 |
| 90 | 9 | 37 |
| 100 | 10 | 41 |
Worked example
Twenty readings in time order (LimitLine's run chart example): 31, 29, 33, 30, 32, 35, 36, 34, 37, 38, 36, 39, 40, 38, 41, 39, 42, 43, 41, 44.
- Median = 37.5. No point sits exactly on it, so N = 20.
- Longest run: 9 points. The limit for N = 20 is 7, so this is a shift.
- Crossings: the line crosses the median 3 times. At least 6 are expected by chance, so this is a signal too.
Both rules point the same way: the process moved up partway through, somewhere between points 9 and 12. Find what changed then before reacting to individual values.
What about the trend rule?
Many improvement teams learned the rules from the US Institute for Healthcare Improvement: a shift is 6 or more points on one side of the median, a trend is 5 or more points going up or down. The NHS-R Community's comparison of rule sets (citing Anhøj's simulation studies) reports that the trend rule gives a false signal around 20% of the time and adds little else, and that the longest-run and crossings rules are more specific. That's why LimitLine uses them for its shift verdict.
Run chart or control chart?
- Run chart when you have few points, a new measure, or data that isn't remotely normal. It answers one question: has something changed?
- Control chart when you have about 20 or more points and want limits that show how much variation to expect, plus the Nelson rules for patterns. See which control chart to use.
Sources
- qicharts2 (J. Anhøj), “Quality Improvement Charts” vignette: run chart rules and Appendix 2, critical values
- J. Anhøj and A. V. Olesen (2014), “Run charts revisited: a simulation study of run chart rules for detection of non-random variation in health care processes”, PLoS ONE 9(11)
- NHS-R Community, “A run chart is not a run chart is not a run chart” (comparison of the Perla, Carey and Anhøj rules)
- R. J. Perla, L. P. Provost and S. K. Murray (2011), “The run chart: a simple analytical tool for learning from variation in healthcare processes”, BMJ Quality & Safety 20(1)