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Nelson rules are a method in process control of determining whether 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 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.Lloyd S. Nelson, "The Shewhart Control Chart—Tests for Special Causes". Journal of Quality Technology 16, no. 4 (October 1984), 238-239. https://doi.org/10.1080/00224065.1984.11978921
The rules are applied to a 
, , width="250pt", One sample (two shown in this case) is grossly out of control.
, -
, , , Nine (or more) points in a row are on the same side of the mean. , , 
, , Some prolonged 
, , This much 
, , There is a medium tendency for samples to be mediumly out of control.
The side of the mean for the third point is unspecified.
, -
, , , 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.
, -
, , , 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.
, -
, {{center, Rule 8 , , Eight points in a row exist, but none within 1 standard deviation of the mean, and the points are in both directions from the mean. , , 
, , Jumping from above to below while 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
Small Business Guidebook to Quality Management (pdf)
Quality control tools Technical communication Statistical charts and diagrams
control chart
Control charts is a graph used in production control to determine whether quality and manufacturing processes are being controlled under stable conditions. (ISO 7870-1)
The hourly status is arranged on the graph, and the occurrence of abnormalit ...
on which the magnitude of some variable
Variable may refer to:
* Variable (computer science), a symbolic name associated with a value and whose associated value may be changed
* Variable (mathematics), a symbol that represents a quantity in a mathematical expression, as used in many ...
is plotted against time. The rules are based on the mean
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set.
For a data set, the '' ari ...
value and the standard deviation of the samples.
{, class="wikitable" style="margin: 1em auto 1em auto"
! Rule, , Description, , Chart Example, , Problem Indicated
, -
, width="75pt", , , width="250pt", One point is more than 3 standard deviations from the mean., , , , width="250pt", One sample (two shown in this case) is grossly out of control.
, -
, , , Nine (or more) points in a row are on the same side of the mean. , , , , Some prolonged bias
Bias is a disproportionate weight ''in favor of'' or ''against'' an idea or thing, usually in a way that is closed-minded, prejudicial, or unfair. Biases can be innate or learned. People may develop biases for or against an individual, a group ...
exists.
, -
, , , Six (or more) points in a row are continually increasing (or decreasing). , , , , A trend
A fad or trend is any form of collective behavior that develops within a culture, a generation or social group in which a group of people enthusiastically follow an impulse for a short period.
Fads are objects or behaviors that achieve shor ...
exists.
, -
, , , Fourteen (or more) points in a row alternate in direction, increasing then decreasing. , , , , This much oscillation
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
is beyond noise
Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference aris ...
.
Note that the rule is concerned with directionality only. The position of the mean and the size of the standard deviation have no bearing.
, -
, , , 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.
, -
, , , 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.
, -
, , , 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.
, -
, {{center, Rule 8 , , Eight points in a row exist, but none within 1 standard deviation of the mean, and the points are in both directions from the mean. , , , , Jumping from above to below while 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
Range may refer to:
Geography
* Range (geographic), a chain of hills or mountains; a somewhat linear, complex mountainous or hilly area (cordillera, sierra)
** Mountain range, a group of mountains bordered by lowlands
* Range, a term used to i ...
chart, can also be 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
Accuracy and precision are two measures of ''observational error''.
''Accuracy'' is how close a given set of measurements ( observations or readings) are to their ''true value'', while ''precision'' is how close the measurements are to each oth ...
is good.
See also
*Common cause and special cause
Common and special causes are the two distinct origins of variation in a process, as defined in the statistical thinking and methods of Walter A. Shewhart and W. Edwards Deming. Briefly, "common causes", also called natural patterns, are the ...
*Statistical process control
Statistical process control (SPC) or statistical quality control (SQC) is the application of statistical methods to monitor and control the quality of a production process. This helps to ensure that the process operates efficiently, producing ...
* Western Electric rules
* Westgard rules
*American Society for Quality
The American Society for Quality (ASQ), formerly the American Society for Quality Control (ASQC), is a society of quality professionals, with nearly 80,000 members.
History
ASQC was established on 16 February 1946 by 253 members in Milwaukee, ...
, Quality Tools
References
External links
Small Business Guidebook to Quality Management (pdf)
Quality control tools Technical communication Statistical charts and diagrams