A Variable Multivariate EWMA Controller for Run-By-Run Process Adjustment

Sheng-Tsaing Tseng ； Fugee Tsung ； Ching-Dar Wu

《中國統計學報》 46卷2期 (2008/06) Pp. 81-105

https://doi.org/10.29973/JCSA.200806.0001

並列摘要

Run by run process control; multivariate EWMA controller; variable discount The exponentially weighted moving average (EWMA) feedback controller (with a fixed discount factor) is a popular run-by-run control scheme for both univariate and multivariate processes 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 is impractical for process with 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, the authors apply a variable discount factor to tackle the problem in multivariate run-by-run processes. They state the main results in which the stability conditions and the optimal variable discount factor of the proposed multivariate EWMA controller are derived, and a heuristic is proposed to simplify the computation of the variable discount factor.

並列關鍵字

Run by run process control ； multivariate EWMA controller ； variable discount factor

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