Statistical surface monitoring by spatial-structure modeling

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.