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Nelson Rules is a set of rules to detect the presence of special causes or non-random behaviour in the process. These are commonly used to check for process stability in Statistical Process Control (SPC).


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Also review the answer provided by Mr Venugopal R, Benchmark Six Sigma's in-house expert.


Q 276. Nelson Rules - Generally, a process is said to be stable if none of the observations are outside the control limits. (Calculators for control limits can be seen at https://www.benchmarksixsigma.com/calculators/)

However, Nelson rules could help us identify special causes even in such a seemingly stable process. What are these Nelson Rules? Highlight areas / processes where all tests as per Nelson Rules should be carried out.


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Benchmark Six Sigma Expert View by Venugopal R

As early as 1924, Walter Shewhart had introduced what we all know as Control Charts, which has become a very popular and important tool in Statistical Process Control. The Upper Control Limit (UCL) and Lower Control Limit (LCL) represent the +/- 3 sigma limits derived based on the historical data generated from the process itself. So long as the process is in statistical control, the probability of any point falling outside these limits as low as 0.003. Hence any point falling outside the UCL or LCL is suspected as an abnormal occurrence and subjected to analysis to look for any assignable cause(s).


Based on the above, it generally implies that so long as the points fall within the control limits, the process is in statistical control and there is no need to suspect any abnormality.


In 1984, Lloyd S.Nelson published in the Journal of Quality Technology, that just as we say that the probability of any points falling outside the control limits is very low, there is a possibility for other situations, with equally low probability of occurrence, even though all the points could be within the control limits. Hence, such situations would also be indicative of existence of special causes. He came out with 8 rules for suspecting presence of special causes, of which the Rule-1 is the original case of a point falling outside the Control limits.


Each of these rules are illustrated below:

















While multiple rules are available, it is important to decide which rule needs to be applied when.

Rule- is the fundamental one and is hence start with it for any situation. Subsequently, Rules 2 to 4 comprise a good set that help for many of the commonly occurring special causes. For an engineering study, adding rules 5 and 6 will increase the sensitivity to changes in the process average. Rules 7 and 8 will help to identify problems relating to sampling, viz. stratification and mixtures.


While this battery of rules is expected by and large to reveal more special causes with higher sensitivity, there are still possibilities of special causes that escape these rules. For example, points may alternate up and down repeatedly, except an adjacent pair of points that may move in the same direction beginning at every nth sub-group. This could mean an underlying special cause that would not get detected by Rule-4. One has to be alert in usage of control charts to detect any patterns that may need attention and at the same time avoiding over-reactions.


Reference: Journal of Quality Technology April 1985 edition


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Lloyd S Nelson came up with 8 Nelson rules in the year 1984 addressing variability in a process or data beyond (+/- 3 points standard deviation from the process mean between the sub groups ). These are also called Special causes Variation or Non Random Variation. 8 Nelson rules helps in performing suitable control charts based on the relevant data type covering all the abnormalities in data to help work on assignable special causes & draw RCA & CAPA/Training. Special causes are generally due to sudden change in the process, machine, shifts, customer, Raw Material, Lot type etc. These kind of causes are normally associated to Manufacturing Industry due to unpredictability in nature. 

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  • Nelson Rules are a method in a process control of determining if some measured variable is out of control.
  • Rules for detecting out of control or non-randomly conditions were first postulated by Walter A. Shewhart in 1920s.
  • The Nelson Rules were first published in October 19848, issue of the Journal of Quality Technology in an article by Lloyd S Nelson.
  • The Nelson Rules are applied to Control chart on which the magnitude of some variable is plotted against time.
  • The Rules are based on mean value and standard deviation of samples.
  • The dashed horizontal line in following illustration represents distances of 1 Sigma and 2 Sigma from centre line.




Which Test you should use to detect specific patterns of special-cause variation?




  • Apply certain test based on your knowledge of the process. If it is likely that it might contain particular pattern you can look for them by choosing appropriate test.
  • Adding more test makes the chart more sensitive but may also increase the chance of getting a false signal.
  • When you use several tests together the chance of obtaining a signal for lack of control increases.


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There were two parts to this question. Only the first part - What is Nelson rules - has been answered. 


Do review the answer provided by Mr Venugopal R, Benchmark Six Sigma's in-house expert.

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