Page 184 - The Handbook for Quality Management a Complete Guide to Operational Excellence

170 P r o c e s s C o n t r o l Q u a n t i f y i n g P r o c e s s Va r i a t i o n 171

Control Charts for Individual Measurements (X Charts)
Individuals control charts (sometimes called X charts) are statistical tools
used to evaluate the central tendency of a process over time. Individuals
control charts are used when it is not feasible to use aver ages for process
control. There are many possible reasons why average control charts may
not be desirable: observations may be expensive to get (e.g., destructive
testing), output may be too homogeneous over short time inter vals (e.g.,
pH of a solution), the production rate may be slow and the interval
between successive observations long, and so forth. Control charts for
indi viduals are often used to monitor batch processes, such as chemical
processes, where the within-batch variation is so small relative to between-
batch varia tion that the control limits on a standard X chart would be too
close together. Range charts (more strictly moving range charts) are used in
conjunction with individuals charts to help monitor dispersion.
Calculations for Moving Ranges Charts As with average and range charts, the
range is computed as shown above,
R = largest in subgroup – smallest in subgroup

Here, the range is calculated as the absolute value of the difference
between a consecutive pair of process measurements, which meets the
requirement of a rational subgroup in estimating short-term variation. The
range control limit is computed as was described for averages and ranges
charts, using the D constant for subgroups of two, which is 3.267. That is,
4
LCL = 0 (for n = 2)
UCL = 3.267 × R
Recent research has supported the idea that the moving range chart
will necessarily identify the same process instability as the individuals
chart: a large value in the observation on the individuals chart is likely to
also create one (often two) moving range values that are out of control. It
is certainly easier to present the individuals chart without the moving
range chart; however, the analyst should be aware there are cases where
the moving range chart has been useful in troubleshooting.
Table 9.4 contains 25 measurements. To facilitate comparison, the mea-
surements are the first observations in each subgroup used in the previous
average/range and average/standard deviation control chart examples.
The control limits for the moving range chart are calculated from this
data as follows:

sum of ranges 196
R = = = 8 17
.
number of ranges 24
LCCL = D R = × 8 17 = 0
0
.
R 3
UCL = D R = 3 267 8 17 = 26 69
×
.
.
.
R 4

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