Manufacturing Quality Control Based on Spatial Point Pattern Analysis

Abstract

Data in the form of spatial point patterns are frequently encountered in some manufacturing processes such as the nanoparticle reinforced composite materials and defects on semiconductor wafers. Their spatial characteristics contain rich information about the fabrication processes and are often strongly related to the final product quality. The distributional characteristics of a spatial point pattern can be summarized by some functional profiles such as the popular Ripley’s K function, L function, pair correlation function and so on. By analyzing these summary functions, the distributional behaviors of spatial points in a point pattern can be effectively monitored.

The investigation begins by approximately fitting the Ripley’s K function with a nonstationary Gaussian process under complete spatial randomness. Theoretical inference is provided and supported by accurate simulation studies. The proposed T2 control chart and EWMA control chart are utilized based on the multivariate normality property for the detection of the non-randomness and compared to the existing detection methods like quadrat-based methods and integration methods of various characteristic functions. The proposed control charts show superior performances in most occasions through numerical simulations.

After the non-randomness is detected in a spatial point pattern, a detailed and accurate diagnosis is crucially desirable. Based on the advancement on modelling the K function using the Gaussian process, a diagnosis procedure through decomposition of a K function-based T2 statistic has been proposed. The decomposition provides a novel way for independently analyzing point interactions at multiple spatial scales, which is particularly useful for fault diagnosis when the process is out-of-control. Improvement can be possible done given the detailed fault information provided by the decomposition results.

For now most statistical analyses are implemented based on two-dimensional (2D) images obtained from three-dimensional (3D) specimens. It would be more straightforward if the 3D distributional features of particles in composite materials can be extracted. A novel approach by inferring the size distribution of 3D particle clusters based on multiple 2D cross-sectional microscopic images has been proposed. The likelihood of the first l biggest 2D cluster radii shown on the 2D cross-sectional image is derived and maximized to obtain the maximum likelihood estimation of the parameters in the parametric distribution of 3D cluster radius. Corresponding simulation studies prove the effectiveness and accuracy of the estimation results. Compared to the existing method, our proposed method is more practical and robust in real cases.

Date of Award	19 Jun 2017
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Qiang ZHOU (Supervisor) & Min XIE (Supervisor)