Statistical design of double EWMA controller

The double exponentially weighted moving average (dEWMA) feedback controller is a popular run‐by‐run (RbR) control scheme for adjusting certain semi‐conductor manufacturing process with a linear drift. Del Castillo (IIE Trans. 1999; 31:1157) introduced an interesting state–space representation of the process output of this control scheme, and then the long‐term stability conditions of this closed‐loop system can be derived. The results; however, are very restricted to the case when the process disturbance follows a white noise series or an IMA(1, q) series. For a general process disturbance such as an ARIMA(p, d, q) model, it is not easy to obtain a state–space representation of the process output of this controller. Hence, some statistical properties (such as stability conditions and process yield) of this controller cannot be addressed by using the state–space theory. To overcome this difficulty, this paper first proposed an analytical expression for the process output of this dEWMA controller. Then the stability conditions and the optimal discount factors of this control scheme (based on the criterion of minimizing the average process fallout rate) can be obtained successfully. Finally, we also address some concluding remarks at the end of this paper.