Abstract
The exponentially weighted moving average（EWMA）feedback controller（with a fixed discount factor）is a popular run by run（RbR）control scheme which primarily uses data from past process runs to adjust settings for the next run. Although the EWMA controller with a small discount factor can guarantee a 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. This will lead to a very severe consequence if the fabrication is in small batches. The reason is that the output deviations are usually very large at the beginning of the first few runs and, as a result, the output may be out of process specifications. In order to reduce a possibly high rework rate, we propose a variable discount factor to tackle the problem. After a motivating example is used to demonstrate the strength of the EWMA controller with a variable discount factor, we state the main results in which the stability conditions and the optimal variable discount factor of the proposed EWMA controller are derived. Moreover, a heuristic method is proposed to simplify the computation of the variable discount factor. It is seen that the proposed method is easy to implement and provides a good approximation to the optimal variable discount factor.