# Online Monitoring and Fault Diagnosis for High-Dimensional Stream with Application in Electron Probe X-Ray Microanalysis

## TL;DR

This paper introduces a new two-stage method for monitoring and diagnosing faults in high-dimensional data streams, showing high accuracy and faster detection than existing methods.

## Contribution

The novel two-stage framework combines EWMA monitoring with a precise fault diagnosis mechanism for high-dimensional sparse-change data streams.

## Key findings

- The method detects anomalies within one or two sampling intervals with near 100% detection power.
- The fault diagnosis mechanism achieves 99.1% accuracy in 200-dimensional streams, outperforming PCA-based methods by 28.0% in precision.

## Abstract

This study introduces an innovative two-stage framework for monitoring and diagnosing high-dimensional data streams with sparse changes. The first stage utilizes an exponentially weighted moving average (EWMA) statistic for online monitoring, identifying change points through extreme value theory and multiple hypothesis testing. The second stage involves a fault diagnosis mechanism that accurately pinpoints abnormal components upon detecting anomalies. Through extensive numerical simulations and electron probe X-ray microanalysis applications, the method demonstrates exceptional performance. It rapidly detects anomalies, often within one or two sampling intervals post-change, achieves near 100% detection power, and maintains type-I error rates around the nominal 5%. The fault diagnosis mechanism shows a 99.1% accuracy in identifying components in 200-dimensional anomaly streams, surpassing principal component analysis (PCA)-based methods by 28.0% in precision and controlling the false discovery rate within 3%. Case analyses confirm the method’s effectiveness in monitoring and identifying abnormal data, aligning with previous studies. These findings represent significant progress in managing high-dimensional sparse-change data streams over existing methods.