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Updated: Apr 18, 2026

Simulation of a Scaled Assembly Process with Collaboration of a Robotic Arm and Monitoring through a Vision System for Quality Control
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Six-sigma approach-based visibility graphs.

Martin Ferenczi1, Alex Kummer2, János Abonyi1

  • 1HUN-REN-PE Complex Systems Monitoring Research Group, University of Pannonia, Egyetem u. 10, H-8200, Veszprém, Hungary.

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Summary
This summary is machine-generated.

This study enhances time series analysis by integrating Statistical Process Control (SPC) with visibility graphs. Zone-labeled graphs reveal how process patterns translate into interpretable network features for anomaly detection.

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Area of Science:

  • Complex networks
  • Time series analysis
  • Statistical Process Control (SPC)

Background:

  • Visibility graphs map time series to networks, but their semantic interpretation is challenging.
  • Understanding what information network characteristics encode is crucial for interpretability.
  • Existing methods lack clear links between graph properties and underlying time series dynamics.

Purpose of the Study:

  • To enhance the interpretability of visibility graphs by integrating Statistical Process Control (SPC).
  • To establish explicit correspondences between SPC patterns and visibility graph signatures.
  • To enable explainable anomaly detection in industrial processes using network representations.

Main Methods:

  • Constructed zone-labeled horizontal visibility graphs (HVGs) using SPC zone classifications (A, B, C, limit violations).
  • Quantized the vertical axis of time series into control chart zones following Six Sigma practices.
  • Analyzed correspondences between SPC patterns and graph signatures like degree distributions, edge weights, motifs, and local communities.

Main Results:

  • Zone-labeled HVGs successfully map SPC-charted time series to interpretable network representations.
  • Specific SPC patterns (long runs, trends, alternations, limit excursions) were linked to distinct graph signatures (skewed degrees, elongated paths, clustering, hubs).
  • The framework provides structured, subgraph-level explanations for process alarms.

Conclusions:

  • Visibility graphs inherently encode actionable information aligned with classical SPC rules.
  • The integration of SPC and visibility graphs provides a novel approach for explainable anomaly detection.
  • This method offers significant potential for industrial process monitoring and quality control applications.