Western Electric (WECO) and other Named Rule Sets

The normal SPC control limit rules display at the 3-sigma level, both high and low. In this case, a simple threshold test determines if a process is in, or out of control. Once a process is brought under control using the simple 3-sigma level tests, quality engineers often want to increase the sensitivity of the control chart, detecting and correcting problems before the 3-sigma control limits are reached. Other, more complex tests rely on more complicated decision-making criteria. These rules utilize historical data and look for a non-random pattern that can signify that the process is out of control, before reaching the normal +-3 sigma limits. The most popular of these are the Western Electric Rules, also know as the WECO Rules, or WE Runtime Rules. First implemented by the Western Electric Co. in the 1920's, these quality control guidelines were codified in the 1950's and form the basis for all of the other rule sets. Different industries across the globe have have developed their own variants on the WECO Rules. Other sets of rules, common enough to have an identifying name, i.e. named rules, are listed below.

WECO Runtime and Supplemental Rules – Western Electric Co. - Western Electric Company (1956), Statistical Quality Control handbook. (1 ed.), Indianapolis, Indiana: Western Electric Co., p. v, OCLC 33858387. Sometimes the Supplemental Rules are referred to as the Montgomery Rules, after the statistical quality control expert Douglas Mongtomery. Introduction to Statistical Quality Control (5 ed.), Hoboken, New Jersey: John Wiley & Sons, ISBN 9780471656319

Nelson Rules – The Nelson rules were first published in the October 1984 issue of the Journal of Quality Technology in an article by Lloyd S Nelson.

AIAG Rules– The (AIAG) Automotive Industry Action Group control rules are published in the their industry group “Statistical Process Control Handbook”.

Juran Rules - Joseph M. Juran was an international expert in quality control and defined these rules in his “Juran's Quality Handbook”, McGraw-Hill Professional; 6 edition (May 19, 2010), ISBN-10: 0071629734

Hughes Rules – The only sources we could find for the Hughes rules were all second hand. If anyone can direct is to an original source for the Hughes Rules, please send an e-mail to support@quinn-curtis.com.

Duncan Rules – Acheson Johnston Duncan was an international expert in quality control and published his rules in the text book “Quality control and industrial statistics” (fifth edition). Irwin, 1986.

Gitlow Rules - Dr. Howard S. Gitlow is an international expert in Sigma Six, TQM and SPC. His rules are found in his book “Tools and Methods for the Improvement of Quality”, 1989, ISBN-10: 0256056803 .

Westgard Rules – The Westgard rules are based on the work of James Westgard, a leading expert in laboratory quality management . They are considered “Laboratory quality control rules”. You can find more information about the Westgard Rules, and James Westgard at the web site: http://www.westgard.com

The rules sets have many individual rules in common. In particular, the WECO rules and the Nelson rules, have 7 out of 8 rules in common, and only differ in the fourth rule.

Western Electric (WECO) Rules

In the Western Electric Rules A process is considered out of control if any of the following criteria are met:

1. The most recent point plots outside one of the 3-sigma control limits. If a point lies outside either of these limits, there is only a 0.3% chance that this was caused by the normal process.

2. Two of the three most recent points plot outside and on the same side as one of the 2-sigma control limits. The probability that any point will fall outside the warning limit is only 5%. The chances that two out of three points in a row fall outside the warning limit is only about 1%.

3. Four of the five most recent points plot outside and on the same side as one of the 1-sigma control limits. In normal processing, 68% of points fall within one sigma of the mean, and 32% fall outside it. The probability that 4 of 5 points fall outside of one sigma is only about 3%.

4. Eight out of the last eight points plot on the same side of the center line, or target value. Sometimes you see this as 9 out of 9, or 7 out of 7. There is an equal chance that any given point will fall above or below the mean. The chances that a point falls on the same side of the mean as the one before it is one in two. The odds that the next point will also fall on the same side of the mean is one in four. The probability of getting eight points on the same side of the mean is only around 1%.

These rules apply to both sides of the center line at a time. Therefore, there are eight actual alarm conditions: four for the above center line sigma levels and four for the below center line sigma levels.

There are also additional WE Rules for trending. These are often referred to as WE Supplemental Rules. Don't rely on the rule number, often these are listed in a different order.

5. Six points in a row increasing or decreasing. The same logic is used here as for rule 4 above. Sometimes this rule is changed to seven points rising or falling.

6. Fifteen points in a row within one sigma. In normal operation, 68% of points will fall within one sigma of the mean. The probability that 15 points in a row will do so, is less than 1%.

7. Fourteen points in a row alternating direction. The chances that the second point is always higher than (or always lower than) the preceding point, for all seven pairs is only about 1%.

8. Eight points in a row outside one sigma. Since 68% of points lie within one sigma of the mean, the probability that eight points in a row fall outside of the one-sigma line is less than 1%.

The rules are described as they appear in the literature. In many cases, a given rule actually specifies two test conditions; the first being a value N out of M above a plus sigma control limit, and the second being a value N out of M below a minus sigma control limit. Examples of this are rules #1, #2 and #3 for WECO and Nelson rules. In other cases, similar rules only contain one test case; N out of M above (or below) a given sigma control limit. Example of this are the Juran rules #2..#5, Hughes Rules #2..#9, Gitlow Rules #2..#5, and Duncan Rules #2..#5.

While the list of named rules below follow what is presented in the literature, the actual rule numbering should be ignored. That is because in the software we implement all rules as simple single condition rules. The first rule in all of the named rule sets is implemented as two rules; a single point greater than 3-sigma; and a single point less than -3-sigma. And WECO and Nelson rules #2 and #3 are implemented as four rules; two N out of M greater than x-sigma condition limits, and two N out of M less than x-sigma condition limits. A complete cross reference to the named rules listed below, and our own rule number system is found in Table 1. This is important, because when you try to access a particular named rule within the software, you must use our rule number system.

 

Basic Rules

The Basic Rules are the default rules for all of the SPC charts. They correspond to the +-3-sigma rules used by almost every industry standard SPC chart implementation.

 

1. One of one point is outside of +-3-sigma control limits

Nelson Rules

The Nelson rules are almost identical to the combination of the WECO Runtime and Supplemental Rules. The only difference is in Rule #4.

 

4. Nine out of the last nine points plot on the same side of the center line, or target value.

    

AIAG Rules

1. One of one point is outside of +-3-sigma control limits

2. Seven out of seven are above or below center line

3. Seven points in a row increasing

4. Seven points in a row decreasing

 

Juran Rules

1. One of one point is outside of +- 3-sigma control limits

2. Two of three points above 2-sigma control limits

3. Two of three points below -2-sigma control limits

4. Four of five points is above 1-sigma control limits

5. Four of five points is below -1-sigma control limit s

6. Six points in a row increasing

7. Six points in a row decreasing

8. Nine out of nine are above or below center line

9. Eight points in a row on both sides of center line, none in zone C

 

Hughes Rules

1. One of one point is outside of +- 3-sigma control limits

2. Two of three points above 2-sigma control limits

3. Two of three points below -2-sigma control limit s

4. Three of seven points above 2-sigma control limits

5. Three of seven points below -2-sigma control limit s

6. Four of ten points above 2-sigma control limits

7. Four of ten points below -2-sigma control limits

8. Four of five points is above 1-sigma control limits

9. Four of five points is below -1-sigma control limits

10. Seven points in a row increasing

11. Seven points in a row decreasing

12. Ten of eleven are above center line

13. Ten of eleven are below center line

14. Twelve of fourteen are above center line

15. Twelve of fourteen are below center line

Gitlow Rules

 

1. One of one point is outside of +- 3-sigma control limits

2. Two of three points above 2-sigma control limits

3. Two of three points below -2-sigma control limits

4. Four of five points is above 1-sigma control limits

5. Four of five points is below -1-sigma control limits

6. Eight points in a row increasing

7. Eight points in a row decreasing

8. Eight out of Eight are above center line

9. Eight out of Eight are below center line

 

Duncan Rules

 

1. One of one point is outside of +- 3-sigma control limits

2. Two of three points above 2-sigma control limits

3. Two of three points below -2-sigma control limits

4. Four of five points is above 1-sigma control limits

5. Four of five points is below -1-sigma control limits

6. Seven points in a row increasing

7. Seven points in a row decreasing

 

Westgard Rules

 

1. One of one point is outside of +- 3-sigma control limits - 13s

2. Two of two points outside +-2-sigma control limits - 22s

3. Four of four points outside +-1-sigma control limits - 41s

4. Ten of ten points on one side of center line - 10x

5. Two adjacent points on opposite sides of +-2-sigma - R4s

6. Seven of seven points in a trend increasing or decreasing - 7T

7. One of one point is outside of +- 2-sigma control limits – 12s

8. Two of three points outside +-2-sigma control limits - 2of32s

9. Three of three points outside +-1-sigma control limits - 31s

10. Six of six points on one side of center line - 6x

11. Eight of eight points on one side of center line - 8x

12. Nine of nine points on one side of center line - 9x

13. Twelve of twelve points on one side of center line – 12x

 

By default, only the first six Westgard rules described above are enabled. The others can be turned on using the UseNamedRuleSet method and setting ruleflags array elements true for the additional rules. Make sure you use our rule numbers and not the rule numbering above.

Control Rule Templates

All of the named rules fall into one of our standard rule categories. Each rule category is a flexible template which can be used to evaluate a test condition across a wide range of parameters. A list of the template categories appears below.

Standardized Templates for Control Rule Evaluation

Template #

       Standard Control Limit tests

1     N of M above X sigma (from center line), used for UCL tests

2     N of M below X sigma (from center line), used for LCL tests

3     Reserved

4     N of M beyond X sigma (from center line, either side) or control limits – points beyond the +- limit values – don't have to all be on one side

 

        Trending

5     N of M trending up (increasing)

6     N of M trending down (decreasing)

7     N of M trending up (increasing) or down (decreasing)

 

        Hugging (lack of variance)

8     N of M within X sigma (from center line, either side)

9     N of M within X sigma of each other (no reference to center line)

 

        Oscillation

10     N of M alternating about X sigma (from center line)

11     N of M alternating (no reference to center line)

 

For example, rule #1 for all of the named rules (a single point plots outside of +- 3 sigma) is implemented as one instance of template #1 (N of M above X sigma, where N=1, M=1 and X = 3) and one instance of template #2 (N of M below X sigma) where N=1, M=1 and X = -3).

Rule #2 for WECO and Nelson ( two of three point plots outside of +- 2 sigma) is implemented as one instance of template #1 (N of M above X sigma, where N=2, M=3 and X = 2) and one instance of template #2 (N of M below X sigma) where N=2, M=3 and X = -2).

Rule #4 and #5 for Hughes (three of seven points above/below 2-sigma control limit ) is implemented as one instance of template #1 (N of M above X sigma, where N=3, M=7 and X = 2) and one instance of template #2 (N of M below X sigma) where N=3, M=7 and X = -2).

Rule #6 for Gitlow (eight points in a row increasing) is implemented as one instance of template #5 (N of M trending up) where N=8 and M=8.

The templates are important because using them you can modify any existing named rule, changing the M, N or X parameter. Or, you can create completely new rules.