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Mathematics
Special Issues
Statistical Monitoring and AI Models
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Statistical Monitoring and AI Models

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 15 June 2025 | Viewed by 6595

Special Issue Editors

Dr. Achraf Cohen

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, Hal Marcus College of Science and Engineering, The University of West Florida, Pensacola, FL, USA
Interests: statistical process monitoring; wavelets analysis; statistical modeling; predictive modeling; data-driven methods; quality engineering; machine learning applicaitons
Prof. Dr. Yichuan Zhao

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA
Interests: nonparametric statistics; survival analysis; empirical likelihood; biostatistics; Bayesian analysis

Special Issue Information

Dear Colleagues,

The fields of Machine Learning (ML), Deep Learning (DL), and Artificial Intelligence (AI) have undergone remarkable expansions over the past few decades. This surge in growth can be largely attributed to significant advancements in computing power and the unprecedented availability of vast amounts of data.

Statistical monitoring plays a crucial role in various fields by creating sophisticated models designed to estimate and evaluate the current state of the systems. By utilizing these models, researchers and practitioners can gain insights into system performance and health.

This Special Issue aims to encourage research that explores innovative techniques and applications across a wide range of statistical monitoring contexts. We are particularly interested in studies that are focused on the monitoring of AI models, which encompasses evaluating their performance, assessing their trustworthiness, and ensuring their reliability. Furthermore, we invite submissions that investigate the application of AI in critical areas such as health monitoring, process monitoring, and other relevant fields.

Key topics of interest include:

- Machine Learning: Techniques that enable systems to learn from data.
- Deep Learning: Advanced algorithms that mimic the human brain to analyze data patterns.
- Large Language Models: Powerful AI tools that process and generate human-like text.
- Statistical Process Monitoring: Methods for tracking the performance of processes in various industries.
- Anomaly Detection: Techniques for identifying irregular patterns or outliers in data.
- AI Trustworthiness: Assessing the ethical implications and reliability of AI systems.
- AI Reliability: Ensuring consistent and dependable performance in AI applications.

We look forward to receiving contributions that push the boundaries of knowledge in these vital areas.

Dr. Achraf Cohen
Prof. Dr. Yichuan Zhao
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • AI models for monitoring systems
  • Statistical Evaluation of AI models
  • Monitoring of AI models
  • Trustworthy AI metrics
  • Statistical monitoring and AI applications

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Published Papers (2 papers)

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Research

12 pages, 270 KiB  
Article
Kernel-Based Multivariate Nonparametric CUSUM Multi-Chart for Detection of Abrupt Changes
by Lei Qiao and Bing Wang
Mathematics 2024, 12(10), 1473; https://doi.org/10.3390/math12101473 - 9 May 2024
Viewed by 1274
Abstract
In many cases, it is difficult to obtain precise distributional information on multivariate sequences. Therefore, there is a need to propose nonparametric methods for monitoring multivariate sequences. This article discusses the multivariate change detection problem and utilizes the kernel function as the statistic [...] Read more.
In many cases, it is difficult to obtain precise distributional information on multivariate sequences. Therefore, there is a need to propose nonparametric methods for monitoring multivariate sequences. This article discusses the multivariate change detection problem and utilizes the kernel function as the statistic to construct the nonparametric Multivariate Cumulative Sum multi-chart, under the assumption that there is prior information about the abrupt changes. Through theoretical and numerical analysis, we show that the proposed control chart is more effective compared to other existing control charts. The good monitoring effect of this method demonstrates a strong potential for application. Full article
(This article belongs to the Special Issue Statistical Monitoring and AI Models)
16 pages, 1986 KiB  
Article
Unknown Health States Recognition with Collective-Decision-Based Deep Learning Networks in Predictive Maintenance Applications
by Chuyue Lou and Mohamed Amine Atoui
Mathematics 2024, 12(1), 89; https://doi.org/10.3390/math12010089 - 26 Dec 2023
Cited by 1 | Viewed by 1632
Abstract
At present, decision-making solutions developed based on deep learning (DL) models have received extensive attention in predictive maintenance (PM) applications along with the rapid improvement of computing power. Relying on the superior properties of shared weights and spatial pooling, convolutional neural networks (CNNs) [...] Read more.
At present, decision-making solutions developed based on deep learning (DL) models have received extensive attention in predictive maintenance (PM) applications along with the rapid improvement of computing power. Relying on the superior properties of shared weights and spatial pooling, convolutional neural networks (CNNs) can learn effective representations of health states from industrial data. Many developed CNN-based schemes, such as advanced CNNs that introduce residual learning and multi-scale learning, have shown good performance in health states recognition tasks under the assumption that all the classes are known. However, these schemes have no ability to deal with new abnormal samples that belong to state classes not part of the training set. In this paper, a collective decision framework for different CNNs is proposed. It is based on a one-vs.-rest network (OVRN) to simultaneously achieve classification of known and unknown health states. OVRNs learn class-specific discriminative features and enhance the ability to reject new abnormal samples incorporated to different CNNs. According to the validation results on the public dataset of the Tennessee Eastman process (TEP), the proposed CNN-based decision schemes incorporating an OVRN have outstanding recognition ability for samples of unknown heath states while maintaining satisfactory accuracy on known states. The results show that the new DL framework outperforms state-of-the-art CNNs, and the one based on residual and multi-scale learning has the best overall performance. Full article
(This article belongs to the Special Issue Statistical Monitoring and AI Models)
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