How do control charts deal with multiple comparisons?
As described, combined Shewhart-CUSUM control charts do not explicitly adjust for multiple comparisons. The effects of verification resampling and increasing number of comparisons produced by multiple wells and constituents generally balance the site-wide false positive and false negative rates at reasonable levels, however, there is no statistical guarantee that they will. Please note that when using control charts it is particularly important to determine site-wide false positive and false negative rates via simulation. Certain states (e.g., California) require that you select the control chart factor based on generating a 5% site-wide false positive rate. DUMPStat allows the user to input the factor in the Statistical Options item of the Settings Menu and the Intra-well Control Chart Power Analysis can be used to determine the site-wide false positive rate for varying choices of the control chart factor.
