Mathematical Sciences: "Nonlinear Modeling of Spatially Correlated Data: Preliminary Investigations"

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Jacqueline M. Hughes-Oliver North Carolina State University Data collection in the semiconductor industry is such that repeated measurements --- obtained over a spatial grid on a single wafer --- are the norm, not the exception. Following this proposed planning period, the projected research goal is the development of methodological advances for nonlinear modeling of spatially correlated data with nonstationary, nonnormal errors. This work is well motivated by two real-life applications, which both indicate immediate need for these advances. A major result of research on the analysis of repeated measurements is the discovery that careful representation of the correlation structure is not necessary, provided the number of experimental units far exceeds the number of repeated measurements. The cost of wafers in the semiconductor industry, however, prohibits collection of data for very many wafers. Hence, careful representation of the possibly nonstationary error covariance structure must be undertaken. This constitutes the first of the planning activities. Specific modeling and estimation techniques must also be investigated in light of the (new) correlation structures. These constitute additional planning activities. Realistic modeling of these semiconductor processes require relaxing the assumption of normality, and a willingness to consider nonlinear models. Planning activities include preliminary investigations of the complications arising from these generalities. The final activity is the development of the regular NSF proposal.