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Western Electric and Nelson Rules for Control Charts

Control chart rules turn a plot of points into a decision: leave the process alone or go look for a special cause. This table lists the four Western Electric rules, the eight Nelson rules and the zone definitions side by side so you can pick a rule set and explain it to operators.

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Rule set	Rule	Pattern that signals	Zone or limit used	Typical process meaning
Western Electric	WE 1	One point beyond the 3 sigma control limit	Beyond Zone A	Large special cause: wrong setup, broken tool, bad lot of material
Western Electric	WE 2	Two out of three consecutive points beyond 2 sigma on the same side	Zone A or beyond	Shift in the mean that is still small enough to hide inside the limits
Western Electric	WE 3	Four out of five consecutive points beyond 1 sigma on the same side	Zone B or beyond	Sustained moderate shift, for example a new material batch
Western Electric	WE 4	Eight consecutive points on the same side of the center line	Zone C or beyond	Small persistent shift in the process average
Nelson	Nelson 1	One point more than 3 sigma from the center line	Beyond Zone A	Single large disturbance or a measurement or data entry error
Nelson	Nelson 2	Nine points in a row on the same side of the center line	Any, one side	Shift in the process mean
Nelson	Nelson 3	Six points in a row steadily increasing or steadily decreasing	Any	Trend such as tool wear, temperature drift or coolant dilution
Nelson	Nelson 4	Fourteen points in a row alternating up and down	Any	Over-adjustment of the process or two alternating sources, such as two spindles or two operators
Nelson	Nelson 5	Two out of three points more than 2 sigma from the center line, same side	Zone A or beyond	Early sign of a mean shift
Nelson	Nelson 6	Four out of five points more than 1 sigma from the center line, same side	Zone B or beyond	Moderate sustained shift or trend starting
Nelson	Nelson 7	Fifteen points in a row within 1 sigma of the center line, either side	Zone C only	Stratification: subgroups mix several streams, or limits are too wide for the data
Nelson	Nelson 8	Eight points in a row more than 1 sigma from the center line, either side	Outside Zone C, both sides	Mixture: data from two populations with no points near the center
Zones	Zone C	Area between the center line and 1 sigma on each side	0 to 1 sigma	Where about 68 percent of points fall for a stable normal process
Zones	Zone B	Area between 1 and 2 sigma on each side	1 to 2 sigma	About 27 percent of points fall in B, split across both sides
Zones	Zone A	Area between 2 and 3 sigma on each side	2 to 3 sigma	About 4.3 percent of points fall in A, split across both sides
Common variant	7-point run	Seven consecutive points on one side of the center line	Any, one side	Mean shift; shorter run than Nelson 2, used by some SPC manuals and software defaults
Common variant	7-point trend	Seven consecutive points all rising or all falling	Any	Drift; more sensitive than Nelson 3 but with more false alarms
Reference	False alarm rate	Rule 1 alone with a stable normal process	3 sigma limits	About 0.27 percent of points, roughly 1 in 370 points, will be flagged by chance

Zone percentages assume a stable, approximately normal process. Applying all eight Nelson rules together raises the false alarm rate, so most plants choose a subset.

Automate rule checks on live data

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How to use the table

Type a word in the search box such as trend, shift or mixture to find the matching rule and its likely cause. Choose one rule set for each chart and write it in the control plan so every shift reacts the same way. Export to Excel or PDF to paste into a work instruction or SPC training deck. Zones are measured from the center line in units of sigma, where sigma is the standard error of the plotted statistic, not the spec tolerance.

Western Electric is a small set of four rules, easy to teach on the floor
Nelson adds trend, alternating, stratification and mixture patterns
Always compute zones from control limits, never from specification limits

Where the rules come from

The Western Electric rules were published in the Western Electric Statistical Quality Control Handbook and rely on dividing the area between the limits into three zones per side. Lloyd Nelson later published a numbered list of eight tests in the Journal of Quality Technology. Both sets are sensitivity tests for non-random patterns. Each added rule catches smaller shifts faster, but it also adds false alarms, so the rule set is a trade-off between detection speed and unnecessary investigation.

Reading a signal correctly

A rule violation is evidence of a special cause, not proof. Check the measurement first: was the gauge calibrated, was the subgroup entered correctly, did the part come from a different fixture? Then look at what changed at the first point of the pattern, not at the last point that triggered the alarm. For example, a Nelson 3 trend of six rising points that began after a tool change points to wear on that tool. Record the cause on the chart so the next signal is faster to diagnose.

Common mistakes

Many teams switch on every rule in the software and drown in alerts. Others apply run rules to charts where the data are autocorrelated, such as a tank temperature sampled every minute, which makes rules 2, 3 and 7 fire constantly. Another frequent error is recalculating limits after each out-of-control point instead of investigating it. Limits should be revised only after a verified, permanent process change.

Pick two or three rules per chart and document them
Do not apply run rules to strongly autocorrelated data
Do not delete signal points without a documented assignable cause

Frequently Asked Questions

Which is better, Western Electric or Nelson rules?

Neither is universally better. Western Electric has fewer rules and fewer false alarms, so it suits operator-level charts. Nelson adds patterns for trends, alternation and stratification, which help engineers diagnose a process. Many plants use rule 1 plus one or two run rules on each chart.

How many false alarms will the rules create?

Rule 1 alone flags about 1 in 370 points on a stable normal process. Each additional rule adds to that rate, and using all eight Nelson rules together can raise it to several percent of points. That is why selecting a subset matters.

Do these rules work on individuals charts?

Yes, but be careful. Individuals charts are more sensitive to non-normal data and autocorrelation, which cause false signals on run rules. Check normality and consider a transformation or a different chart before adding many rules.

Does a rule violation mean I must scrap parts?

No. A control chart signal says the process changed, not that parts are out of specification. Compare the data with specification limits and your containment procedure to decide on part disposition separately.

If your control chart data sits in an ERP or QMS and nobody reviews the signals, Netray can help wire rule checks to the live data with read-only access.

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