Statistics for Environmental Engineers

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The reference distribution for the daily values will always give a warning before the MA does. The MA is conservative. It flattens one-day upsets, even fairly large ones, and rolls smoothly through short intervals of minor disturbances without giving much notice. The moving average is like a shock absorber on a car in that it smooths out the small bumps. Also, just as a shock absorber needs to have the right stiffness, a moving average needs to have the right length of memory to do its job well. A 30-day MA is an interesting statistic to plot only because effluent standards use a 30-day average, but it is too sluggish to usefully warn of trouble. At best, it can confirm that trouble has existed. The seven-day average is more responsive to change and serves as a better warning signal. Exponentially weighted moving averages (see Chapter 4) are also responsive and reference distributions can be constructed for them as well.

Just as there is no reason to judge process performance on the basis of only one variable, there is no reason to select and use only one reference distribution for any particular single variable. One statistic and its reference distribution might be most useful for process control while another is best for judging

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compliance. Some might give early warnings while others provide confirmation. Because reference distributions are easy to construct and use, they should be plentiful and prominent in the control room.


Berthouex, P. M. and W. G. Hunter, (1983). “How to Construct a Reference Distribution to Evaluate Treatment Plant Performance,” J. Water Poll. Cont. Fed., 55, 1417-1424.

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