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Monthly sampling over a five year period would result, on average, <br />three points or false alarms plotting out of control. Wider or <br />narrower control limits would result in fewer or more "false <br />alarms," respectively. No information is gained if the limits are <br />so wide that no points plot out of control, and conversely if the <br />limits are too narrow, many false alarms will be generated. <br />The proposed sampling frequency for the Animas River is a single <br />sample per month. A sample standard deviation cannot be calculated <br />for a single sample, so a range chart cannot be constructed. <br />Increasing the sampling frequency to weekly yielding a sample size <br />of four, may increase monitoring costs to an unacceptable level. <br />Averaging monthly samples for quarterly points results in four <br />points a year, but it would require 15 years to yield, on average, <br />three out of control points. Narrow control limits are recommended <br />because of the relatively low sampling effort. <br />Comments on the SGC Control Chart <br />The SGC control chart methodology does not have adequate <br />sensitivity for the expected sampling intensity (frequency and <br />number of samples). The criteria for identifying an out of control <br />condition and corrective actions to follow also need to be expanded <br />upon. I suggest that 1) three separate charts proposed by SGC be <br />combined into a single chart to increase the statistical power, <br />thereby increasing its sensitivity; 2) that the control limit be <br />based on 1.645 standard deviations which is more suitable for the <br />proposed monitoring frequency; and 3) that additional sensitizing <br />criteria be applied to the chart which include a warning limit <br />placed at one standard deviation and a runs test based on a <br />consecutive number of points above the center line. Consideration <br />should also be given to including an EWMA chart, because the <br />proposed sampling effort does not provide for an range chart. The <br />EWMA chart does not necessarily require the same sensitizing <br />criteria as the Shewart chart. <br />A single chart provides a continuous water quality record and the <br />random variation of single measurements is distributed among a <br />larder number of samples which increases the statistical power to <br />identify a shift in the mean water quality. The three control <br />charts proposed by SGC can be combined into one by removing known <br />causes of variation in the zinc concentration, i. e. streamflow, <br />and charting the deviations (residuals) rather than the raw data <br />values. This is accomplished through a variance reduction <br />procedure, i.e. regression. The residuals, arranged in time <br />series, plot randomly about the mean and are normally distributed <br />which satisfies the condition 4 on page 2 of the SGC Technical <br />Memorandum. <br />