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In some manufacturing processes, the quality characteristic is represented by a two-dimensional (2-D) surface. Surface data can generally be treated as a special profile with one response variable and two explanatory variables, for which spatial correlations are commonly observed. Existing parametric charts for profile monitoring are unable to adequately describe the spatial correlations among variables in 2-D surface data, and nonparametric charts cannot be applied to a 2-D data structure directly. In this study, we propose a new chart based on the Gaussian-Kriging model, in which the spatial correlations within the 2-D surface profile are represented by a parametric function. We construct a parametric model that considers three components of the surface—the global trend, the spatial correlations, and independent errors. Then we monitor the process by detecting changes in the estimated parameters. We utilize this method to monitor a wafer-manufacturing process and compare its performance with that of an existing profile-monitoring method through simulation.

In some manufacturing processes, the quality characteristic is represented by a two-dimensional (2-D) surface. Surface data can generally be treated as a special profile with one response variable and two explanatory variables, for which spatial correlations are commonly observed. Existing parametric charts for profile monitoring are unable to adequately describe the spatial correlations among variables in 2-D surface data, and nonparametric charts cannot be applied to a 2-D data structure directly. In this study, we propose a new chart based on the Gaussian-Kriging model, in which the spatial correlations within the 2-D surface profile are represented by a parametric function. We construct a parametric model that considers three components of the surface—the global trend, the spatial correlations, and independent errors. Then we monitor the process by detecting changes in the estimated parameters. We utilize this method to monitor a wafer-manufacturing process and compare its performance with that of an existing profile-monitoring method through simulation.

The study and computation of nonlinear charged-particle transfer maps is fundamental to understanding single-particle beam dynamics in accelerator devices. Transfer maps for individual elements of the beamline can in general depend sensitively on nonlinear fringe-field and high-multipole effects. The inclusion of these effects requires a detailed and realistic model of the interior and fringe magnetic fields, including knowledge of high spatial derivatives. Current methods for computing such maps often rely on idealized models of beamline elements. This Dissertation describes the development and implementation of a collection of techniques for computing realistic (as opposed to idealized) charged-particle transfer maps for general beamline elements, together with corresponding estimates of numerical error. Each of these techniques makes use of 3-dimensional measured or numerical field data on a grid as provided, for example, by various 3-dimensional finite element field codes. The required high derivatives of the corresponding vector potential A, required to compute transfer maps, cannot be reliably computed directly from this data by numerical differentiation due to numerical noise whose effect becomes progressively worse with the order of derivative desired. The effect of this noise, and its amplification by numerical differentiation, can be overcome by fitting on a bounding surface far from the axis and then interpolating inward using the Maxwell equations. The key ingredients are the use of surface data and the smoothing property of the inverse Laplacian operator. We explore the advantages of map computation using realistic field data on surfaces of various geometry. Maps obtained using these techniques can then be used to compute realistically all derived linear and nonlinear properties of both single pass and circular machines. Although the methods of this Dissertation have been applied primarily to magnetic beamline elements, they can also be

The effects of surface roughness on production of steel sheet are critically reviewed. New developments in the measurement and characterisation of surface roughness seem likely to improve our understanding of its effect on sheet metal production. Much useful information can still be acquired by 2D techniques but increasingly the evidence is that sheet metal surface roughness is better measured and characterised by 3D methods. The facility for direct surface visualization in 3D is shown to be particularly helpful. When measuring 3D the measurement area size and sampling space are critical and for evaluation the filtering of surface data into roughness and waviness is more complicated than for 2D profiles.

This technical note addresses operational mesoanalysis associated with convective weather. It discusses physical interpretations of the dynamics which govern the atmosphere and, in particular, convection. The technical note describes upper air data analysis with emphasis on vertical motion, thermodynamic and kinematic considerations and soundings; surface data analysis including topics on discontinuities, boundaries, pressure and thermal analysis, and terrain features. Also discussed are objective analysis tools and interpretation of numerical guidance. The technical note emphasizes the fact that mesoanalysis must be based upon physical rather than tie analysis process to particular weather charts and develop a set of parameters, the concept of integrating all available analysis tools into a physically consistent picture in heavily stressed., Also available as Rept. no. NOAA-TM-NWS-NSSFC-5.