We address the Statistical Process Control (SPC) of high-dimensional, dynamic industrial processes from two complementary perspectives: manifold fitting and manifold learning, both of which assume data lies on an underlying nonlinear, lower dimensional space. We propose two distinct monitoring frameworks for online or 'phase II' Statistical Process Control (SPC). The first method leverages state-of-the-art techniques in manifold fitting to accurately approximate the manifold where the data resides within the ambient high-dimensional space. It then monitors deviations from this manifold using a novel scalar distribution-free control chart. In contrast, the second method adopts a more traditional approach, akin to those used in linear dimensionality reduction SPC techniques, by first embedding the data into a lower-dimensional space before monitoring the embedded observations. We prove how both methods provide a controllable Type I error probability, after which they are contrasted for their corresponding fault detection ability. Extensive numerical experiments on a synthetic process and on a replicated Tennessee Eastman Process show that the conceptually simpler manifold-fitting approach achieves performance competitive with, and sometimes superior to, the more classical lower-dimensional manifold monitoring methods. In addition, we demonstrate the practical applicability of the proposed manifold-fitting approach by successfully detecting surface anomalies in a real image dataset of electrical commutators.

This research integrates deep learning, copula functions, and survival analysis to effectively handle highly correlated and right-censored multivariate survival data. It introduces copula-based activation functions (Clayton, Gumbel, and their combinations) to model the nonlinear dependencies inherent in such data. Through simulation studies and analysis of real breast cancer data, our proposed CNN-LSTM with copula-based activation functions for multivariate multi-types of survival responses enhances prediction accuracy by explicitly addressing right-censored data and capturing complex patterns. The model's performance is evaluated using Shewhart control charts, focusing on the average run length (ARL).

It has been 100 years since statistical process control (SPC) or statistical process monitoring (SPM) was first introduced for production processes and later applied to service, healthcare, and other industries. The techniques applied to SPM applications are mostly statistically oriented. Recent advances in Artificial Intelligence (AI) have reinvigorated the imagination of adopting AI for SPM applications. This manuscript begins with a concise review of the historical development of the statistically based SPM methods. Next, this manuscript explores AI and Machine Learning (ML) algorithms and methods applied in various SPM applications, addressing quality characteristics of univariate, multivariate, profile, and image. These AI methods can be classified into the following categories: classification, pattern recognition, time series applications, and generative AI. Specifically, different kinds of neural networks, such as artificial neural networks (ANN), convolutional neural networks (CNN), recurrent neural networks (RNN), and generative adversarial networks (GAN), are among the most implemented AI methods impacting SPM. Finally, this manuscript outlines a couple of future directions that harness the potential of the Large Multimodal Model (LMM) for advancing SPM research and applications in complex systems. The ultimate objective is to transform statistical process monitoring (SPM) into smart process control (SMPC), where corrective actions are autonomously implemented to either prevent quality issues or restore process performance.

Detecting anomalous behavior in dynamic networks remains a constant challenge. This problem is further exacerbated when the underlying topology of these networks is affected by individual highly-dimensional node attributes. We address this issue by tracking a network's modularity as a proxy of its community structure. We leverage Graph Neural Networks (GNNs) to estimate each snapshot's modularity. GNNs can account for both network structure and high-dimensional node attributes, providing a comprehensive approach for estimating network statistics. Our method is validated through simulations that demonstrate its ability to detect changes in highly-attributed networks by analyzing shifts in modularity. Moreover, we find our method is able to detect a real-world event within the \#Iran Twitter reply network, where each node has high-dimensional textual attributes.

The recurrent neural network and its variants have shown great success in processing sequences in recent years. However, this deep neural network has not aroused much attention in anomaly detection through predictively process monitoring. Furthermore, the traditional statistic models work on assumptions and hypothesis tests, while neural network (NN) models do not need that many assumptions. This flexibility enables NN models to work efficiently on data with time-varying variability, a common inherent aspect of data in practice. This paper explores the ability of the recurrent neural network structure to monitor processes and proposes a control chart based on long short-term memory (LSTM) prediction intervals for data with time-varying variability. The simulation studies provide empirical evidence that the proposed model outperforms other NN-based predictive monitoring methods for mean shift detection. The proposed method is also applied to time series sensor data, which confirms that the proposed method is an effective technique for detecting abnormalities.

The rapid advancement of models based on artificial intelligence demands innovative monitoring techniques which can operate in real time with low computational costs. In machine learning, especially if we consider artificial neural networks (ANNs), the models are often trained in a supervised manner. Consequently, the learned relationship between the input and the output must remain valid during the model's deployment. If this stationarity assumption holds, we can conclude that the ANN provides accurate predictions. Otherwise, the retraining or rebuilding of the model is required. We propose considering the latent feature representation of the data (called "embedding") generated by the ANN to determine the time when the data stream starts being nonstationary. In particular, we monitor embeddings by applying multivariate control charts based on the data depth calculation and normalized ranks. The performance of the introduced method is compared with benchmark approaches for various ANN architectures and different underlying data formats.

Generative Artificial Intelligence (AI) models such as OpenAI's ChatGPT have the potential to revolutionize Statistical Process Control (SPC) practice, learning, and research. However, these tools are in the early stages of development and can be easily misused or misunderstood. In this paper, we give an overview of the development of Generative AI. Specifically, we explore ChatGPT's ability to provide code, explain basic concepts, and create knowledge related to SPC practice, learning, and research. By investigating responses to structured prompts, we highlight the benefits and limitations of the results. Our study indicates that the current version of ChatGPT performs well for structured tasks, such as translating code from one language to another and explaining well-known concepts but struggles with more nuanced tasks, such as explaining less widely known terms and creating code from scratch. We find that using new AI tools may help practitioners, educators, and researchers to be more efficient and productive. However, in their current stages of development, some results are misleading and wrong. Overall, the use of generative AI models in SPC must be properly validated and used in conjunction with other methods to ensure accurate results.

--Hydropower plants are one of the most convenient option for power generation, as they generate energy exploiting a renewable source, they have relatively low operating and maintenance costs, and they may be used to provide ancillary services, exploiting the large reservoirs of available water . The recent advances in Information and Communication T echnologies (ICT) and in machine learning methodologies are seen as fundamental enablers to upgrade and modernize the current operation of most hydropower plants, in terms of condition monitoring, early diagnostics and eventually predictive maintenance. While very few works, or running technologies, have been documented so far for the hydro case, in this paper we propose a novel Key Performance Indicator (KPI) that we have recently developed and tested on operating hydropower plants. In particular, we show that after more than one year of operation it has been able to identify several faults, and to support the operation and maintenance tasks of plant operators. S power generation from renewable sources is increasingly seen as a fundamental component in a joint effort to support decarbonization strategies, hydroelectric power generation is experiencing a new golden age. In fact, hydropower has a number of advantages compared to other types of power generation from renewable sources. Most notably, hydropower generation can be ramped up and down, which provides a valuable source of flexibility for the power grid, for instance, to support the integration of power generation from other renewable energy sources, like wind and solar. In addition, water in hydropower plants' large reservoirs may be seen as an energy storage resource in low-demand periods and transformed into electricity when needed [1], [2].

Control charts have traditionally been used in industrial statistics, but are constantly seeing new areas of application, especially in the age of Industry 4.0. This paper introduces a new method, which is suitable for applications in the healthcare sector, especially for monitoring a health-characteristic of a patient. We adapt a Markov chain-based approach and develop a method in which not only the shift size (i.e. the degradation of the patient's health) can be random, but the effect of the repair (i.e. treatment) and time between samplings (i.e. visits) too. This means that we do not use many often-present assumptions which are usually not applicable for medical treatments. The average cost of the protocol, which is determined by the time between samplings and the control limit, can be estimated using the stationary distribution of the Markov chain. Furthermore, we incorporate the standard deviation of the cost into the optimisation procedure, which is often very important from a process control viewpoint. The sensitivity of the optimal parameters and the resulting average cost and cost standard deviation on different parameter values is investigated. We demonstrate the usefulness of the approach for real-life data of patients treated in Hungary: namely the monitoring of cholesterol level of patients with cardiovascular event risk. The results showed that the optimal parameters from our approach can be somewhat different from the original medical parameters.

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