Monitoring Spatial Uniformity of Particle Distributions in Manufacturing Processes Using the K Function

Xiaohu Huang; Qiang Zhou; Li Zeng; Xiaodong Li

doi:10.1109/TASE.2015.2479088

Monitoring Spatial Uniformity of Particle Distributions in Manufacturing Processes Using the K Function

Xiaohu Huang, Qiang Zhou, Li Zeng, Xiaodong Li

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

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 product quality. The distributional characteristics of a spatial point pattern can be summarized by functional profiles such as the popular Ripley's K function. By analyzing the K function, we can effectively monitor the distributional behaviors of the spatial point data. In this study, statistical properties of the K function are investigated, and a Gaussian process is found to be appropriate in characterizing its behavior under complete spatial randomness. A control chart is proposed based on the results to monitor the uniformity of point patterns. Our proposed approach has been compared with existing methods through numerical simulations and shown superior performances.

Original language	English (US)
Pages (from-to)	1031-1041
Number of pages	11
Journal	IEEE Transactions on Automation Science and Engineering
Volume	14
Issue number	2
DOIs	https://doi.org/10.1109/TASE.2015.2479088
State	Published - Apr 2017
Externally published	Yes

Keywords

Complete spatial randomness
control chart
Gaussian process model
K function
spatial point pattern

ASJC Scopus subject areas

Control and Systems Engineering
Electrical and Electronic Engineering

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10.1109/TASE.2015.2479088

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title = "Monitoring Spatial Uniformity of Particle Distributions in Manufacturing Processes Using the K Function",

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 product quality. The distributional characteristics of a spatial point pattern can be summarized by functional profiles such as the popular Ripley's K function. By analyzing the K function, we can effectively monitor the distributional behaviors of the spatial point data. In this study, statistical properties of the K function are investigated, and a Gaussian process is found to be appropriate in characterizing its behavior under complete spatial randomness. A control chart is proposed based on the results to monitor the uniformity of point patterns. Our proposed approach has been compared with existing methods through numerical simulations and shown superior performances.",

keywords = "Complete spatial randomness, control chart, Gaussian process model, K function, spatial point pattern",

author = "Xiaohu Huang and Qiang Zhou and Li Zeng and Xiaodong Li",

note = "Funding Information: This paper was recommended for publication by Associate Editor Q. Huang and Editor M. Wang upon evaluation of the reviewers' comments. This work was supported in part by the Hong Kong Research Grants Council under ECS Grant 138213 and in part by the National Science Foundation under Grant CMMI-1266225. Publisher Copyright: {\textcopyright} 2017 IEEE.",

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AU - Huang, Xiaohu

AU - Zhou, Qiang

AU - Zeng, Li

AU - Li, Xiaodong

N1 - Funding Information: This paper was recommended for publication by Associate Editor Q. Huang and Editor M. Wang upon evaluation of the reviewers' comments. This work was supported in part by the Hong Kong Research Grants Council under ECS Grant 138213 and in part by the National Science Foundation under Grant CMMI-1266225. Publisher Copyright: © 2017 IEEE.

PY - 2017/4

Y1 - 2017/4

N2 - 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 product quality. The distributional characteristics of a spatial point pattern can be summarized by functional profiles such as the popular Ripley's K function. By analyzing the K function, we can effectively monitor the distributional behaviors of the spatial point data. In this study, statistical properties of the K function are investigated, and a Gaussian process is found to be appropriate in characterizing its behavior under complete spatial randomness. A control chart is proposed based on the results to monitor the uniformity of point patterns. Our proposed approach has been compared with existing methods through numerical simulations and shown superior performances.

AB - 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 product quality. The distributional characteristics of a spatial point pattern can be summarized by functional profiles such as the popular Ripley's K function. By analyzing the K function, we can effectively monitor the distributional behaviors of the spatial point data. In this study, statistical properties of the K function are investigated, and a Gaussian process is found to be appropriate in characterizing its behavior under complete spatial randomness. A control chart is proposed based on the results to monitor the uniformity of point patterns. Our proposed approach has been compared with existing methods through numerical simulations and shown superior performances.

KW - Complete spatial randomness

KW - control chart

KW - Gaussian process model

KW - K function

KW - spatial point pattern

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Monitoring Spatial Uniformity of Particle Distributions in Manufacturing Processes Using the K Function

Abstract

Keywords

ASJC Scopus subject areas

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