Nonparametric Monitoring of Spatial Dependence

2024-08-30

AI Summary

Existing nonparametric process monitoring methods struggle to effectively detect changes in spatial dependence—particularly under nonlinear, bidirectional, or outlier-contaminated conditions. To address this, we propose a distribution-free control chart based on Spatial Ordinal Patterns (SOP), applicable to two- or three-dimensional regular grid data without requiring Phase-I modeling. Our method innovatively integrates SOP with a Box–Pierce–type higher-order spatial autocorrelation test to construct a robust, nonparametric statistic for monitoring spatial dependence. Simulation studies demonstrate substantial performance gains over conventional parametric approaches. The method is validated on three real-world applications: extreme rainfall events in Germany, wildfire detection in Ukrainian conflict zones, and textile defect inspection. An open-source Julia package, OrdinalPatterns.jl, implementing the methodology, is publicly available.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

In process monitoring, it is common for measurements to be taken regularly or randomly from different spatial locations in two or three dimensions. While there are nonparametric methods for process monitoring with such spatial data to detect changes in the mean, there is a gap in the literature for nonparametric control charting methods developed to monitor spatial dependence. This study considers streams of regular, rectangular data sets using spatial ordinal patterns (SOPs) as a nonparametric method to detect spatial dependencies. We propose novel SOP control charts, which are distribution-free and do not require prior Phase-I analysis. To uncover higher-order dependencies, we develop a new class of statistics that combines SOPs with the Box-Pierce approach. An extensive simulation study demonstrates the superiority and effectiveness of our proposed charts over traditional parametric approaches, particularly when the spatial dependence is nonlinear or bilateral or when the spatial data contains outliers. The proposed SOP control charts are illustrated using real-world datasets to detect (i) heavy rainfall in Germany, (ii) war-related fires in (eastern) Ukraine, and (iii) manufacturing defects in textile production. This wide range of applications and findings demonstrates the broad utility of the proposed nonparametric control charts. In addition, all methods in this study are provided as a publicly available exttt{Julia} package on href{https://github.com/AdaemmerP/OrdinalPatterns.jl}{GitHub} for further implementations.

Problem

• Nonparametric monitoring of spatial dependence in data
• Detecting spatial dependencies without distribution assumptions
• Handling nonlinear or bilateral spatial dependencies and outliers

Innovation

• Uses spatial ordinal patterns for nonparametric monitoring
• Combines SOPs with Box-Pierce for higher-order dependencies
• Provides distribution-free control charts without Phase-I analysis