An EWMA Algorithm With a Cycled Resetting (CR) Discount Factor for Drift and Fault of High-Mix Run-to-Run Control

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Run-to-run controllers based on the exponential weighted moving average (EWMA) statistic are probably the most frequently used for the quality control of certain semiconductor manufacturing process steps. The threaded-EWMA run-to-run control is an important stable control scheme. However, the process outputs will deviate largely in the first few runs of each cycle if the disturbance follows an IMA(1,1) series with deterministic linear drift and the thread has a long break length. In this paper, the output of the threaded-EWMA run-to-run control is derived, stability conditions are given, and the causes of large deviations in the first few runs of each cycle are found. Based on the analysis of system performance, a cycled resetting (CR) algorithm for discount factor is proposed to reduce the large deviations, as well as to achieve the minimum asymptotic variance control. Furthermore, how to deal with step fault is also discussed in this paper. By analyzing the influence of the fault, a discount factor resetting fault-tolerant (RFT) approach is proposed. Simulation study shows both the mean square error (MSE) and variance of the output by the proposed algorithm is about 30% to 50% lower than that of the algorithm with fixed discount factor in the process with and without oscillation. This verifies the effectiveness of the proposed approach. </para>