Nelson rules
2015211
221266675
2008-06-23T19:50:57Z
168.156.42.181
'''Nelson rules''' are a method in [[process control]] of determining if some measured variable is out of control (unpredictable versus consistent). Rules, for detecting "out-of-control" or non-random conditions were first postulated by [[Walter A. Shewhart]] <ref>[http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc32.htm Engineering Statistics Handbook 6.3.2], NIST/SEMATECH e-Handbook of Statistical Methods [[National Institute of Standards and Technology]], Dec 2006</ref> in the [[1920s]]. The Nelson rules were first published in the October 1984 issue of the ''[[Journal of Quality Technology]]'' in an article by [[Lloyd S Nelson]] <ref> Lloyd S. Nelson, "Technical Aids," Journal of Quality Technology 16, no. 4 (October 1984), 238-239.</ref>.
The rules are applied to a [[control chart]] on which the magnitude of some [[variable]] is plotted against time. The rules are based around the [[mean]] value and the [[standard deviation]] of the samples.
'''Rule 1:''' One point is more than 3 standard deviations from the mean.
*''One sample is grossly out of control.''
'''Rule 2:''' Nine (or more) points in a row are on the same side of the mean.
*''Some prolonged [[systematic bias|bias]] exists.''
'''Rule 3:''' Six (or more) points in a row are continually increasing (or decreasing).
*''A [[trend estimation|trend]] exists.''
*This is directional and the position of the mean and size of the standard deviation do not affect this rule.
'''Rule 4:''' Fourteen (or more) points in a row alternate in direction, increasing then decreasing.
*''This much [[Oscillation (mathematics)|oscillation]] is beyond [[Signal noise|noise]].''
*This is directional and the position of the mean and size of the standard deviation do not affect this rule.
'''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.
*''There is a medium tendency for samples to be mediumly out of control.''
*''The side of the mean for the third point is unspecified.''
'''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.
*''There is a strong tendency for samples to be slightly out of control.''
*''The side of the mean for the fifth point is unspecified.''
'''Rule 7:''' Fifteen points in a row are all within 1 standard deviation of the mean on either side of the mean.
*''With 1 standard deviation, greater variation would be expected.''
'''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.
*''Jumping from above to below whilst missing the first standard deviation band is rarely random.''
The above eight rules apply to a chart of a variable value.
A second chart, the moving [[Range (statistics)|range]] chart, can also used but only with rules 1, 2, 3 and 4. Such a chart plots a graph of the maximum value - minimum value of '''N''' adjacent points against the time sample of the range.
An example moving range: if N = 3 and values are 1, 3, 5, 3, 3, 2, 4, 5 then the sets of adjacent points are (1,3,5) (3,5,3) (5,3,3) (3,3,2) (3,2,4) (2,4,5) resulting in moving range values of (5-1) (5-3) (5-3) (3-2) (4-2) (5-2) = 4, 2, 2, 1, 2, 3.
Applying these rules indicates when a potential "out of control" situation has arisen. However there will always be some false alerts and the more rules applied the more will occur. For some processes, it may be beneficial to omit one or more rules. Equally there may be some missing alerts where some specific "out of control" situation is not detected. Empirically, the detection [[accuracy]] is good.
==See also==
*[[Common cause and special cause]]
*[[Statistical process control]]
*[[Western Electric rules]]
*[http://www.asq.org/learn-about-quality/data-collection-analysis-tools/overview/control-chart.html Control Chart] [[American Society for Quality]], Quality Tools
== External links ==
* [http://www.masteradvisory.com/Small%20Business%20Guideline%20Book%20to%20Quality%20Management.pdf Small Business Guidebook to Quality Management (pdf)]
==Sources==
<references/>
[[Category:Quality control tools]]
[[Category:Technical communication]]
[[Category:Statistical charts and diagrams]]