Some Properties of EWMA Feedback Quality Adjustment Schemes for Drifting Disturbances

Abstract

Control schemes that are simple enough for operators to implement and that are robust with respect to the underlying model assumptions are usually sought in the area of process adjustment. In the last few years, process adjustment schemes based on the Exponentially-Weighted-Moving-Average (EWMA) statistic have gained popularity in the manufacturing of semiconductors. In the literature, the analysis of this type of adjustment technique has concentrated on a single EWMA controller applied to a system that experiences a deterministic trend disturbance. Although other types of drift models can provide a better description of the disturbance, the performance analysis of EWMA controllers under such conditions has not been undertaken in the past. In this paper we present practical stability and robustness results for single and double EWMA controllers under a variety of process disturbances acting on a “responsive” system. Drift disturbances considered include a random walk with drift, IMA(1,1), and an ARMA disturbance with drift. The effects of errors in the model gain estimate are studied for single EWMA controllers applied to these disturbances. The optimal weight parameter of a single EWMA controller is derived for the case of a random walk with drift disturbance. It is shown that the conditions required for obtaining a stable quality characteristic under the adjustments of the controller are invariant with respect to a large family of drift disturbances. A method is presented for choosing the weights in a double EWMA controller under the assumption that the process gain is known.