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Sample Size Determination for Achieving Stability of Double Multivariate Exponentially Weighted Moving Average Controller

Summary: ´╗┐[This abstract is based on the authors' abstract.] Semiconductor manufacturing processes that have multiple-input and multiple-output (MIMO) variables often use the double multivariate exponentially weighted moving average run-to-run controller for adjusting the process mean to a desired target. The long-term stability of this closed-loop MIMO system using a controller with estimated process parameters depends on whether an initial input-output predicted model is available to accurately estimate these process parameters. Stability conditions for the MIMO process depend on the estimated controller and are expressed in terms of probability. A formula is derived for the adequate sample size to achieve stability with guaranteed probability. Two MIMO examples are used to illustrate the proposed procedure.

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  • Topics: Statistics
  • Keywords: Correlation, Canonical analysis, Exponentially weighted moving average (EWMA), Input/Output Analysis, Process control, Run order, Stability, Semiconductors
  • Author: Tseng, Sheng-Tsaing; Tang, Jen; Lin, Chien-Hua
  • Journal: Technometrics