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The normal distribution is NOT assumed nor required in the calculation of control limits. Thus making the IndX/mR chart a very robust tool. This is demonstrated by Wheeler using real-world data [4], [5] and for a number of highly non-normal probability distributions. [6]
As with the ¯ and s and individuals control charts, the ¯ chart is only valid if the within-sample variability is constant. [4] Thus, the R chart is examined before the ¯ chart; if the R chart indicates the sample variability is in statistical control, then the ¯ chart is examined to determine if the sample mean is also in statistical control.
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.
As with the ¯ and R and individuals control charts, the ¯ chart is only valid if the within-sample variability is constant. [5] Thus, the s chart is examined before the ¯ chart; if the s chart indicates the sample variability is in statistical control, then the ¯ chart is examined to determine if the sample mean is also in statistical control.
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.
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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.
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