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I II <br />TO: <br />Pat Nelson <br />Dave Holm <br />FROM: Bob Owen <br />DATE: July 5, 1995 <br />M E M O R A N D U M <br />SUBJECT: Design and Use of the Control Chart for SGC <br />A water quality control at A -72 provides SGC and the WQCD <br />operational criteria, based on Animas River water quality, on which <br />to determine the need to add or terminate the number of mitigation <br />projects, when it is appropriate to cease treatment of Cement <br />Creek, the success or failure of the plug at the American Tunnel, <br />and ultimately when SGC has met the water quality conditions for <br />permit release in accordance with the Consent Decree. <br />SGC proposed a Shewart control chart, which usually consists of a <br />mean or X -bar chart and a range or R chart that measures <br />variability. Each point for the X -bar chart consists of sample of <br />size n, plotted in time series, about a center line (the mean of <br />means). The R or Range chart is similar except that each point is <br />the standard deviation or range of the n samples. Control limits, <br />UCL and LCL, are based on multiple standard deviations of the <br />means. The mean and the range, plotted in time series, enables the <br />user to identify the stability of the mean and its variation over <br />time. The Shewart Chart quickly identifies points that are "out of <br />control," however it is not sensitive to small shifts in the mean, <br />i. e. less than around 1.5 standard deviations (Montgomery, 1991). <br />An alternative to the Shewart Chart is the exponentially weighted <br />moving average (EWMA) control chart. An averaging period and <br />appvopriate control limits must be selected. The EWMA chart is <br />recommended for situations with individual observations and for <br />small changes in the mean, i. e. 0.5 to 2 standard deviations. <br />Examples of Shewart and EWMA charts for A -72 are shown in Figure 1. <br />The control chart design needs to consider the sample size, sample <br />frequency and average run length (ARL) or the number of points that <br />must be plotted to indicate an "out of control" condition. Some <br />points are expected to plot outside the control limits, i. e. false <br />alarms however if more than the expected number of exceedances <br />occur, then an out of control condition probably exists. A control <br />limit based on a 5% chance that any point will plot out of control, <br />will have one point out of twenty plot out of control on average. <br />