Abstract
The thesis includes three research topics and the contents are given as follows: 1. For a drifted multiple-input and multiple-output (MIMO) system, the double multivariate exponentially weighted moving average (dMEWMA) controller is a popular run-to-run (RTR) controller for adjusting the process mean to a desired target. Although the stability and performance of conventional dMEWMA controller had been widely studied in literature, the issue of “how to choose an appropriate initial setting for the input recipe” had not been well discussed in detail. Obviously, if the initial recipe is not chosen appropriately, it usually requires a moderately large number of runs to bring the process output to approach its desired target. In this thesis, by using a Mahalanobis distance approach, we obtain an optimal initial setting for the input recipe in such a way that the process output will approach its desired target rapidly. 2. To implement the conventional dMEWMA controller, we need to build an input-output (I-O) predicted model at the off-line stage. Recently, Tseng et al. (2007) presented an explicit formula for determining a minimum sample size (which is needed to construct I-O 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 I-O 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 thesis proposes a stable dMEWMA controller with which the sample size (required at the off-line stage) only depends on the canonical correlation of I-O variables. Hence, the sample size can be reduced significantly. 3. RTR feedback control methodologies in literature are implemented based on the assumption that process response variables can be successfully measured. In practical applications, due to the metrology capacity limitations, process response variables cannot be measured completely. Hence, “how to implement a skip-lot RTR feedback control scheme” becomes an important research topic. In this thesis, we investigate both the process long-term stability conditions and short-term performance. In addition, by controlling TMSE (total mean square error) less than a specific level, we also provide a simple rule to determine an allowable capacity for the metrology equipment.