Editing Control chart (section)

==Performance of control charts==

When a point falls outside the limits established for a given control chart, those responsible for the underlying process are expected to determine whether a special cause has occurred. If one has, it is appropriate to determine if the results with the special cause are better than or worse than results from common causes alone. If worse, then that cause should be eliminated if possible. If better, it may be appropriate to intentionally retain the special cause within the system producing the results.{{Citation needed|date=September 2010}}

Even when a process is ''in control'' (that is, no special causes are present in the system), there is approximately a 0.27% probability of a point exceeding ''3-sigma'' control limits. So, even an in control process plotted on a properly constructed control chart will eventually signal the possible presence of a special cause, even though one may not have actually occurred. For a Shewhart control chart using ''3-sigma'' limits, this ''false alarm'' occurs on average once every 1/0.0027 or 370.4 observations. Therefore, the ''in-control average run length'' (or in-control ARL) of a Shewhart chart is 370.4.{{Citation needed|date=September 2010}}

Meanwhile, if a special cause does occur, it may not be of sufficient magnitude for the chart to produce an immediate ''alarm condition''. If a special cause occurs, one can describe that cause by measuring the change in the mean and/or variance of the process in question. When those changes are quantified, it is possible to determine the out-of-control ARL for the chart.{{Citation needed|date=September 2010}}  <!-- example here? -->

It turns out that Shewhart charts are quite good at detecting large changes in the process mean or variance, as their out-of-control ARLs are fairly short in these cases. However, for smaller changes (such as a ''1-'' or ''2-sigma'' change in the mean), the Shewhart chart does not detect these changes efficiently. Other types of control charts have been developed, such as the [[EWMA chart]], the [[CUSUM]] chart and the real-time contrasts chart, which detect smaller changes more efficiently by making use of information from observations collected prior to the most recent data point.<ref name="Deng2012">{{cite journal
|author=Deng, H.|author2=Runger, G. |author3=Tuv, E.
 |title= System monitoring with real-time contrasts
|journal= Journal of Quality Technology |volume=44 |issue=1 |at= pp. 9–27
|year=2012 |doi=10.1080/00224065.2012.11917878 |s2cid=119835984 }}</ref>

Many control charts work best for numeric data with Gaussian assumptions. The real-time contrasts chart was proposed to monitor process with complex characteristics, e.g. high-dimensional, mix numerical and categorical, missing-valued, non-Gaussian, non-linear relationship.<ref name="Deng2012" />