Towards Universal Representation-Based Process Control

2026-09-25

AI Summary

This study addresses the limitation of traditional local window monitoring, which relies on fixed parametric assumptions and struggles to adapt to empirical reference distributions. To overcome this, we reformulate window-level monitoring as a reference-based nonparametric hypothesis test. Specifically, representations are extracted via a pretrained time series encoder, and kernel density estimation is employed to define the null hypothesis using empirical distributions. Conformal calibration is further introduced to ensure valid inference under finite-sample conditions. This approach transcends parametric constraints and unifies concepts such as stationarity, significantly enhancing detection sensitivity to window-level distribution shifts while maintaining rigorous calibration in stable regimes. Consequently, the proposed method is broadly applicable to diverse time series monitoring tasks.

Abstract

Many temporal process learning and monitoring pipelines operate in local windows, making window-level decisions unavoidable in practice. In such settings, classical statistical tests can be applied to individual windows, but they typically evaluate predefined parametric hypotheses-such as unit-root or moment-based conditions-thereby limiting flexibility when reference behavior is defined empirically from task- or domain-specific data. In this work, we view window-level monitoring as a process control problem and reformulate it as reference-based hypothesis testing, where the null hypothesis is specified by an empirical reference distribution rather than a fixed parametric model. We operationalize this perspective through a representation-based, nonparametric framework that combines pretrained time series encoders, kernel density estimation, and conformal calibration, yielding finite-sample valid inference in learned representation space. Classical notions such as stationarity and cyclostationarity arise as natural instantiations of empirical reference sets within this framework. Through experiments, we demonstrate sensitivity to window-level distributional deviations while maintaining well-calibrated inference under stable reference regimes, highlighting the applicability of the proposed approach to a broad class of time series process control and monitoring tasks.

Problem

• process control
• time series monitoring
• window-level hypothesis testing
• nonparametric reference distribution
• representation learning

Innovation

• Process Control
• Representation Learning
• Nonparametric Hypothesis Testing
• Conformal Calibration
• Time Series Monitoring