Designing a Variable EWMA Controller for Process Disturbance Subject to Linear Drift and Step Changes

Linear drift and step changes are two commonly encountered disturbances in many semiconductor manufacturing processes. The former may be typically caused by the aging of equipment or tool wearing, while the latter may be caused by using different batches of raw material, preventive maintenance, and sudden changes in manufacturing environment, which are prevalent in the integrated circuit industries. However, most of the existent literature on run-to-run controls has only dealt with processes with linear drift or step changes. Until now, there has been no efficient run-to-run controller to simultaneously adjust the process with these disturbances. In this paper, we first derive the stability conditions and optimal sequence of variable discount factors of the modified variable exponentially weighted moving average controller analytically. Next, we demonstrate that the proposed method is capable of reducing total mean square error (TMSE) of the process output efficiently when both types of process disturbances are present. Finally, a comprehensive comparison is presented to address the process performance of the proposed method compared to the conventional method. The results demonstrate that the proposed method is quite robust in that it is able to reduce the process TMSE even when the process parameters are not accurately estimated.