Theoretical foundation
Motivation, assumptions, multilinear representation, tensor Q and T² monitoring logic, and the statistical interpretation of structured versus residual variation.
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Tensor-Structured Statistical Process Control
A technical monograph on high-dimensional process monitoring using tensor methods, including theory, implementation, simulation, ARL and detection-delay analysis, and comparative evaluation against vectorized PCA baselines.
Abstract
Publication Summary
Tensor-structured statistical process control extends classical multivariate monitoring by preserving multiway structure rather than collapsing observations into vectorized forms. This work develops the theoretical foundation, implementation workflow, and simulation-based evaluation of tensor Q and tensor T² monitoring, together with comparative benchmarks against vectorized PCA baselines. The resulting framework is designed for high-dimensional, structured process data where interpretability, structure-aware detection, and extensibility are central.
Overview
What this work covers
Implementation workflow
Practical development through tensor foundations, Tucker/HOSVD decomposition, score-space monitoring, and sequential SPC extensions.
Comparative evaluation
Simulation studies comparing tensor monitoring to vectorized PCA through detection behavior, Monte Carlo benchmarking, ARL analysis, and curated results.
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Citation
Publication Details
Title: Tensor-Structured Statistical Process Control
Author: Jeff M.
Year: 2026
DOI:
https://doi.org/10.5281/zenodo.19701711
Recommended citation:
Jeff M. (2026). Tensor-Structured Statistical Process Control. Zenodo.
https://doi.org/10.5281/zenodo.19701711