Western Electric and Nelson Rules for Control Charts

What the Western Electric and Nelson rules are

The Western Electric and Nelson rules are pattern tests applied to a control chart to detect special-cause variation even when no point has crossed the ±3-sigma limits. They look at runs, trends and clusters of points relative to the center line and the 1-, 2- and 3-sigma zones.

The four Western Electric rules come from the company’s statistical quality control handbook (1956). Lloyd Nelson extended the set to eight tests in 1984. Anyone running statistical process control uses them to react sooner to mean shifts and changes in process behavior.

Visual map of the Western Electric and Nelson rules

The map summarizes zones A, B and C, the four Western Electric rules, Nelson’s extra tests and the worked example.

Zones A, B and C on the chart

To apply any rule, divide the chart into six bands, three on each side of the center line (CL), each one sigma wide (the sigma of the plotted statistic, for example the subgroup mean).

With normal data and a stable process, about 68% of points fall within ±1 sigma, 95% within ±2 sigma and 99.73% within ±3 sigma. For a refresher, see normal distribution and standard deviation. The limits come from estimates such as those in the X-bar and R chart or the I-MR chart.

The 4 Western Electric rules

In every rule, the points must be on the same side of the center line.

Rule 1 is the classic control limit. Rules 2, 3 and 4 exist to catch moderate shifts that rule 1 takes a long time to notice.

The 8 Nelson tests

Nelson’s set includes the tests above (with 9 points in the run rule instead of 8) and adds trend patterns and abnormal-variation patterns.

Tests 7 and 8 flag the opposite of what you might expect: points hugging the center line are also a signal. They usually mean subgroups mix different sources (machines, cavities, shifts) or the limits were calculated from unsuitable data.

Worked example: no point outside the limits, yet the process moved

Illustrative example: a chart of diameter means (mm) with subgroups of 5 parts. Center line 50.0 and sigma of the mean 0.5. The limits are 48.5 and 51.5; the 1-sigma lines are at 49.5 and 50.5; the 2-sigma lines at 49.0 and 51.0.

Means of the 24 subgroups: 50.2; 49.8; 50.4; 49.9; 50.1; 50.3; 49.7; 50.6; 51.2; 50.4; 51.1; 49.9; 50.2; 50.5; 50.8; 50.6; 50.9; 50.7; 50.3; 50.6; 50.8; 50.4; 50.5; 50.2. The highest value is 51.2, below 51.5. By the limits alone, the process looks in control. Applying the tests:

The first alert comes at subgroup 11. The run stays above the center line to the end (subgroup 24), and the means suggest the process rose by about 0.4 mm. Waiting for a point to exceed 51.5 could take far longer. Action: stop watching only the limits, investigate what changed around subgroups 8 to 9 (material lot, setup, tooling) and only then recalculate the chart.

How to use the rules without false alarms

1. Stabilize the chart first. Calculate the limits from a period when the process was stable.
2. Pick a few rules. Each rule you add raises the false-alarm rate. A common starting point: rule 1, rule 2 (2 of 3 beyond 2 sigma) and the run of 8 or 9 points.
3. Mark the signal point on the chart and note the rule, date and shift.
4. Investigate the special cause with the 6Ms or the 5 Whys before adjusting the machine.
5. Do not adjust for noise. Tampering with a process that gave no signal increases variation.
6. Record the action and check that the chart returns to its pattern. Recalculate the limits if the change is permanent.

If the goal is to detect small shifts as fast as possible, the memory charts CUSUM and EWMA are an alternative to stacking rules. And when the process is stable but outside specification, the issue is centering or spread, covered in process capability (Cp and Cpk).

Common mistakes

• Applying every rule all the time. False alarms pile up and the team starts ignoring the chart.
• Counting on the wrong side. Runs and the 2-sigma and 1-sigma counts must be on the same side of the center line (except tests 4, 7 and 8).
• Adjusting at every alert without investigating. The signal says a special cause exists, not what it is.
• Using the sigma of individual parts instead of the sigma of the plotted statistic. Zones on a chart of means are narrower than the spread of the parts.
• Confusing control limits with specification limits. The rules assess stability, not conformance to tolerance.
• Ignoring the low-variation tests (7 and 8). Points stuck to the center line often mean inflated limits or mixed subgroups.

Frequently asked questions

What is the difference between the Western Electric and Nelson rules?

Western Electric has 4 rules (published in 1956). Nelson has 8 tests (1984): the run becomes 9 points, and he adds a 6-point trend, 14-point alternation and the 15-point and 8-point tests around 1 sigma.

What does 2 of 3 points beyond 2 sigma mean?

Of three consecutive points, two are in zone A (beyond 2 sigma) on the same side of the center line. It signals a mean shift.

How many points in a row on one side indicate a special cause?

Eight under the Western Electric rules, or nine under Nelson test 2.

Can I use all the rules at once?

You can, but it produces more false alarms. Prefer a few rules that match the real problems of your process.

Do the rules work on attribute charts?

Generally yes, with care: zones only make sense when the plotted statistic is roughly symmetric. On p and c charts with low values the distribution is skewed and zone alerts lose accuracy.

Does a flagged point mean the product is out of specification?

No. It means the process changed behavior. Conformance is judged by the tolerance and by capability.

About the author

Vagner Soares

Lean Manufacturing & Behavioral Management Specialist

Over 20 years in the automotive and metalworking industries (GM and Dana), Lean Manufacturing practitioner since 2006. SENAI instructor and mentor in Brazil’s Brasil Mais Produtivo program, delivering consulting, training and audits for 50+ companies, combining quality, productivity and people development.

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