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The power of the Cusum chart is generalized in the Cuscore charts, which also accumulate information
about deviations from the normal pattern. They are designed for deviations of a special kind: a bump,
a sine wave, a change in slope, or a change in a process parameter.

References
Box, G. E. P. and A. Luceno (1997). Statistical Control by Monitoring and Feedback Adjustment, New York,
Wiley Interscience.
Box, G. E. P. and J. Ramirez (1992). “Cumulative Score Charts,” Qual. Rel. Eng. Int., 8, 17–27.
Tiao, George et al., Eds. (2000). Box on Quality and Discovery with Design, Control, and Robustness, New
York, John Wiley & Sons.

Exercises

13.1 Find the Disturbance. Based on historical information, five machines vary randomly about an
average level of 11.2 with a standard deviation of 1.0. The table below gives a series of
operating data for each machine. Check each machine for change in average level, a “bump”
of width = 3, a sinusoidal disturbance with period p = 12 and period p = 24, and a change
in slope from 0 to 0.02.

Machine Machine
Time 1 2 3 4 5 Time 1 2 3 4 5
1 11.8 11.8 11.8 11.8 11.8 26 11.4 12.3 14.9 11.4 11.9
2 11.7 11.7 11.7 11.7 11.7 27 13.0 14.0 16.5 13.0 13.5
3 13.0 13.0 13.0 13.0 13.0 28 10.6 11.5 14.1 10.6 11.2
4 11.1 11.1 11.1 11.1 11.1 29 11.3 11.8 14.8 11.3 11.9
5 10.5 10.5 10.5 10.5 10.5 30 10.9 10.9 14.4 10.9 11.5
6 10.5 10.5 10.5 10.5 10.5 31 13.2 12.7 16.7 13.2 13.8
7 11.3 11.3 11.3 15.6 11.3 32 13.4 12.6 16.9 13.4 14.1
8 10.5 10.5 13.0 10.5 10.5 33 13.4 12.4 13.4 13.4 14.0
9 12.3 12.3 14.8 12.3 12.3 34 12.8 12.0 12.8 12.8 13.5
10 11.6 11.6 14.1 11.6 11.6 35 12.3 11.8 12.3 12.3 13.0
11 11.7 11.7 14.2 11.7 11.7 36 11.1 11.1 11.1 11.1 11.1
12 11.0 11.0 13.5 13.3 11.2 37 11.8 11.8 11.8 11.8 11.8
13 10.5 10.5 10.5 10.5 10.8 38 12.7 12.7 12.7 12.7 12.7
14 10.9 11.4 10.9 10.9 11.2 39 12.8 12.8 12.8 12.8 12.8
15 10.5 11.4 10.5 7.4 10.8 40 10.9 10.9 10.9 10.9 10.9
16 11.5 12.4 11.5 11.5 11.9 41 11.7 11.7 11.7 11.7 11.7
17 10.8 11.3 10.8 10.8 11.1 42 12.0 12.0 12.0 12.0 12.0
18 12.8 12.8 12.8 12.8 13.1 43 11.7 11.7 11.7 11.7 11.7
19 9.9 9.4 9.9 9.9 10.3 44 10.4 10.4 10.4 10.4 10.4
20 11.4 10.6 11.4 11.4 11.8 45 9.8 9.8 9.8 9.8 9.8
21 13.6 12.6 13.6 13.6 14.0 46 10.2 10.2 10.2 10.2 10.2
22 12.7 11.8 12.7 12.7 13.1 47 11.4 11.4 11.4 11.4 11.4
23 12.1 11.6 12.1 12.1 12.5 48 12.3 12.3 12.3 12.3 12.3
24 10.6 10.6 14.1 10.6 11.1 49 11.8 11.8 11.8 11.8 11.8
25 9.1 9.6 12.6 9.1 9.6 50 10.9 10.9 10.9 10.9 10.9

13.2 Real World. Visit a nearby treatment plant or manufacturing plant to discover what kind of
data they collect. Do not focus only on process or product quality. Pay attention to machine
maintenance, chemical use, and energy use. Propose applications of Cuscore charts.

© 2002 By CRC Press LLC