In statistical quality control, the individual/moving-range chart is a type of control chart used to monitor variables data from a business or industrial process for which it is impractical to use rational subgroups.

As with other control charts, these two charts enable the user to monitor a process for shifts in the process that alter the mean or variance of the measured statistic.

As with other control charts, the individuals and moving range charts consist of points plotted with the control limits, or natural process limits.

These limits reflect what the process will deliver without fundamental changes.

Similarly, runs of points on one side of the average line should also be interpreted as a signal of some change in the process.

When such signals exist, action should be taken to identify and eliminate them.

When no such signals are present, no changes to the process control variables (i.e. "tampering") are necessary or desirable.

[3]: 125 The normal distribution is NOT assumed nor required in the calculation of control limits.

This is demonstrated by Wheeler using real-world data[4], [5] and for a number of highly non-normal probability distributions.

The value 3.267 is taken from the sample size-specific D4 anti-biasing constant for n=2, as given in most textbooks on statistical process control (see, for example, Montgomery[2]: 725 ).

Next, the upper control limit (UCL) and lower control limit (LCL) for the individual values (or upper and lower natural process limits) are calculated by adding or subtracting 2.66 times the average moving range to the process average:

The value 2.66 is obtained by dividing 3 by the sample size-specific d2 anti-biasing constant for n=2, as given in most textbooks on statistical process control (see, for example, Montgomery[2]: 725 ).

Once the averages and limits are calculated, all of the individuals data are plotted serially, in the order in which they were recorded.

On a separate graph, the calculated ranges MRi are plotted.

At the least, any points above either upper control limits or below the lower control limit are marked and considered a signal of changes in the underlying process that are worth further investigation.

The moving ranges involved are serially correlated so runs or cycles can show up on the moving average chart that do not indicate real problems in the underlying process.

[2]: 237 In some cases, it may be advisable to use the median of the moving range rather than its average, as when the calculated range data contains a few large values that may inflate the estimate of the population's dispersion.

[7] Some have alleged that departures in normality in the process output significantly reduce the effectiveness of the charts to the point where it may require control limits to be set based on percentiles of the empirically-determined distribution of the process output[2]: 237  although this assertion has been consistently refuted.

Many software packages will, given the individuals data, perform all of the needed calculations and plot the results.

Care should be taken to ensure that the control limits are correctly calculated, per the above and standard texts on SPC.

Sample data and results are presented by Wheeler for the explicit purpose of testing SPC software.