Motivated by the monitoring of automobile complaint data, quality monitoring methods require effective models for analyzing over-dispersed integer-valued time series (INTS) with network dependence and heterogeneous node-level dynamics. Existing count time series models often have limitations in simultaneously characterizing over-dispersion, network interactions, group heterogeneity, and covariate effects, which may reduce their effectiveness in monitoring structural changes in complex networked count processes. To address these challenges, we propose a Grouped Negative-Binomial Network Auto-Regressive (G-NB-NAR) model, in which network nodes are divided into groups and group-specific parameters are introduced to characterize heterogeneous dynamic patterns. The proposed model adopts the negative binomial distribution to accommodate over-dispersion, uses an adjacency matrix to describe network dependence, and incorporates covariates to account for additional explanatory information.The stationarity and ergodicity of the G-NB-NAR model are established, and the consistency and asymptotic normality of the maximum likelihood estimator are derived. For the online monitoring, the fitted model is combined with a top-q CUSUM scheme to detect sparse or localized structural changes in the over-dispersed network count data. Extensive simulations show that the proposed framework performs well in both parameter estimation and change detection. Further ablation experiments and robustness analyses demonstrate that the grouping structure, network dependence, and covariate information all contribute to the monitoring performance, and that the proposed framework remains stable under alternative grouping schemes, mis-specified adjacency structures, unequal group sizes, different network densities, different choices of q in the CUSUM monitoring scheme, and various shift patterns. Finally, an empirical study based on the automobile complaint data illustrates the practical usefulness and interpretability of the proposed method.

Count data are commonly used in the fields of public health surveillance, manufacturing, and safety monitoring. In practice, sample sizes of count data collected at different times often vary over time. Thus, statistical process control for count data with time-varying sample sizes is important and has received considerable attention in the literature. Most existing methods on this topic rely on parametric modeling, assuming a Poisson or negative binomial data distribution. However, such assumptions of the parametric methods are often invalid in practice, leading to unreliable performance of the associated control charts. Additionally, the mean of the process under monitoring is usually assumed to be constant over time, which does not hold in many applications, including disease surveillance where the disease incidence rate often displays a sinusoidal seasonal pattern. To address these issues, this paper develops a nonparametric exponentially weighted moving average control chart for monitoring count data with time-varying sample sizes, based on data categorization and categorical data modeling. Numerical studies show that this method can provide effective and robust process monitoring.

To evaluate the performance of exponentially weighted moving average (EWMA), cumulative sum (CUSUM) and Shewhart charts for monitoring the time between events (TBE), the conditional expected delay (CED) indicator is applied in this paper as a new metric. The Monte Carlo simulation is performed to obtain the CED profiles, which are plotted for different parameter settings. Under different upward or downward change sizes, a detailed comparison is conducted among these TBE charts. The results show that both EWMA TBE and CUSUM TBE charts outperform the Shewhart TBE chart in terms of the CED profiles under both small and large changes. Moreover, both the EWMA and CUSUM TBE charts have their own strengths and weaknesses under certain specific changes and a guide on selecting EWMA or CUSUM TBE chart based on the change sizes is provided. Finally, a real dataset of organic light-emitting diodes (OLEDs) failure time from Samsung company is applied to show the feasibility of the CED indicator in monitoring the process.

Modern quality monitoring in complex systems, such as advanced manufacturing systems andproduct-line networks, requires analyzing over-dispersed integer-valued time series (INTS) with network dependencies. However, modeling such data poses substantial challenges due to the simultaneous presence of network interactions and heterogeneous node-level dynamics.Traditional approaches often underperform due to their inability to account for network structure and node heterogeneity. To overcome these limitations, we propose a Grouped Negative-Binomial Network Auto-Regressive (G-NB-NAR) model that captures heterogeneous node dynamics through group-speciffc parameters. We present the stationarity and ergodicity of the G-NB-NAR model and study the asymptotic properties of the maximum likelihood estimation. For practical implementation to detect any sparse changes in the network data, we integrate the model with a top-r Cumulative Sum (CUSUM) scheme to enhance the anomaly detection ability. Extensive simulations and an empirical study using the automobile complaint data demonstrate the proposed framework’s superior performance over conventional methods, providing an effective statistical tool for quality monitoring in the network data.

Recognized for their simplicity and effectiveness, the run-sum (RS) and exponentially weighted moving average (EWMA) charts are frequently used for monitoring process mean shifts. Although these charts are commonly applied under the normal distribution, many practical manufacturing processes exhibit non-normal distribution. Therefore, this article introduces two one-sided RS and EWMA X̅ charts for non-normal processes, particularly the gamma process. Using the Markov chain approach, theoretical formulations of the run-length metrics, i.e., the average run length (ARL) and the expected ARL (EARL) under the gamma distribution are derived. Both zero-state and steady-state modes are examined. The optimal designs of the one-sided RS X̅ and EWMA X̅ charts by minimizing the out-of-control EARL for the unknown shift-size scenario are developed under the gamma distribution. This article also details the optimal charting parameters specific to gamma distribution. With the implementation of these new designs, our findings reveal that the proposed optimal one-sided RS X̅ and EWMA X̅ charts are effective and efficient in monitoring process mean shifts in gamma processes, outperforming other existing charts. Finally, the practicality and applicability of these proposed optimal charts are demonstrated using real-life manufacturing wafer process data.

This study proposes one-sided self-starting truncated EWMA (SST-EWMA) control charts for effective high-quality process monitoring in situations where extensive in-control time-between-events (TBE) observations are unavailable. By constructing a pivot quantity and establishing variable mappings, a self-starting framework specifically tailored for Gamma distributed TBE observations is developed. The integration of a variable truncation mechanism into this framework further enhances sensitivity to small to moderate process shifts. To investigate the detection properties of the proposed schemes, simulation were conducted to examine the effects of the shape parameter alpha, the number of reference TBE observations M, and the smoothing parameter lambda on the average time to signal (ATS). Based on the simulation results, guidelines are provided for achieving ATS performance comparable to that of the corresponding known-parameter schemes. Comparative analysis demonstrates that, although slightly inferior to the one-sided TEWMA TBE charts under known parameters, the proposed charts exhibit superior adaptability in scenarios with scarce TBE data, and also outperform the existing self-starting EWMA TBE chart, validating the effectiveness of the variable truncation mechanism. Finally, two case studies are presented to illustrate the practical implementation of the proposed control charts in industrial engineering applications.

Due to the stochastic nature of textured surfaces, in-situ quality monitoring for texture-related defects using statistical process monitoring (SPM) is important yet challenging in academic research and industrial applications. This article presents an in-situ EWMA monitoring scheme based on the likelihood ratio test to quantify and detect unexpected global shifts in textured surfaces. We employ Gradient Boosting Regression Trees to implicitly characterise the joint distribution of textile image pixels and for the texture modelling. With the limited number of Phase I samples, the proposed scheme with a data-driven control limit algorithm can estimate the distribution of the charting statistics via the kernel density estimation (KDE) method, continuously update the probability limits at each time point during the monitoring phase and implement the dynamic monitoring to identify defective surfaces with a relatively satisfying in-control monitoring performance. The simulated stochastic experiments confirm the advantage of the proposed method. Also, a real layerwise images monitoring case based on Fused Deposition Modeling from Additive Manufacturing (AM) is provided.

The two-parameter exponential distribution offers greater flexibility and suitability than the classical exponential distribution with a single scale parameter for modelling product lifetimes in reliability analysis and inventory management. Unlike existing schemes designed based on order statistics, new one-sided EWMA schemes using the truncation method are developed in this paper to monitor data following a two-parameter exponential distribution with sample sizes n = 1 as well as n > 1, indifferently. Furthermore, detailed instructions for constructing the Markov chain model and the Monte Carlo simulation are provided to investigate the detecting properties of the recommended schemes, along with cross- validation to verify their effectiveness. Meanwhile, detecting performance comparisons between the proposed lower-sided scheme and the latest relevant scheme are carried out. The simulation results demonstrate that the proposed chart is not only superior to the comparative chart in monitoring efficiency and its resistance to biases in average run length (ARL) and average time to signal (ATS), but it is also more straightforward and accessible for practitioners. Finally, two illustrative examples are presented to demonstrate the implementation of the proposed schemes.

In recent years, different monitoring schemes have been developed to simultaneously detect shifts in the mean parameter of the distributions of time between events ($T$T) and the amplitude ($X$X), generally known as time between events and amplitude (TBEA) monitoring schemes or charts. A vast majority of existing research works focus mainly on monitoring the ratio statistic ${Z_2} = X/T$Z2=X/T between variables T and X. Aside from the ratio statistic, two other statistics, constructed as ${Z_1} = X- T$Z1=X-T and ${Z_3} = X+ 1/T$Z3=X+1/T, have also been investigated by researchers for the process monitoring. Instead of focusing only on monitoring the ratio statistic ${Z_2}$Z2, this paper aims at simultaneously detecting shifts in the mean parameter of $X$X and $T$T with statistics ${Z_1}$Z1, ${Z_2}$Z2 and ${Z_3}$Z3 and further proposes several Exponentially Weighted Moving Average (EWMA) TBEA monitoring schemes, aiming at increasing existing TBEA chart's performance for small to moderate mean shifts. To better align with reality, both skewed and normal distributions are considered for modelling the amplitude $X$X. By using the Markov chain method, the run length properties of the proposed EWMA TBEA schemes are derived. Numerical evaluations are extensively conducted to demonstrate the outperformance of the EWMA TBEA schemes in detecting shifts in different scenarios. A detailed comparison is conducted between the proposed EWMA TBEA schemes with statistics ${Z_1}$Z1, ${Z_2}$Z2 and ${Z_3}$Z3. Moreover, a robustness of the distribution mis-specification for modelling the amplitude $X$X is conducted. Extensive simulations demonstrate that the proposed EWMA TBEA schemes are comparable to the CUSUM TBEA schemes and superior to the existing Shewhart TBEA schemes, especially for small mean shifts. Finally, a real data example of France forest fires is presented to show the implementation of the EWMA TBEA schemes.

Feedback information concerning automotive quality often suffers from significant delays, making online consumer complaints an invaluable real-time source of information for monitoring and assessing product quality. Given that the frequency of online complaints is influenced by numerous factors, such as automobile quality, sales, Internet development, and public awareness of rights protection, it exhibits significant auto-correlation and dynamics. However, the existing modeling methods have been proven to be unreliable in practical applications, because they often assume that in-control (IC) processes remain static and employ models with fixed parameters. To this end, a dynamic modeling framework that integrates generalized linear regression with an integer-valued auto-regressive (INAR) state space model is proposed to capture the evolving nature of the process. Then, a procedure combining the Extended Kalman Smoothing (EKS) with the Expectation Maximization (EM) algorithm, referred to as EM-EKS, is used to estimate the model parameters. Furthermore, for online monitoring of any upward shifts in the number of complaints, a control chart (denoted as SDC-INAR(1)-G) with one-step-ahead forecasting value as the plotting statistic is constructed. Simulation studies show that the proposed SDC-INAR(1)-G method consistently exhibits much better performance than three benchmark approaches in different scenarios. Finally, the proposed SDC-INAR(1)-G method is applied to monitor online complaints of the Volkswagen Sagitar, focusing on two specific cases: the stationary process of "brake abnormal noise" and the non-stationary process of "transmission abnormal noise." The results further demonstrate that the SDC-INAR(1)-G method outperforms the static approaches in both cases. The state-space framework and adaptive EM-EKS parameter estimation of the proposed SDC-INAR(1)-G method ensure robust sensitivities to different shifts, offering reliable monitoring for both stationary and non-stationary data, at the same time, remaining computationally efficient for real-world applications.

Compositional data (CoDa) monitoring in production processes often relies on multivariate control charts (CCs) with isometric log-ratio () transformation to distinguish in-control and out-of-control (OOC) conditions. Traditional CCs effectively detect shifts in the mean vector but struggle with anomalies affecting specific variables. A recurrent neural network (RNN) with backpropagation through time is introduced to interpret OOC signals in the multivariate exponentially weighted moving average CoDa control chart (MEWMA-CoDa CC) to address this challenge. The proposed model pinpoints anomalous variables responsible for OOC events, enhancing process control strategies and improving production efficiency. The model's effectiveness is demonstrated through two CoDa case studies. A P = 5-part CoDa dataset on oil production across five U.S. states (Alaska, Arkansas, Arizona, Colorado, California) is analyzed, with the RNN achieving 93.5% accuracy in identifying the shifted variable. Another case examines agricultural production across four Chinese cities using a P = 4-part CoDa framework, comparing MEWMA-CoDa CC to Hotelling's -CoDa CC. Results indicate superior accuracy for MEWMA-CoDa CC in interpreting OOC signals. A novel approach for CoDa process control is presented, offering significant advancements in anomaly detection and production process optimization.

Recent years have seen Machine learning (ML) integrated into magnetic materials research to accelerate property prediction and discovery. Conventional experimental methods and first-principles calculations remain indispensable for understanding magnetism, but their application is often constrained by high computational cost, limited throughput, and difficulties in treating strongly correlated d/f electrons or spin-orbit-coupled systems. In this context, ML provides a practical data-driven complement that enables the efficient exploration of large compositional and structural spaces and supports the targeted search for materials with desired magnetic characteristics, including Curie temperature, magnetocrystalline anisotropy, magnetization, and magnetocaloric response. This review surveys recent progress in the application of ML to magnetic materials, with a focus on dataset construction, descriptor design, model development, uncertainty assessment, and learning strategies suitable for limited or noisy data. Particular attention is given to challenges that are specific to magnetic-property prediction, such as sparse and inconsistent datasets, correlation-induced errors, and the need for physically interpretable features. Representative case studies are discussed, ranging from the classification of magnetic ground states to the optimization of functional magnetic materials. This review further expands the role of ML in magnetic materials research.

The Luang Prabang Suture Zone, characterized by its unique amalgamation of terranes from varied microcontinents, exhibits distinct metamorphic and paleogeographic histories, impacting the stability of infrastructure such as tunnels. This study addresses the challenges posed by complex tectonic stress patterns and the inherent weakness of rock masses in the suture zones, particularly influencing the China–Laos Railway tunnels. We conducted comprehensive tests, including tectonic stress assessments, rock strength measurements, tunnel loosening zone evaluations, and primary support stress analyses. Our findings reveal that the predominant crustal stress pattern, σ H > σ h > σ v , promotes thrust fault development, with significant deformations observed in carbonaceous slate exhibiting lump structures at suture boundaries. These deformations are primarily manifested through asymmetric sidewall squeezing, exacerbated by the expansion of surrounding rock loosening zones. In response, we propose a novel active control technology, verified through field application. This involves optimizing tunnel cross-sections, refining excavation techniques, employing a strategic long–short bolt system, and enhancing the stiffness of primary supports. Our research not only provides practical solutions for tunnel stability in similar complex geological environments but also extends the theoretical understanding of such geological settings. Future work will focus on refining these innovative control technologies for broader application in challenging tunneling scenarios.

The Maxwell distribution has recently been widely used for life modelling. This paper proposes a new control chart, called the EWMA-LR control chart, for monitoring the Maxwell distribution's quality characteristics with type-II right censored data. We provide the approximate maximum likelihood estimate of the scale parameter for the Maxwell distribution with type-II right censored data. We constructed an EWMA-LR control chart to monitor the shift in the scale parameter of the Maxwell distribution based on the likelihood ratio test. The EWMA-LR control chart is efficient whether it is based on complete or censored data. We evaluate the performance of EWMA-LR control chart using various metrics, including the mean of run length (ARL), the standard deviation of run length (SDRL), and the median of run length (MDRL). Finally, two examples from actual industrial production illustrate the effectiveness of the EWMA-LR control chart in practice.

The ratio of two normal random variables (RZ) is widely used to measure the quality characteristic in many fields or processes, including manufacturing, finance, medicine and so on. Monitoring changes in the RZ is of great importance for the timely detection of any problems and prevention of risks in processes. Due to the insensitivity of the Shewhart scheme to small shifts and the Exponentially Weighted Moving Average (EWMA) scheme to large shifts, some pioneer researchers have suggested the combined Shewhart-EWMA scheme for monitoring both small and large shifts. However, this method is gradually being replaced by another more effective and simple method, namely the Adaptive EWMA (AEWMA) scheme. To improve the detection efficiency of existing RZ charts for both small and large shifts, and at the same time without increasing the RZ charts' complexity, this paper constructs an AEWMA-RZ scheme by introducing an adaptive method. The control limit h, average run length (ARL) and the standard deviation of the run length (SDRL) of the proposed AEWMA-RZ scheme are obtained by numerical Monte Carlo (MC) simulations, and the influence of different parameter combinations on the performance of the proposed AEWMA-RZ scheme is further investigated. A detailed comparison is made between the proposed AEWMA-RZ and two existing RZ monitoring schemes, namely the EWMA-RZ and the combined Shewhart-EWMA-RZ (CSEWMA-RZ) schemes. Simulation results show that the proposed AEWMA-RZ scheme is superior to the EWMA-RZ and CSEWMA-RZ schemes. Finally an example of the food industry ends the paper.

In modern industrial processes, product quality characteristics can sometimes be modeled as statistical regression relationships or functions, often referred to as profiles in the statistical process monitoring field. In practice, the corresponding process parameters are usually unknown and, most of the time, only a few number of samples can be used to estimate these regression coefficients, especially in the case of short run production processes. To adjust the monitoring of quality characteristic profiles under the impact of estimated process parameters in the case of short run production, a single self-starting chart based on the likelihood ratio test and recursive residuals is developed in this paper. This scheme can update the process parameters and monitor the process stability simultaneously, in real-time. Using Monte Carlo simulations, the run length performance of the proposed chart is obtained and compared with other existing charts under various shift case scenarios. Two real case studies from semiconductor and additive manufacturing processes are provided to illustrate and validate the proposed schemes.

In modeling the multivariate time between events (MTBE), Gumbel's Bivariate Exponential (GBE) distribution has played an important role in industrial or service processes. Some works have been conducted on monitoring the processes that follow the GBE distribution. However, existing works on monitoring the GBE distributed processes are mostly on constructing the chart for the specific change size, which actually may vary or not to be known in practice. This may cause the existing designed GBE monitoring schemes' poor detection performance for different changes. To overcome this limitation and improve the existing GBE charts' detection ability for different change sizes, this paper proposes a new multivariate exponentially weighted moving average (MEWMA) chart with an adaptive structure, named as AMEWMA, for monitoring the process following the GBE distribution. Monte Carlo simulation method is employed to obtain the run length (RL) properties, i.e., the average RL, standard deviation of RL, and median of RL, of the proposed monitoring scheme. By selecting different smoothing parameter, the charting parameters of the proposed AMEWMA GBE chart are obtained and the corresponding out-of-control RL performances are studied for different change sizes. A detailed comparative analysis is conducted between the proposed chart and some existing multivariate GBE charts. The findings indicate that the proposed AMEWMA GBE chart generally performs better than the competitors for all sizes of change, in terms of different RL measures. Moreover, in detecting a wide range of changes, it significantly outperforms its counterparts in terms of the RL's overall performance measures. Finally, a genuine dataset of patient headache relief times is utilized to demonstrate the application and execution of the AMEWMA GBE chart.

Weibull distribution has been widely applied in modeling the lifetime in the reliability tests. While in many lifetime tests, the censoring tests are usually employed to save time and cost. As the real lifetimes are only partially observed and the process change may not be fully reflected in the collected samples, this makes it more difficult to improve the production quality and enhance the product lifetime management in statistical process monitoring (SPM). Then the monitoring performance of control charts for the Weibull distributed lifetime may be unsatisfied. To improve the detection ability of control charts for the censored lifetimes, the one-sided weighted adaptive cumulative sum (WACUSUM) chart based on exponentially weighted maximum likelihood estimation is developed for monitoring the Type I censored Weibull distributed lifetimes. Furthermore, to deal with the varying batch sizes and varying censoring rates, the data-driven dynamic probability limits are adopted to the proposed WACUSUM chart. Numerous simulation experiments and a rust-test example are provided to illustrate the proposed chart’s performance and its practical application.

In the area of multivariate process quality control, it is sometimes important to monitor the ratio of two normal random variables denoted by RZ over time. The concept of control charts has often been harnessed in this field, leading to the application of various types of statistical models, including Shewhart, Exponentially Weighted Moving Average (EWMA), and so forth. However, there is little attention to implementation of machine learning-based control charts. To bridge this gap, a novel machine learning based model incorporating the attention mechanism approach, as an implemented Artificial Intelligence (AI) model, is proposed to monitor the RZ in Phase II applications. The proposed RZ method not only provides quicker Out-of-Control (OC) shift detection than conventional RZ control charts but also does not require the quality controller to have any prior information about the upward or downward shift patterns, which is a major assumption in most of the previous RZ models. We provide extensive performance comparison results to discuss the statistical performance of our proposed method through Monte Carlo simulations. Moreover, a comprehensive real example about surveillance of the cryptocurrency market is provided to illustrate the practical application of our proposed method. Through simulation and back-testing results, it is shown how the proposed method can lead to an automated trading strategy.

Parameter estimation has a great effect on the control chart monitoring performance. Collecting sufficient samples may be impossible or time-consuming in some applications. Such dilemma has resulted in the development of self-starting charts that allow the charts to update the process parameters continuously and detect the process change during the monitoring phase. Over the past two decades, much effort has been devoted to profile monitoring aiming to monitor the functional relationship between the response $ \boldsymbol{y} $ y and explanatory $ \boldsymbol{x} $ x variables. However, different practitioners have different in-control samples; the corresponding constructed control limit varies from different practitioners and affects the chart's monitoring efficiency. This paper takes this practitioner-to-practitioner variability into account when monitoring the linear profile with a self-starting scheme. It turns out that the practitioner-to-practitioner variability makes significant variation in the in-control and out-of-control monitoring performance. Several suggestions are provided to alleviate this problem.