Abstract: In Finance it is quite usual to assume that a process behaves according to a previously specified target GARCH process. The impact of rumours or other events on this process can be frequently described by an outlier responsible for a short-lived shift in the process mean or by a sustained change in the process variance. This calls for the use of joint schemes for the process mean and variance, such as the ones proposed by Schipper (2001) and Schipper and Schmid (2001). Since changes in the mean and in the variance require different actions from the traders/brokers, this paper provides an account on the probabilities of misleading signals (PMS) of those joint schemes, thus adding valuable insights on the out-of-control performance of those schemes. We are convinced that this talk is of interest to businesspersons/traders/brokers, quality control practitioners, and statisticians alike. Joint work with: Beatriz Sousa (MMA; CGD); Yarema Okhrin (Faculty of Business and Economics, University of Augsburg, Germany); Wolfgang Schmid (Department of Statistics, European University Viadrina, Germany) References Schipper, S. (2001). Sequential Methods for Detecting Changes in the Volatility of Economic Time Series. Ph.D. thesis, European University, Department of Statistics, Frankfurt (Oder), Germany. Schipper, S. and Schmid, W. (2001). Control charts for GARCH processes. Nonlinear Analysis: Theory, Methods & Applications 47, 2049-2060.