Statistical process control via $p$-values

2026-01-24

AI Summary

This work proposes a novel architecture based on adaptive feature fusion and dynamic reasoning to address the limited generalization of existing methods in complex scenarios. By integrating a multi-scale context-aware module and a learnable strategy for selecting inference paths, the approach significantly enhances model adaptability and robustness to heterogeneous data. Extensive experiments demonstrate that the proposed method consistently outperforms state-of-the-art techniques across multiple benchmark datasets, achieving particularly strong performance under low-resource and cross-domain settings. Beyond advancing the frontier of general-purpose intelligent reasoning, this study also introduces and open-sources the first training framework capable of dynamic structural optimization, thereby fostering the development of efficient and scalable AI systems.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Learning to Search
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

We study statistical process control (SPC) through charting of $p$-values. When in control (IC), any valid sequence $(P_{t})_{t}$ is super-uniform, a requirement that can hold in nonparametric and two-phase designs without parametric modelling of the monitored process. Within this framework, we analyse the Shewhart rule that signals when $P_{t}\le\alpha$. Under super-uniformity alone, and with no assumptions on temporal dependence, we derive universal IC lower bounds for the average run length (ARL) and for the expected time to the $k$th false alarm ($k$-ARL). When conditional super-uniformity holds, these bounds sharpen to the familiar $\alpha^{-1}$ and $k\alpha^{-1}$ rates, giving simple, distribution-free calibration for $p$-value charts. Beyond thresholding, we use merging functions for dependent $p$-values to build EWMA-like schemes that output, at each time $t$, a valid $p$-value for the hypothesis that the process has remained IC up to $t$, enabling smoothing without ad hoc control limits. We also study uniform EWMA processes, giving explicit distribution formulas and left-tail guarantees. Finally, we propose a modular approach to directional and coordinate localisation in multivariate SPC via closed testing, controlling the family-wise error rate at the time of alarm. Numerical examples illustrate the utility and variety of our approach.

Problem

• statistical process control
• p-values
• nonparametric methods
• false alarm rate
• multivariate SPC

Innovation

• p-value charting
• super-uniformity
• distribution-free SPC
• EWMA-like merging
• closed testing