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Variable EWMA run-to-run controller for drifted processes

In semiconductor production, the double Exponentially Weighted Moving Average (dEWMA) feedback controller is a popular model-based run-to-run controller for drift processes. Whilst a dEWMA controller with suitable discount factors can guarantee long-term stability under fairly regular conditions, it usually requires a moderately large number of runs to bring the output of a process to its target value. This is impractical for a process with small batches. To reduce a possibly high rework rate, we propose a variable discount factor to tackle the problem. The stability conditions and the optimal variable discount factor of the proposed EWMA controller are derived. The main advantage of the proposed controller is that it is very easy for implementing a run-to-run control scheme. In addition, our proposed controller achieves a better performance than that of a dEWMA controller unless the drift rate is poorly estimated. Hence, it provides us with an efficient tool to adjust a drifted run-to-run process.