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Process monitoring plays a vital role in ensuring quality stability, and, operational efficiency across fields such as manufacturing, finance, biomedical science, and environmental monitoring. Among statistical tools, control charts are widely adopted for detecting variability and abnormal patterns. Since the introduction of the basic X-bar control chart by Shewhart in the 1920s, various improved methods have emerged to address the challenge of identifying small and latent process shifts, including CUSUM, MA, EWMA, and Exp-EWMA control charts. This study introduces a novel control chart—the Moving Average–Exponentiated Exponentially Weighted Moving Average (MA-Exp-EWMA) control chart—combining the smoothing effect of MA and the adaptive weighting of Exp-EWMA. Its goal is to improve the detection of small shifts and gradual changes. Performance is evaluated using average run length (ARL), standard deviation of run length (SDRL), and median run length (MRL). Monte Carlo simulations under different distributions (normal, exponential, gamma, and Student’s t) and parameter settings assess the control chart’s sensitivity under various shift scenarios. Comparisons with existing control charts and an application to real data demonstrate the practical effectiveness of the proposed method in detecting small shifts.

Control charts are widely used as a tool in process quality monitoring to detect anomalies and to improve the quality of a process and product. Nevertheless, their limitations have increased in the face of increasingly complex manufacturing processes. They do not have capability of handling large streams of non-normal and autocorrelated multivariate data, which is in most real applications. This may lead to an increase in false alarm signals and/or missed detection of anomalies. They are not designed to automatically identify the root causes of an anomaly when the process is out-of-control. Several machine-learning techniques were integrated with control charts to improve the sensitivity and specificity of anomaly detection. Nevertheless, some existing techniques still produce a high false alarm rate and/or missed detection. The root cause analysis is seldom performed. In this paper, we propose a new integration that combines the logical analysis of data regression technique (LADR) and the exponential weighted moving average (EWMA) as a new model-based control chart. LADR is based on the traditional LAD methodology, which is a supervised data mining technique for pattern generation. LADR transforms the original independent variables into pattern variables by using cbmLAD software to develop a regression model. The LADR–EWMA increases the sensitivity of anomaly detection in the process and uses the patterns to perform root cause analysis of that anomaly. We applied LADR–EWMA to a real application: a concrete manufacturing process. We compared its performance with Linear regression, Support vector regression, Partial Least Square regression, and Multivariate adaptive regression Spline. The results demonstrate that the LADR–EWMA, which is based on pattern recognition, performs better compared to the other techniques in terms of a reduction of false alarms and missed detection. In addition, LADR–EWMA facilitates interpretation and identification of the root cause of the detected anomaly.

The Max-Mixed EWMA Exponentially Weighted Moving Average (MM EWMA) control chart is a statistical process control technique used for joint monitoring of the mean and variance of a process. This control chart is designed to detect small and moderate shifts in the mean and variance of a process by comparing the maximum of two statistics, one based on the mean and the other on the variance. In this paper, we propose a new MM EWMA control chart. The proposed chart is compared with existing control charts using simulation studies, and the results show that the chart performs better in detecting small and moderate shifts in both the mean and variance. The proposed chart can be helpful in quality control applications, where joint monitoring of mean and variance is necessary to ensure a product’s or process’s quality. The real-life application of the proposed control chart on yogurt packing in a cup data set shows the outperformance of the MM EWMA control chart. Both simulations & real-life application results demonstrate the better performance of the proposed chart in detecting smaller shifts during the production process.

Background: The stock exchange, as a regulated financial market, in modern economies reflects their economic development level. The stock market indicates the mood of investors in the development of a country and is an important ingredient for growth. Objectives: This paper aims to introduce an additional statistical tool used to support the decision-making process in stock trading, and it investigate the usage of statistical process control (SPC) methods into the stock trading process. Methods/Approach: The individual (I), exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts were used for gaining trade signals. The open and the average prices of CROBEX10 index stocks on the Zagreb Stock Exchange were used in the analysis. The statistical control charts capabilities for stock trading in the short-run were analysed. Results: The statistical control chart analysis pointed out too many signals to buy or sell stocks. Most of them are considered as false alarms. So, the statistical control charts showed to be not so much useful in stock trading or in a portfolio analysis. Conclusions: The presence of non-normality and autocorellation has great impact on statistical control charts performances. It is assumed that if these two problems are solved, the use of statistical control charts in a portfolio analysis could be greatly improved.

This study introduces a novel Variable Sample Size Exponentially Weighted Moving Average (VSS-EWMA) control chart for monitoring the coefficient of variation, termed as Dynamic Adaptive CV (DACV) chart. Tailored for dynamic production settings where both the process mean and variability are subject to change, the proposed chart integrates an adaptive sampling strategy within the EWMA framework, allowing real-time adjustment of sample size in response to process conditions. Comparative analysis with the conventional Fixed Sample Size EWMA (FEWMA) chart reveals that DACV chart exhibits enhanced sensitivity in detecting small to moderate shifts in variability. Its performance is rigorously evaluated using Average Run Length (ARL), Standard Deviation of Run Length (SDRL), and run-length percentiles. Visualizations through heat maps further affirm its robustness across a wide range of shift magnitudes and smoothing parameters. A real-world application using semiconductor manufacturing data demonstrates the practical utility of DACV chart, underscoring its potential in contemporary quality monitoring systems.

EWMA control charts are based on the intuitive idea of accumulating information over the time by exponentially discounted weighting of the observations and hence these charts are known to be relatively effective in detecting small to moderate sized shifts in the mean. The inspiration of this study is to present an overview of the EWMA control charting technique suitable for detecting intrusions in quality management. EWMA control charts with intelligent systems are reviewed. Future directions are provided considering recent developments for EWMA control charts.

This study aims to examine the explicit solution for calculating the Average Run Length (ARL) on the triple exponentially weighted moving average (TEWMA) control chart applied to autoregressive model (AR(p)), where AR(p) is an autoregressive model of order p, representing a time series with dependencies on its p previous values. Additionally, the study evaluates the accuracy of both explicit and numerical integral equation (NIE) solutions for AR(p) using the TEWMA control chart, focusing on the absolute percentage relative error. The results indicate that the explicit and approximate solutions are in close agreement. Furthermore, the study investigates the performance of exponentially weighted moving average (EWMA) and TEWMA control charts in detecting changes in the process, using the relative mean index (RMI) as a measure. The findings demonstrate that the TEWMA control chart outperforms the EWMA control chart in detecting process changes, especially when the value of λ is sufficiently large. In addition, an analysis using historical data from the SET index between January 2024 and May 2024 and historical data of global annual plastic production, the results of both data sets also emphasize the superior performance of the TEWMA control chart.

This study presents an innovative development of the exponentially weighted moving average (EWMA) control chart, explicitly adapted for the examination of time series data distinguished by seasonal autoregressive moving average behavior—SARMA(1,1)L under exponential white noise. Unlike previous works that rely on simplified models such as AR(1) or assume independence, this research derives for the first time an exact two-sided Average Run Length (ARL) formula for the Modified EWMA chart under SARMA(1,1)L conditions, using a mathematically rigorous Fredholm integral approach. The derived formulas are validated against numerical integral equation (NIE) solutions, showing strong agreement and significantly reduced computational burden. Additionally, a performance comparison index (PCI) is introduced to assess the chart’s detection capability. Results demonstrate that the proposed method exhibits superior sensitivity to mean shifts in autocorrelated environments, outperforming existing approaches. The findings offer a new, efficient framework for real-time quality control in complex seasonal processes, with potential applications in environmental monitoring and intelligent manufacturing systems.

The inevitability of faults arises due to prolonged exposure of photovoltaic (PV) power plants to intricate environmental conditions. Therefore, fault diagnosis of PV power plants is crucial to ensure the continuity and reliability of power generation. This paper proposes a fault diagnosis method that integrates PV power prediction and an exponentially weighted moving average (EWMA) control chart. This method predicts the PV power based on meteorological factors using the adaptive particle swarm algorithm-back propagation neural network (APSO-BPNN) model and takes its error from the actual value as a control quantity for the EWMA control chart. The EWMA control chart then monitors the error values to identify fault types. Finally, it is verified by comparison with the discrete rate (DR) analysis method. The results showed that the coefficient of determination of the prediction model of the proposed method reached 0.98. Although the DR analysis can evaluate the overall performance of the inverter and identify the faults, it often fails to point out the specific location of the faults accurately. In contrast, the EWMA control chart can monitor abnormal states such as open and short circuits and accurately locate the string where the fault occurs.

The accurate modeling and predicting of landslide deformation is crucial to the prevention of landslide hazard. This paper presents a pioneering study of modeling and predicting the reservoir landslide displacement with deep learning algorithm. A data-driven framework using deep belief network and control chart has been introduced to explore the temporal patterns of displacement and potential of identifying seasonal faster displacement. First, the continuous wavelet analysis has been applied to decompose the time-series precipitation, reservoir water level, and displacement into seasonal and residual components. Second, the deep belief network has been constructed to predict the future displacement. Third, it utilizes the exponentially weighted moving average (EWMA) control chart to derive the boundaries as alarm conditions of seasonal faster displacement. A group of tests are conducted to compare the performance of the deep belief network with other state-of-the-art machine learning algorithms. Computational results demonstrated the effectiveness of the deep belief network in extracting highly non-linear data features. In addition, the advantage of utilizing control charts has been further validated by the accuracy of examining the seasonal faster displacement based on the case study in Baishuihe landslide in Three Gorges Reservoir, China.