Relationships among control charts used with feedback control

Feedback control is common in modern manufacturing processes and there is a need to combine statistical process control in such systems. Typical types of assignable causes are described and fault signatures are calculated. A fault signature can be attenuated by the controller and an implicit confounding among faults of different types is discussed. Furthermore, the relationships between various control statistics are developed. Control charts have been proposed previously for deviations from target and for control adjustments. We describe why one or the other can be effective in some cases, but that neither directly incorporates the magnitude (or signature) of an assignable cause. Various disturbance models and control schemes, both optimal and non-optimal, are included in a mathematically simple model that obtains results through properties of linear filters. We provide analytical results for a widely-used model of feedback control.