Experimental design methods for nano-fabrication processes
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Most design of experiments assumes predetermined design regions. Design regions with uncertainty are of interest in the first chapter. This chapter proposes optimal designs under a two-part model to handle the uncertainty in the design region. In particular, the logit model in the two-part model is used to assess the uncertainty on the boundary of the design region. The second chapter proposes an efficient and effective multi-layer data collection scheme (Layers of Experiments) for building accurate statistical models to meet tight tolerance requirement commonly encountered in nano-fabrication. "Layers-of-Experiments" (LOE) obtain sub-regions of interest (layer) where the process optimum is expected to lie and collect more data in the sub-regions with concentrated focus. The third chapter contributes a new design criterion combining model-based optimal design and model-free space-filling design in a constraint manner. The proposed design is useful when the fitted statistical model is required to have both characteristics: accuracy in statistical inference and design space exploration. The fourth chapter proposes adaptive combined designs in the layers of experiments. This chapter also develops methods to improve model quality by combining information from various layers and from engineering models. Combined designs are modified to improve its efficiency by incorporate collected field data from several layers of experiments. Updated engineering models are used to build more accurate statistical models.