Nelson rules: the 8 tests for an out-of-control process
A point outside the control limits is the most obvious signal on a control chart, but many problems show up as patterns long before a point crosses a limit. In 1984 Lloyd S. Nelson published eight tests for such patterns in the Journal of Quality Technology. They are now built into most SPC software.
The zones are measured from the center line in steps of one standard deviation (σ) of the plotted statistic. The 3σ lines are the control limits.
| Rule | Pattern | What it usually means |
|---|---|---|
| 1 | One point more than 3σ from the center line | A single large special cause — wrong setting, bad part, measurement error |
| 2 | Nine points in a row on the same side of the center line | The process mean has shifted |
| 3 | Six points in a row steadily increasing or decreasing | A trend — tool wear, temperature drift, depleting material |
| 4 | Fourteen points in a row alternating up and down | Over-adjustment or two alternating sources (two machines, two operators) |
| 5 | Two out of three points in a row more than 2σ from the center line, same side | A moderate shift starting |
| 6 | Four out of five points in a row more than 1σ from the center line, same side | A small but persistent shift |
| 7 | Fifteen points in a row within 1σ of the center line, either side | Variation smaller than expected — limits from old data, or stratified sampling mixing streams |
| 8 | Eight points in a row more than 1σ from the center line, on both sides | A mixture of two distributions — e.g. two process streams plotted together |
How to use them sensibly
- More rules, more false alarms. Each extra test raises the chance of flagging a stable process. Many teams start with rules 1–4 and add others only where they help.
- Range and moving range charts. The ranges are not normally distributed and their chart is not symmetric, so the zone-based tests (5–8) do not apply. Use rule 1 — and, at most, the run tests — on R and MR charts.
- A signal is a question, not a verdict. Note what changed at that time (shift change, material lot, maintenance) and investigate before adjusting the process.
- Western Electric rules are an older set from the 1950s with similar zone tests. The run rule there uses eight points in a row instead of nine.
Check rules 1–4 automatically
Paste your data into the free calculator: it draws an I-MR or X̄-R chart and marks every point that triggers Nelson rules 1–4.
Open the free control chart tool →