Control chart rules for special causes
The eight Nelson tests that Minitab and SpcLite run on control charts, how they relate to the Western Electric rules, and what each pattern usually means on the shop floor.
The eight Nelson tests
σ here is the standard error of the plotted statistic, estimated from the data (for example MR̄/1.128 on an I chart). The run lengths below are Minitab’s defaults; SpcLite lets you change each one.
| Test | Pattern | What it usually means | Western Electric |
|---|---|---|---|
| 1 | 1 point more than 3σ from the center line | A sudden, large special cause: wrong material, setup error, measurement blunder. | WE rule 1 |
| 2 | 9 points in a row on the same side of the center line | The process mean has shifted (new lot, tool change, operator change). | WE rule 4 uses 8 points |
| 3 | 6 points in a row, all increasing or all decreasing | A trend: tool wear, temperature drift, depleting chemistry. | — |
| 4 | 14 points in a row, alternating up and down | Over-adjustment or two alternating streams (two machines, two fixtures). | — |
| 5 | 2 out of 3 points more than 2σ from the center line (same side) | A moderate shift that has not yet produced a point beyond 3σ. | WE rule 2 |
| 6 | 4 out of 5 points more than 1σ from the center line (same side) | A small sustained shift in the mean. | WE rule 3 |
| 7 | 15 points in a row within 1σ of the center line (either side) | Stratification: limits too wide, mixed streams in each subgroup, or edited data. | — |
| 8 | 8 points in a row more than 1σ from the center line (either side) | Mixture: two distributions, e.g. alternating between two set points. | — |
Nelson rules vs Western Electric rules
The Western Electric Statistical Quality Control Handbook (1956) defined four zone tests. Lloyd Nelson extended them to eight in 1984, adding trend, alternation, stratification, and mixture patterns. Minitab’s “tests for special causes” are the Nelson set, with the same-side run defaulting to 9 points instead of Western Electric’s 8.
How many tests should you turn on?
Each extra test raises the false-alarm rate. A common practice is tests 1, 2, 5, and 6 for routine monitoring and all eight during process studies. On range, moving range, and S charts, SpcLite applies only test 1, because the plotted statistic is not symmetric.
Try it on your data
SpcLite marks every failing point with its test number on I-MR, Xbar-R, Xbar-S, and p/np/c/u charts. See the control chart constants for how the limits are computed.
Open SpcLite