<P> 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 . </P> <P> 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 . </P> <P> 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 . </P> <P> 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 . </P>

Provide a definition for a control chart and describe how control charts are used