16-6 CONTROL CHARTS FOR INDIVIDUAL MEASUREMENTS 617d 2 1.128. For the data in Table 16-3 we haveThe control chart for individual concentration measurements is shown as the upper con-
trol chart in Fig. 16-11. There is no indication of an out-of-control condition.The chart for individuals can be interpreted much like an ordinary control chart. A shift
in the process average will result in either a point (or points) outside the control limits, or a
pattern consisting of a run on one side of the center line.
Some care should be exercised in interpreting patterns on the moving-range chart. The
moving ranges are correlated, and this correlation may often induce a pattern of runs or cycles
on the chart. The individual measurements are assumed to be uncorrelated, however, and any
apparent pattern on the individuals’control chart should be carefully investigated.
The control chart for individuals is very insensitive to small shifts in the process mean.
For example, if the size of the shift in the mean is one standard deviation, the average number
of points to detect this shift is 43.9. This result is shown later in the chapter. While the per-
formance of the control chart for individuals is much better for large shifts, in many situations
the shift of interest is not large and more rapid shift detection is desirable. In these cases, we
recommend the cumulative sum control chart(discussed in Section 16-10) or an exponentially
weighted moving-average chart(Montgomery, 2001).XLCLx 3mr
d 299.1 32.59
1.12892.21CLx99.1UCLx 3mr
d 299.1 32.59
1.128105.99Table 16-3 Chemical Process Concentration Measurements
Concentration Moving Range
Observation xmr
1 102.0
2 94.8 7.2
3 98.3 3.5
4 98.4 0.1
5 102.0 3.6
6 98.5 3.5
7 99.0 0.5
8 97.7 1.3
9 100.0 2.3
10 98.1 1.9
11 101.3 3.2
12 98.7 2.6
13 101.1 2.4
14 98.4 2.7
15 97.0 1.4
16 96.7 0.3
17 100.3 3.6
18 101.4 1.1
19 97.2 4.2
20 101.0 3.8
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