Control limits, also known as natural process limits, are horizontal lines drawn on a statistical process control chart, usually at a distance of ±3 standard deviations of the plotted statistic from the statistic's mean.
Control limits should not be confused with tolerance limits or specifications, which are completely independent of the distribution of the plotted sample statistic. Control limits describe what a process is capable of producing (sometimes referred to as the “voice of the process”), while tolerances and specifications describe how the product should perform to meet the customer's expectations (referred to as the “voice of the customer”).
Control limits are used to detect signals in process data that indicate that a process is not in control and, therefore, not operating predictably.
There are several sets of rules for detecting signals - see Control chart - in one specification:
A signal is defined as any single point outside of the control limits. A process is also considered out of control if there are seven consecutive points, still inside the control limits but on one single side of the mean.
For normally distributed statistics, the area bracketed by the control limits will on average contain 99.73% of all the plot points on the chart, as long as the process is and remains in statistical control. A false-detection rate of at least 0.27% is therefore expected.
However it is often not known whether a particular process generates data that conform to particular distributions, fortunately the Chebyshev's inequality and the Vysochanskij–Petunin inequality allow us to infer that for any unimodal distribution at least 95% of the data will be encapsulated by limits placed at 3 sigma.
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