What are the Western Electric rules?

Four zone tests: one point beyond 3σ; two of three consecutive points beyond 2σ on the same side; four of five beyond 1σ on the same side; and eight consecutive points on one side of the centre line. Many references add two supplementary rules — six points trending and fourteen alternating — which this checker includes as rules 5 and 6.

What are the 8 Nelson rules?

1: one point beyond 3σ. 2: nine in a row on one side. 3: six in a row increasing or decreasing. 4: fourteen in a row alternating up and down. 5: two of three beyond 2σ, same side. 6: four of five beyond 1σ, same side. 7: fifteen in a row within 1σ. 8: eight in a row beyond 1σ, either side.

Which run rules should I use?

The rules your organisation or customer specifies. Without a requirement, many teams start with the 3σ test alone on a new chart and add the run test (rule 2 in Nelson, rule 4 in Western Electric) once the limits are established, because every extra rule adds false alarms.

Does a point exactly on the control limit count as out of control?

No. Out of control means beyond the limit, strictly. NIST’s own c-chart example has a point exactly on the UCL and does not treat it as a signal, and this checker follows the same convention.

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Western Electric and Nelson Rules Checker — Which Points Are Out of Control?

Paste a series of values and see which Nelson, Western Electric or ISO 7870-2 run rules fire, on which point and why. Use the centre line and sigma from your data, from an earlier study, or straight off the limits of an existing chart.

Values, in time order

40 values · one per line, or comma-separated

Rule set

Centre line and sigma

9 points flagged by 9 rule violations. CL = 10.0600, σ = 0.4045 — σ̂ = MR̄/d₂ from these values (the I-MR chart’s estimate); centre line = their mean. Demonstration data: synthetic, written to make the rule sets disagree. Switch between Nelson and Western Electric and watch points 13 to 20.

Western Electric (WECO) — which rules fired
Rule	Test	Fired at point
1	Any point beyond ±3σ	34
2	2 of the last 3 points beyond ±2σ, same side	—
3	4 of the last 5 points beyond ±1σ, same side	26, 27
4	8 consecutive points on one side of the centre line	20, 28, 29
5	6 consecutive points trending up or down	30, 31, 32
6	14 consecutive points alternating up and down	—

NIST records the cost: with the WECO rules applied, the in-control false-alarm rate rises from about 1 point in 371 to about 1 in 91.75.

For a full chart with the moving-range panel, batch boundaries and SVG or PNG export, paste the same values into the I-MR chart; for runs tests about the median with p-values, the run chart.

Everything on this page is calculated in your browser tab. Nothing you type is uploaded.

How to read a control chart

A point beyond a control limit is only the most obvious signal. A process that has shifted by one standard deviation will rarely put a point outside three sigma, but it will very quickly put a long run of points on one side of the centre line. The run rules exist to catch exactly those patterns: runs, trends, clusters near a limit, and points that hug the centre line too closely.

Every extra rule buys sensitivity at the cost of false alarms. NIST records that switching on the full Western Electric set moves the in-control false-alarm rate from about one point in 371 to about one in 92. That is why the default on every chart on this site is the 3σ test alone, and why the rule set is always printed on the figure.

Nelson, Western Electric and ISO disagree — on purpose

The three published sets use different run lengths for the same idea: Nelson flags 9 points in a row on one side of the centre line, Western Electric flags 8, and ISO 7870-2 flags 7. The demonstration series on this page has a run of exactly eight, so switching between the sets shows a point that one rule book calls a signal and another does not.

Neither is wrong. Pick the set your organisation or your customer specifies, state it on the chart, and use the same set every time the chart is read.

What each pattern usually means

A point beyond 3σ: a one-off special cause — a wrong setting, a bad batch of material, a measurement error. A run on one side: a sustained shift in the mean, such as a new operator, tool or supplier lot. A trend: tool wear, temperature drift, a depleting bath. Two of three beyond 2σ / four of five beyond 1σ: a moderate shift caught earlier than the run rule would catch it.

Fifteen points within 1σ: too little variation — often stratification, where each subgroup mixes several streams and the limits were computed too wide. Eight points beyond 1σ on both sides: a mixture of two processes. Fourteen points alternating: over-adjustment, or two alternating sources such as two fixtures or two shifts.

Common questions

What are the Western Electric rules?: Four zone tests: one point beyond 3σ; two of three consecutive points beyond 2σ on the same side; four of five beyond 1σ on the same side; and eight consecutive points on one side of the centre line. Many references add two supplementary rules — six points trending and fourteen alternating — which this checker includes as rules 5 and 6.
What are the 8 Nelson rules?: 1: one point beyond 3σ. 2: nine in a row on one side. 3: six in a row increasing or decreasing. 4: fourteen in a row alternating up and down. 5: two of three beyond 2σ, same side. 6: four of five beyond 1σ, same side. 7: fifteen in a row within 1σ. 8: eight in a row beyond 1σ, either side.
Which run rules should I use?: The rules your organisation or customer specifies. Without a requirement, many teams start with the 3σ test alone on a new chart and add the run test (rule 2 in Nelson, rule 4 in Western Electric) once the limits are established, because every extra rule adds false alarms.
Does a point exactly on the control limit count as out of control?: No. Out of control means beyond the limit, strictly. NIST’s own c-chart example has a point exactly on the UCL and does not treat it as a signal, and this checker follows the same convention.