This paper unifies and extends previously published characterizations of moving average, geometric moving average, and cumulative sum control chart procedures. It presents comparable characterizations of two procedures based on tests described but not evaluated in earlier papers. One of these procedures is based on a test devised by Girshick and Rubin that is optimal under a particular set of idealized conditions. The other procedure is based on run sum tests, which are generalizations of the type of run test that counts the number of consecutive points that exceed a limit, the generalization taking into account the extent that points in such a run exceed the limit.