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 journalArticlepeer-review

8 Scopus citations


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 languageEnglish (US)
Pages (from-to)1031-1041
Number of pages11
JournalIEEE Transactions on Automation Science and Engineering
Issue number2
StatePublished - Apr 2017
Externally publishedYes


  • 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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