When to use an XmR Chart

An XmR chart is used to monitor a process where:

• each sample consists of an individual item, or
• the data for each sample is only available at irregular or infrequent intervals (e.g. one measurement per day), or
• the natural ordering of the data is unknown.

Control charts use information about the short-term variation in a process to find out whether the long term variation is controlled or excessive. This is usually achieved by the use of subgroups. The short-term variation is measured by the range or standard deviation of the subgroup, and the long-term variation is measured by the differences in the means of the subgroups.

Because we are dealing with individual values and not subgroups, we cannot simply use the range of each subgroup as a measure of short-term variation. Instead we use an implicit moving subgroup of size 2, made up of each pair of successive X values. The diagram below shows how this works.

We can then use the range of this moving subgroup (i.e. the moving range) to establish the short-term variation in the process.