Statistics for Environmental Engineers

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Control charts have developed well beyond the classical design of Shewhart. Automated data collection provides information that does not always fit a Shewhart chart. Individual observations are charted, and often there is no central limit property to rely on, so the reference distribution of the plotted values is not always the normal distribution. Autocorrelation and process drift are common, and data transformations are needed. Also, statistics other than the mean value are charted. Disturbances other than a simple shift in mean are important: a change in slope signals wear of a machine or tool, a sinusoidal disturbance signals vibration of a compressor shaft, a bump signals a possible harmful shock to the system, and so on.

The Cusum chart shown in Chapter 12 was one powerful development. It serves the same purpose as a Shewhart chart but has greater sensitivity. It will detect a smaller change than a Shewhart chart can detect. It gains this sensitivity by plotting the cumulative change from the target level. The accumulation of information about deviations provides useful knowledge about a process.

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.


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.

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