Dynamic response of residuals to external deviations in a controlled production process

We present a general method for studying residual behavior of controlled au tocorrelated processes subject to special-cause changes. Understanding resi dual response to a particular type of process change is important for selec ting a proper control chart to monitor the process effectively. The method is introduced by analyzing the residual behavior of a controlled machining process described by a state-space model that has a simple structure and is representative of many real processes. The general method is then develope d and applied to an ARIMA(p, l, p) process and to some special processes wh ose residual behavior has been investigated in the literature. Residual res ponse to a general disturbance sequence is determined, and it is shown that the residual properties are independent of the type of feedback control ap plied to the process. Implications of this property for process control and monitoring are discussed.