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In the empirical sciences, the so-called three-sigma rule of thumb (or 3 σ rule) expresses a conventional heuristic that nearly all values are taken to lie within three standard deviations of the mean, and thus it is empirically useful to treat 99.7% probability as near certainty.
The Western Electric rules are decision rules in statistical process control for detecting out-of-control or non-random conditions on control charts. [1] Locations of the observations relative to the control chart control limits (typically at ±3 standard deviations) and centerline indicate whether the process in question should be investigated for assignable causes.
About 68% of values drawn from a normal distribution are within one standard deviation σ from the mean; about 95% of the values lie within two standard deviations; and about 99.7% are within three standard deviations. [8] This fact is known as the 68–95–99.7 (empirical) rule, or the 3-sigma rule.
[3]: 43 Points outside of these control limits are signals indicating that the process is not operating as consistently as possible; that some assignable cause has resulted in a change in the process. Similarly, runs of points on one side of the average line should also be interpreted as a signal of some change in the process.
Control charts are graphical plots used in production control to determine whether quality and manufacturing processes are being controlled under stable conditions. (ISO 7870-1) [1] The hourly status is arranged on the graph, and the occurrence of abnormalities is judged based on the presence of data that differs from the conventional trend or deviates from the control limit line.
The above eight rules apply to a chart of a variable value. A second chart, the moving range 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.
This defines a point P = (x 1, x 2, x 3) in R 3. Consider the line L = {(r, r, r) : r ∈ R}. This is the "main diagonal" going through the origin. If our three given values were all equal, then the standard deviation would be zero and P would lie on L. So it is not unreasonable to assume that the standard deviation is related to the distance ...
In statistical process control (SPC), the ¯ and R chart is a type of scheme, popularly known as control chart, used to monitor the mean and range of a normally distributed variables simultaneously, when samples are collected at regular intervals from a business or industrial process. [1]
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