Control Chart Thresholds - Data360_DQ+ - Latest

Data360 DQ+ Help

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Software
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Verify
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Data360
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Data360 DQ+
Version
Latest
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English
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Data360 DQ+
Title
Data360 DQ+ Help
Copyright
2024
First publish date
2016
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2024-07-09
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2024-07-09T15:09:58.774265

Western Electric Rules and Nelson Rules are process control rule sets invented by statisticians. You can select these rules only for a Control Chart, when plotting measures against time. Western Electric and Nelson rules do not need to be configured.

Western Electric Rules

This rule set was invented by the Western Electric Company and was first published in 1956. It was first applied to achieve statistical control of manufacturing processes. The rule set consists of the four rules described below. Each rule evaluates how points on the control chart fall within three chart zones.

Western Electric Chart Zones

 

Zone A - Between 2 and 3 standard deviations from the center line mean.

Zone B - Between 1 and 2 standard deviations from the center line mean.

Zone C - Within 1 standard deviation of the center line mean.

UCL - Upper Control Limit

LCL - Lower Control Limit

The 4 Western Electric Rules

Western Electric Rule 1

Any single point falls outside the Upper Control Limit (UCL) or Lower Control Limit (LCL). A point at such a position is over 3 standard deviations away from the center line mean, i.e. beyond Zone A.

 

Western Electric Rule 2

Two consecutive points out of three, on the same side of the center line, fall beyond Zone B, i.e. beyond two standard deviations from the mean. These points can fall within Zone A or beyond.

 

Note: This point also breaks Western Electric Rule 1.

Western Electric Rule 3

Four consecutive points out of five, on the same side of the center line, fall beyond Zone C, i.e. beyond one standard deviation from the mean. These points can fall in Zone B, Zone A, or beyond.

 

Western Electric Rule 4

Nine consecutive points fall on the same side of the center line mean, in any Zone.

Nelson Rules

This rule set was first published in the October 1984 issue of the Journal of Quality Technology in an article by Lloyd S. Nelson. Like Western Electric, the Nelson rules are a process control rule set that can be applied to a measure over time. The Nelson rules feature the 8 rules described below, each of which are designed to find trends in a data set. Unlike the Western Electric Rules, Nelson rules do not use the Zone terminology; instead, only standard deviation lines are used.

The 8 Nelson Rules

Nelson Rule 1

Any single point falls outside the Upper Control Limit (UCL) or Lower Control Limit (LCL). A point at such a position is over 3 standard deviations away from the center line mean. This is the same as Western Electric Rule 1.

 

Nelson Rule 2

Nine or more consecutive points fall on the same side of the center line mean. This is similar to Western Electric Rule 4.

 

Nelson Rule 3

Six or more consecutive points are continually increasing or continually decreasing.

Nelson Rule 4

Fourteen or more consecutive points continuously alternate in direction, i.e. extended oscillation.

Nelson Rule 5

Two or three consecutive points out of three, on the same side of the center line, fall beyond two standard deviations from the mean. This is similar to Western Electric Rule 2.

Nelson Rule 6

Four or five consecutive points out of five, on the same side of the center line, fall beyond one standard deviation from the mean. This is similar to Western Electric Rule 3.

Nelson Rule 7

Fifteen consecutive points are all within one standard deviation from the mean.

Nelson Rule 8

Eight consecutive points where no point is within one standard deviation from the mean. These points can be found above the mean and below the mean.

Tooltips and overlapping threshold rules violation

When using either the Western Electric or the Nelson rules sets, multiple rules within these sets can be violated at the same time. For example, see the chart above which depicts Western Electric Rule 2 (but also depicts Rule 1).

This situation can also occur when multiple rule sets are used at the same time. For example, if you were using both Western Electric and Nelson on the same chart, Rule 1 from each rule set would always be applied whenever any point beyond 3 standard deviations from the mean occurred. Depending on the data set, a Multipoint or Expression rule could also simultaneously be broken.

To account for this behavior, Control Charts have a tool tip functionality that shows all rules that are broken at highlighted points. To activate this functionality, make sure the Toggle data tooltips option is on and then hover over a highlighted point.

Standard deviation date filter override for control charts

When using control charts, standard deviation lines are drawn based on the standard deviation of the entire date range present in the visualization. This can be overridden, however, by using the Standard Deviation Date Filter Override option. Like other measure options, this option is available by clicking on the measure tab that is being used in your control chart.

Once configured, the override redraws standard deviation lines based on the standard deviation of measured values within the specified date range. At the same time, all measured points will still be plotted on your control chart, allowing you to compare points both inside and outside of the override date range to that date range's standard deviation lines.