中央研究院統計科學研究所 學 術 演 講 講 題：Efficient Design of a Stable Double Multivariate Exponentially Weighted Moving Average Controller
時 間：2008年10月13日(星期一)上午10:3012:00 地 點：中央研究院統計科學研究所蔡元培館二樓208演講廳 ※茶會：上午10：10統計所蔡元培館二樓 摘 要
Many semiconductor manufacturing processes have, by nature, multipleinput and multipleoutput (MIMO) variables. For the firstorder MIMO manufacturing processes with linear drifts, the double multivariate exponentially weighted moving average (dMEWMA) controller is a popular runtorun (R2R) controller for adjusting the process mean to a desired target. To implement this feedback control scheme, we need to build an inputoutput (IO) predicted model at the offline stage. Recently, Tseng, et al. (2007) presented an explicit formula for determining a minimum sample size (which is needed to construct IO predicted model) in such a way that the asymptotic stability of dMEWMA controller can be achieved with a guaranteed probability. This formula indicates that two key components on the sample size determination are: the canonical correlation of IO variables and the condition number of the covariance matrix of input variables. Since this condition number is a nuisance parameter, the problem on how to minimize its effect on the sample size determination is of great practical importance. This paper proposes a stable dMEWMA controller with which the sample size (required at the offline stage) only depends on the canonical correlation of IO variables. Hence, the sample size can be reduced significantly.
