Nelson Rules

A 1984 update by Lloyd S. Nelson to the popular Western Electric Rules (WECO Rules), in order to make the probability of detecting an out of control condition by chance approximately equal across all tests. The Western Electric Rules have probabilities that have more variability from one another (some are more likely than others to occur by chance).

There are 8 different Nelson Rules ¹

Rule 1: One point is more than 3 standard deviations from the mean (outlier)

Rule 2: Nine (or more) points in a row are on the same side of the mean (shift)

Rule 3: Six (or more) points in a row are continually increasing (or decreasing) (trend)

Rule 4: Fourteen (or more) points in a row alternate in direction, increasing then decreasing (bimodal, 2 or more factors in data set)

Rule 5: Two (or three) out of three points in a row are more than 2 standard deviations from the mean in the same direction (shift)

Rule 6: Four (or five) out of five points in a row are more than 1 standard deviation from the mean in the same direction (shift or trend)

Rule 7: Fifteen points in a row are all within 1 standard deviation of the mean on either side of the mean (reduced variation or measurement issue)

Rule 8: Eight points in a row exist with none within 1 standard deviation of the mean and the points are in both directions from the mean (bimodal, 2 or more factors in data set)

Rules 1, 2, 5 and 6 are defined by the Western Electric Co (1958) as the original 4 rules, except Rule #2 which was “Eight (or more) points in a row are on the same side of the mean (shift)” instead of nine in a row.

It is recommended that you focus on Rule #1, according to Donald Wheeler. He states that this rule “has proven to be sufficient in most cases. Rule one strikes a balance between the consequences of either getting a false alarm or missing a signal of economic importance.”

¹ Nelson rules, https://en.wikipedia.org/w/index.php?title=Nelson_rules&oldid=803907968 (last visited May 15, 2018).

Links

• The Shewhart Control Chart Tests for Special Causes by Lloyd Nelson (1984) – Journal of Quality and Technology
• Western Electric Rules (WECO Rules)
• More out of control condition tests
• Applying the Out of Control Tests
• When Should We Use Extra Detection Rules? by Donald Wheeler