Use of Combined Shewhart‐CUSUM Control Charts for Ground Water Monitoring Applications

Statistical properties of combined Shewhart-CUSUM control charts are examined in terms of the site-wide false positive rate, false negative rate, and average run length (i.e., the average number of sampling events that it takes to detect a significant exceedance). The effects of multiple comparisons (i.e., multiple monitoring wells and constituents), verification resampling, background sample size, and background updating are incorporated into the analysis. The effects of (1) verification resampling plans including no resampling, pass one resample, pass one of two resamples, and pass two of two resamples; (2) background sample sizes (n = 8,12,16,20, and 24); and (3) multiple comparisons (k = 1 to 500 future comparisons) were examined. In addition, various alternative control limit factors (h = SCL= 4.5, 5.0,5.5, and 6.0) were considered, where the control limit is x + hs. Results of simulations revealed that it is possible to balance site-wide false positive and false negative rates at low levels using combined Shewhart-CUSUM control charts. The results revealed that it is important to select the appropriate multiplier, verification resampling plan, number of background samples, and number of intervening samples prior to updating background.