Walter A. Shewhart altered the course of industry on May 16, 1924, with a historic memorandum to his superiors at Bell Laboratories, namely George D. Edwards. In this memorandum Shewhart proposed the control chart, a tool used to track process performance over time and to detect changes in parameters which can indicate a deterioration in quality. Joint schemes for the process mean and variance are essential to satisfy Shewhart’s dictum that proper process control implies monitoring both location and dispersion. Misleading signals (MS) can occur while using these joint schemes, and correspond to valid signals that lead to a misinterpretation of a shift in the mean as a shift in the variance, or vice versa. This book assesses the impact of autocorrelation and shifts on the probability of a MS in joint schemes for the mean and variance of stationary processes, and also the impact of falsely assuming independent and identically distributed output. In the second part of the book, the concept of MS is extended to a multivariate normal setting. This book contributes to a greater awareness of a phenomenon often ignored by practitioners, the misleading signals.