All variable charts have two graphs on which the data
are plotted, one of which monitors location
(how close each subgroup is to the process average), while the other
monitors dispersion (the amount of variation
within successive subgroups). The names of the major variable charts
reflect the particular statistics plotted on each of these two graphs.
You will often find them referred to by their shorthand names (given
in brackets in the list below). The most commonly used are:
- The Mean & Range ( & R)
Chart: the most commonly used chart of all, this chart
records the mean (simple average) of each
subgroup together with the range (the
difference between the highest and lowest values). It is
very sensitive to changes in the process and requires little
calculation, hence its popularity.
- The Mean & Standard Deviation (
& s) Chart: this is similar
to the previous chart except it uses the standard
deviation instead of the range as the measure of subgroup
dispersion. The standard deviation is a more efficient indicator of
process variability than the range and is more reliable with larger
subgroups. However, the calculation required is much more complicated
than that for the range, therefore this type of chart is rarely used
except in SPC software packages.
- The Median & Range (
& R) Chart: this chart uses the
median value of each subgroup as the
measure of location. The median is the middle value of a set of
numbers when they are ordered numerically. It is not as sensitive
as the mean & range chart, but was devised because it requires
almost no calculation. The sample values are written onto the chart
in descending order so finding the median is simply a case of
picking the value in the middle. The only calculation required
is to subtract the bottom value from the top one to find the range.
- The Individual & Moving Range (XmR) Chart:
although control charts were originally conceived to work with
subgroups, this is not always possible (for example when data volumes
are low, or when the original ordering of the data is unknown). In
these situations, an XmR chart can be used to record the individual
values, as opposed to a subgroup statistic such as the mean.
Later in this course, we will be looking in greater detail
at the mean & range and the
individual & moving range charts.