<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> <P> 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 . </P>

Control charts in statistical process control (spc) allow companies to