Assignable causes and autocorrelation: Control charts for observations or residuals?

In many industrial processes, the disturbance generated by an assignable cause is affected by the same inertial elements as the observations from the common-cause system. In these cases, the manifestation of the assignable cause differs from that in many common models. A control chart based on the observations can be effective for statistical process control, but its success depends on the relationship of the time-series model produced by the inertial elements to the magnitude of the disturbance in the input. This characterization provides insight into the research that compares charts based on residuals to those based on the raw data. A simple example of a dynamic system is provided.