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Keywords = Statistical Process Control (SPC)

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20 pages, 489 KB  
Systematic Review
Mathematical and Algorithmic Advances in Machine Learning for Statistical Process Control: A Systematic Review
by Yulong Qiao, Tingting Han, Zixing Wu, Ge Jin, Qian Zhang and Qin Xu
Entropy 2026, 28(2), 151; https://doi.org/10.3390/e28020151 - 29 Jan 2026
Viewed by 264
Abstract
Integrating machine learning (ML) with Statistical Process Control (SPC) is important for Industry 4.0 environments. Contemporary manufacturing data exhibit high-dimensionality, autocorrelation, non-stationarity, and class imbalance, which challenge classical SPC assumptions. This systematic review, conducted following the PRISMA 2020 guidelines, provides a problem-driven synthesis [...] Read more.
Integrating machine learning (ML) with Statistical Process Control (SPC) is important for Industry 4.0 environments. Contemporary manufacturing data exhibit high-dimensionality, autocorrelation, non-stationarity, and class imbalance, which challenge classical SPC assumptions. This systematic review, conducted following the PRISMA 2020 guidelines, provides a problem-driven synthesis that links these data challenges to corresponding methodological families in ML-based SPC. Specifically, we review approaches for (1) high-dimensional and redundant data (dimensionality reduction and feature selection), (2) autocorrelated and dynamic processes (time-series and state-space models), and (3) data scarcity and imbalance (cost-sensitive learning, generative modeling, and transfer learning). Nonlinearity is treated as a cross-cutting property within each category. For each, we outline the mathematical rationale of representative algorithms and illustrate their use with industrial examples. We also summarize open issues in interpretability, thresholding, and real-time deployment. This review offers structured guidance for selecting ML techniques suited to complex manufacturing data and for designing reliable online monitoring pipelines. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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10 pages, 452 KB  
Proceeding Paper
A Generic Model Integrating Machine Learning and Lean Six Sigma
by Fadwa Farchi, Chayma Farchi, Badr Touzi and Charif Mabrouki
Eng. Proc. 2025, 112(1), 81; https://doi.org/10.3390/engproc2025112081 - 19 Jan 2026
Viewed by 204
Abstract
With rapid urbanization and population growth, efficient transportation systems are increasingly crucial, particularly in sectors like healthcare and pharmaceutical logistics, which face unique challenges. In Morocco, there is a lack of studies on pharmaceutical transport, especially regarding costs and delivery conditions, creating a [...] Read more.
With rapid urbanization and population growth, efficient transportation systems are increasingly crucial, particularly in sectors like healthcare and pharmaceutical logistics, which face unique challenges. In Morocco, there is a lack of studies on pharmaceutical transport, especially regarding costs and delivery conditions, creating a need for a specialized model. This research presents the development and validation of a predictive model for optimizing urban transport in Morocco. Tested across key sectors—pharmaceuticals, agri-food, electronics, and manufactured goods—the model demonstrated strong performance, though variations emerged based on product complexity. Notably, the agri-food sector presented greater logistical challenges, while the manufacturing and electronics sectors yielded higher prediction accuracy. By integrating statistical process control (SPC) and Lean Six Sigma principles, the model ensures ongoing performance monitoring and continuous improvement. It supports cost reduction, time optimization, and lower environmental impact through enhanced route planning and delivery efficiency. The pharmaceutical sector was selected as a case study due to its critical logistical constraints, such as cold chain requirements and the need for high reliability. Python was used for model development, enabling rapid iteration and collaborative validation. The results confirm the model’s adaptability and generalizability to similar urban environments across North and Sub-Saharan Africa. The study offers a robust and scalable framework for improving transport efficiency while aligning with sustainability and smart mobility goals. Full article
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25 pages, 4742 KB  
Article
Comparison of EWMA, MA, and MQ Under a Unified PBRTQC Framework for Thyroid and Coagulation Tests
by Banjiu Zhaxi, Chaochao Ma, Qian Chen, Yingying Hu, Wenyi Ding, Xiaoqi Li and Ling Qiu
Diagnostics 2026, 16(2), 288; https://doi.org/10.3390/diagnostics16020288 - 16 Jan 2026
Viewed by 314
Abstract
Background: Patient-based real-time quality control (PBRTQC) enables continuous analytical monitoring using routine patient results; however, the performance of classical statistical process control (SPC) algorithms varies across analytes, and standardized evaluation and optimization strategies remain limited. To address this gap, this study compared three [...] Read more.
Background: Patient-based real-time quality control (PBRTQC) enables continuous analytical monitoring using routine patient results; however, the performance of classical statistical process control (SPC) algorithms varies across analytes, and standardized evaluation and optimization strategies remain limited. To address this gap, this study compared three SPC algorithms—moving average (MA), moving quantile (MQ), and exponentially weighted moving average (EWMA)—within a unified preprocessing framework and proposed a composite performance metric for parameter optimization. Methods: Routine patient results from six laboratory analytes were analyzed using a standardized “transform–truncate–alarm” PBRTQC workflow. Simulated systematic biases were introduced for model training, and algorithm-specific parameters were optimized using a composite metric integrating sensitivity, false-positive rate (FPR), and detection delay. Performance was subsequently evaluated on an independent validation dataset. Results: For most analytes, all three SPC algorithms demonstrated robust PBRTQC performance, achieving high sensitivity (generally ≥0.85), very low false-positive rates (<0.002), and rapid detection of systematic bias. EWMA showed more balanced performance for thyroid-stimulating hormone (TSH), with improved sensitivity and shorter detection delay compared with MA and MQ. The proposed composite metric effectively facilitated clinically meaningful parameter optimization across algorithms. Conclusions: Under a unified preprocessing framework, classical SPC algorithms provided reliable PBRTQC performance across multiple analytes, with EWMA offering advantages for more variable measurements. The proposed composite metric supports standardized, practical, and analyte-adaptive PBRTQC implementation in clinical laboratories. Full article
(This article belongs to the Section Clinical Laboratory Medicine)
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25 pages, 4730 KB  
Article
Process Capability Assessment and Surface Quality Monitoring in Cathodic Electrodeposition of S235JRC+N Electric-Charging Station
by Martin Piroh, Damián Peti, Patrik Fejko, Miroslav Gombár and Michal Hatala
Materials 2026, 19(2), 330; https://doi.org/10.3390/ma19020330 - 14 Jan 2026
Viewed by 309
Abstract
This study presents a statistically robust quality-engineering evaluation of an industrial cathodic electrodeposition (CED) process applied to large electric-charging station components. In contrast to predominantly laboratory-scale studies, the analysis is based on 1250 thickness measurements, enabling reliable assessment of process uniformity, positional effects, [...] Read more.
This study presents a statistically robust quality-engineering evaluation of an industrial cathodic electrodeposition (CED) process applied to large electric-charging station components. In contrast to predominantly laboratory-scale studies, the analysis is based on 1250 thickness measurements, enabling reliable assessment of process uniformity, positional effects, and long-term stability under real production conditions. The mean coating thickness was specified at 21.84 µm with a standard deviation of 3.14 µm, fully within the specified tolerance window of 15–30 µm. One-way ANOVA revealed statistically significant but technologically small inter-station differences (F(49, 1200) = 3.49, p < 0.001), with an effect size of η2 ≈ 12.5%, indicating that most variability originates from inherent within-station common causes. Shewhart X¯–R–S control charts confirmed process stability, with all subgroup means and dispersions well inside the control limits and no evidence of special-cause variation. Distribution tests (χ2, Kolmogorov–Smirnov, Shapiro–Wilk, Anderson–Darling) detected deviations from perfect normality, primarily in the tails, attributable to the superposition of slightly heterogeneous station-specific distributions rather than fundamental non-Gaussian behaviour. Capability and performance indices were evaluated using Statistica and PalstatCAQ according to ISO 22514; the results (Cp = 0.878, Cpk = 0.808, Pp = 0.797, Ppk = 0.726) classify the process as conditionally capable, with improvement potential mainly linked to reducing positional effects and centering the mean closer to the target thickness. To complement the statistical findings, an AIAG–VDA FMEA was conducted across the entire value stream. The highest-risk failure modes—surface contamination, incorrect bath chemistry, and improper hanging—corresponded to the same mechanisms identified by SPC and ANOVA as contributors to thickness variability. Proposed corrective actions reduced RPN values by 50–62.5%, demonstrating strong potential for capability improvement. A predictive machine-learning model was implemented to estimate layer thickness and successfully reproduced the global trend while filtering process-related noise, offering a practical tool for future predictive quality control. Full article
(This article belongs to the Section Electronic Materials)
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19 pages, 554 KB  
Article
Enhancing Industry 4.0 Energy Efficiency: A Data-Driven Dynamic Control for Pull-Flow Lines
by Paolo Renna
Appl. Sci. 2026, 16(1), 467; https://doi.org/10.3390/app16010467 - 1 Jan 2026
Viewed by 409
Abstract
This paper investigates the effectiveness of dynamic switch-off policies in flow line production systems, aiming to balance energy efficiency and operational performance. A three-machine simulation model is developed and tested under steady-state and fluctuating processing conditions. The proposed policy, based on adaptive thresholds [...] Read more.
This paper investigates the effectiveness of dynamic switch-off policies in flow line production systems, aiming to balance energy efficiency and operational performance. A three-machine simulation model is developed and tested under steady-state and fluctuating processing conditions. The proposed policy, based on adaptive thresholds and Statistical Process Control (SPC) logic, is compared against two benchmarks: the traditional always-on model and a fixed switch-off policy. Simulation results demonstrate that the dynamic policy reduces customer-related performance measures—specifically queue lengths and waiting times—by approximately 50–56% compared to fixed policies. Crucially, this improvement is achieved while maintaining energy savings (~11%) and work-in-process reduction (~38%) comparable to the static approach. These benefits remain consistent even under high-variability scenarios, confirming the robustness of the proposed control architecture for Industry 4.0 sustainable manufacturing. Full article
(This article belongs to the Special Issue Advanced Technologies for Industry 4.0 and Industry 5.0, 2nd Edition)
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39 pages, 4591 KB  
Article
Capability of New Modified EWMA Control Chart for Integrated and Fractionally Integrated Time-Series: Application to US Stock Prices
by Kotchaporn Karoon and Yupaporn Areepong
Symmetry 2026, 18(1), 5; https://doi.org/10.3390/sym18010005 - 19 Dec 2025
Viewed by 279
Abstract
Among various statistical process-control (SPC) methods, control charts are widely employed as essential instruments for monitoring and improving process quality. This study focuses on a new modified exponentially weighted moving-average (New Modified EWMA) control chart that enhances detection capability under integrated and fractionally [...] Read more.
Among various statistical process-control (SPC) methods, control charts are widely employed as essential instruments for monitoring and improving process quality. This study focuses on a new modified exponentially weighted moving-average (New Modified EWMA) control chart that enhances detection capability under integrated and fractionally integrated time-series processes. Special attention is given to the effect of symmetry on the chart structure and performance. The proposed chart preserves a symmetric monitoring configuration, in which the two-sided design (LCL>0) establishes control limits that are equally spaced around the center line, enabling balanced detection of both upward and downward shifts. Conversely, the one-sided version (LCL=0) introduces a deliberate asymmetry to increase sensitivity to upward mean shifts, which is particularly useful when downward deviations are physically implausible or less critical. The efficacy of the control chart utilizing both models is assessed through Average Run Length (ARL). Herein, the explicit formula of ARL is derived and compared to the ARL obtained from the Numerical Integral Equation (NIE) in terms of both accuracy and computational time. The accuracy of the analytical ARL expression is validated by its negligible percentage difference (%diff) in comparison to the results derived using the NIE approach, and the display processing time not exceeding 3 s. To confirm the highest capability, the suggested method is compared to both the classic EWMA and the modified EWMA charts using evaluation metrics such as ARL and SDRL (standard deviation run length), as well as RMI (relative mean index) and PCI (performance comparison index). Since asset values are volatile due to positive and negative market influences, symmetry is crucial in financial monitoring. Thus, symmetric control-chart structures reduce directional bias and better portray financial market activity by balancing upward and downward movements. Finally, examination of US stock prices illustrates performance, employing a symmetrical two-sided control chart for the rapid detection of changes through the new modified EWMA, in contrast to standard EWMA and modified EWMA charts. Full article
(This article belongs to the Section Mathematics)
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25 pages, 1753 KB  
Article
Improving the Detection Ability of Binary CUSUM Risk-Adjusted Control Charts with Run Rules
by Zoha Hussain, Ali Yeganeh, Sifiso Vilakati, Frans F. Koning and Sandile C. Shongwe
Symmetry 2025, 17(12), 2114; https://doi.org/10.3390/sym17122114 - 9 Dec 2025
Viewed by 552
Abstract
Conventional statistical process control (SPC) charting, an efficient monitoring and diagnosis scheme, is under development in several fields of healthcare monitoring. Investigation of clinical binary outcomes using risk-adjusted (RA) control charts is an important subject in this area. Different researchers have extended the [...] Read more.
Conventional statistical process control (SPC) charting, an efficient monitoring and diagnosis scheme, is under development in several fields of healthcare monitoring. Investigation of clinical binary outcomes using risk-adjusted (RA) control charts is an important subject in this area. Different researchers have extended the monitoring of the binary outcomes of cardiac surgeries by fitting a logistic model for a patient’s death probability against the patient’s risk. As a result, different RA-based cumulative sum (CUSUM) charts have been proposed for monitoring a patient’s 30-day mortality in several studies. Here, a novel run rules method is introduced in conjunction with the RA CUSUM control chart. The suggested approach was tested and benchmarked through simulation studies based on the average run length (ARL) metric. The outcomes showed favourable results, and further analysis under beta-distributed conditions confirmed its robustness. A worked example was presented to illustrate its implementation. Full article
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17 pages, 1332 KB  
Article
A Dynamic Empirical Bayes Signal Model for Attribute Defect Detection
by Yadpirun Supharakonsakun
Signals 2025, 6(4), 71; https://doi.org/10.3390/signals6040071 - 8 Dec 2025
Viewed by 627
Abstract
This study evaluates Empirical Bayes (EB) c-charts for monitoring count-type data under precautionary (PLF) and logarithmic (LLF) loss functions. By assuming an exponential prior for the Poisson mean, the EB framework enables the construction of predictive densities for future observations. Simulation studies and [...] Read more.
This study evaluates Empirical Bayes (EB) c-charts for monitoring count-type data under precautionary (PLF) and logarithmic (LLF) loss functions. By assuming an exponential prior for the Poisson mean, the EB framework enables the construction of predictive densities for future observations. Simulation studies and a real-world dataset on missing rivets in large aircraft were used to compare the methods’ ability to detect out-of-control conditions. The results show that EB–LLF charts exhibit high sensitivity for small and moderate process shifts, and both EB approaches outperform the classical c-chart by integrating prior information to detect shifts earlier while controlling false alarms. These findings highlight the importance of loss function choice and demonstrate the effectiveness of EB charts for robust process monitoring. Full article
(This article belongs to the Special Issue Recent Development of Signal Detection and Processing)
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21 pages, 4528 KB  
Article
Influence of Shock Absorber Construction on Production Parameters of Its Prototype Solutions
by Marek Stembalski, Szymon Ręczkowski and Tomasz Szydłowski
Appl. Sci. 2025, 15(23), 12567; https://doi.org/10.3390/app152312567 - 27 Nov 2025
Viewed by 614
Abstract
This article describes the conducted examinations of five different prototype shock absorbers. The differences resulted from deliberate modifications to their components. The tests were divided into five series of measurements, each involving testing five identical shock absorber designs. The authors assessed the repeatability [...] Read more.
This article describes the conducted examinations of five different prototype shock absorbers. The differences resulted from deliberate modifications to their components. The tests were divided into five series of measurements, each involving testing five identical shock absorber designs. The authors assessed the repeatability and process capability of the production process for each shock absorber design. The study also aimed to identify factors that could lead to undesirable variations in the shock absorber’s dynamic parameters, such as damping force, the shape of the force–displacement characteristic, differences in the system’s response during compression and rebound, and the variability of the response depending on the piston’s speed. The results were then analyzed by using various research methods, among which the most important is the SPC (Statistical Process Control) method. Furthermore, statistical results, such as Cp, Cpk, stability graphs, and process repeatability, are presented. Full article
(This article belongs to the Section Mechanical Engineering)
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13 pages, 1075 KB  
Article
Research on the Structural Model of Welding Process Specifications for Aviation Products Based on Trade-Off Design
by Xichang Wang, Guangli Li, Yuansong Zeng, Xufeng Wang, Xiaochun Lyu and Yukun Cao
Standards 2025, 5(4), 31; https://doi.org/10.3390/standards5040031 - 14 Nov 2025
Viewed by 570
Abstract
The formulation of robust Welding Procedure Specifications (WPS) is paramount in aviation manufacturing, where quality directly impacts structural integrity and flight safety. Current practices, however, often rely on experiential knowledge and lack a systematic methodology for balancing performance, reliability, and economy, leading to [...] Read more.
The formulation of robust Welding Procedure Specifications (WPS) is paramount in aviation manufacturing, where quality directly impacts structural integrity and flight safety. Current practices, however, often rely on experiential knowledge and lack a systematic methodology for balancing performance, reliability, and economy, leading to unstable product quality and limited forward-design capability. This study addresses these gaps by proposing a novel, three-layer structural model for aviation WPS based on trade-off design principles. The model integrates a comprehensive correlation matrix linking product requirements to process elements, a modular architecture for enhanced reusability, and a knowledge-driven validation workflow. A key feature of the validation method is the use of a scientifically designed process test matrix and Statistical Process Control (SPC) to quantitatively determine process margins and capability indices (Cv, Cpk), moving beyond traditional pass/fail criteria. The application of this methodology is demonstrated and validated through a case study on electron beam welding. The results indicate that the proposed framework provides a systematic approach for developing stable, economical, and digitally ready welding process specifications, thereby significantly improving the forward-design capability in aviation welding. Full article
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24 pages, 2940 KB  
Article
Driving Green Through Lean: A Structured Causal Analysis of Lean Practices in Automotive Sustainability
by Matteo Ferrazzi and Alberto Portioli-Staudacher
Eng 2025, 6(11), 296; https://doi.org/10.3390/eng6110296 - 1 Nov 2025
Viewed by 640
Abstract
The urgent global challenge of environmental sustainability has intensified interest in integrating Lean Management practices with environmental objectives, particularly within the automotive industry, a sector known for both innovation and high environmental impact. This study investigates the systemic relationships between 16 lean practices [...] Read more.
The urgent global challenge of environmental sustainability has intensified interest in integrating Lean Management practices with environmental objectives, particularly within the automotive industry, a sector known for both innovation and high environmental impact. This study investigates the systemic relationships between 16 lean practices and three environmental performance metrics: energy consumption, CO2 emissions, and waste generation. Using the Fuzzy Decision-Making Trial And Evaluation Laboratory (DEMATEL) methodology, data were collected from seven lean experts in the Italian automotive industry to model the cause–effect dynamics among the selected practices. The analysis revealed that certain practices, such as Total Productive Maintenance (TPM), just-in-time (JIT), and one-piece-flow, consistently act as influential drivers across all environmental objectives. Conversely, practices like Statistical Process Control (SPC) and Total Quality Management (TQM) were identified as highly dependent, delivering full benefits only when preceded by foundational practices. The results suggest a strategic three-step implementation roadmap tailored to each environmental goal, providing decision-makers with actionable guidance for sustainable transformation. This study contributes to the literature by offering a structured perspective on lean and environmental sustainability in the context of the automotive sector in Italy. The research is supported by a data-driven method to prioritize practices based on their systemic influence and contextual effectiveness. Full article
(This article belongs to the Section Chemical, Civil and Environmental Engineering)
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7 pages, 1263 KB  
Proceeding Paper
Servo Motor Predictive Maintenance by Kafka Streams and Deep Learning Based on Acoustic Data
by Attila Aradi and Attila Károly Varga
Eng. Proc. 2025, 113(1), 1; https://doi.org/10.3390/engproc2025113001 - 28 Oct 2025
Viewed by 1169
Abstract
Servo motors, which are critical for high-precision industrial applications, require predictive maintenance to minimize downtime, aligning with Industry 5.0’s human-centric manufacturing. This study presents a system for Delta servo motors using acoustic data. An ESP32 LyraT module streams audio via HTTP to a [...] Read more.
Servo motors, which are critical for high-precision industrial applications, require predictive maintenance to minimize downtime, aligning with Industry 5.0’s human-centric manufacturing. This study presents a system for Delta servo motors using acoustic data. An ESP32 LyraT module streams audio via HTTP to a server, which forwards it to Apache Kafka. Convolutional neural networks (CNNs) detect anomalies; Statistical Process Control (SPC) identifies early faults; and ARIMA, LSTM, and Prophet forecast maintenance. A device architecture with IP-based device ID and a GUI supports monitoring. Experiments with an ESP32 LyraT (Espressif Systems, Shanghai, China) monitoring Delta ASDA-A3 motors (Delta Electronics, Taipei, Taiwan) over 72 h achieved 91% anomaly detection accuracy for anomalous sounds, 84% early fault detection, and LSTM forecasting of MSE trends with MAE 0.0078 for 24 h predictions. The system supported 32 kB/s with <1% packet loss. The system offers accurate monitoring, advancing Industry 5.0. Future work will include vibration data and web dashboards. Full article
(This article belongs to the Proceedings of The Sustainable Mobility and Transportation Symposium 2025)
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16 pages, 1240 KB  
Article
Fault Diagnosis Method and Application for GTs Based on Dynamic Quantile SPC and Prior Knowledge
by Guanlin Wang, Zhikuan Jiao, Xiyue Yang and Xiaoyong Gao
Processes 2025, 13(10), 3092; https://doi.org/10.3390/pr13103092 - 27 Sep 2025
Viewed by 631
Abstract
This paper addresses the challenges of fault diagnosis in gas turbines (GTs) utilized in oil and gas pipeline systems by proposing a novel multiparameter analysis framework that integrates dynamic, quantile-based Statistical Process Control (SPC) with prior domain knowledge. The proposed approach initially employs [...] Read more.
This paper addresses the challenges of fault diagnosis in gas turbines (GTs) utilized in oil and gas pipeline systems by proposing a novel multiparameter analysis framework that integrates dynamic, quantile-based Statistical Process Control (SPC) with prior domain knowledge. The proposed approach initially employs a dynamic quantile SPC model to establish adaptive control limits, effectively handling the non-stationarity and non-normality of gas turbine operational data. By analyzing parameter variations under typical operating conditions and incorporating expert insights, a multiparameter fault analysis matrix and corresponding weighting factors are constructed to facilitate fault diagnosis with prior knowledge. Furthermore, a fault probability model based on parameter change rates and weighting factors is developed to quantify the likelihood of different fault modes. An operating condition clustering and correction mechanism enables the dynamic adjustment of control limits, thereby preventing misdiagnoses caused by varying operational states. The validity of the proposed method is demonstrated using real data from a domestic pipeline gas turbine, validated by real domestic pipeline GT data, outperforming existing models, with a fault accuracy up to 10%. The approach efficiently estimates fault probabilities and accurately detects both sudden and gradual faults, significantly enhancing intelligent fault diagnosis capabilities for gas turbines. Full article
(This article belongs to the Section Process Control and Monitoring)
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16 pages, 751 KB  
Article
Enhancing Sensitivity of Nonparametric Tukey Extended EWMA-MA Charts for Effective Process Mean Monitoring
by Khanittha Talordphop, Yupaporn Areepong and Saowanit Sukparungsee
Symmetry 2025, 17(9), 1457; https://doi.org/10.3390/sym17091457 - 4 Sep 2025
Viewed by 758
Abstract
A control chart is a crucial statistical process control (SPC) instrument for identifying method variances that may undermine product efficacy. The combined control chart has been utilized to enhance recognition capability. When testing a methodology, nonparametric statistics make a strong and compelling case [...] Read more.
A control chart is a crucial statistical process control (SPC) instrument for identifying method variances that may undermine product efficacy. The combined control chart has been utilized to enhance recognition capability. When testing a methodology, nonparametric statistics make a strong and compelling case when the distribution of a quality feature is uncertain. The primary focus of monitoring this work is to offer a novel control chart to support the surveillance of mean activities. This chart will incorporate a Tukey method, an extended exponentially weighted moving average control chart, and a moving average control chart called the Nonparametric EEWMA-MA chart. The Monte Carlo simulation facilitates assessments for evaluating system performance using average run lengths (ARL) based on zero-state. The comparison analysis demonstrates that the sensitivity of the suggested chart surpasses that of the conventional control chart (including the moving average (MA) chart, the extended exponentially weighted moving average (EEWMA) chart, and the mixed extended exponentially weighted moving average-moving average (EEWMA-MA) chart) in rapidly detecting changes that fluctuate with varying parameter settings by examining the minimal ARL. A simplified monitoring scenario using data on vinyl chloride can be employed to demonstrate the feasibility of the proposed technique. Full article
(This article belongs to the Section Mathematics)
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18 pages, 3979 KB  
Article
Generation and Classification of Novel Segmented Control Charts (SCC) Based on Hu’s Invariant Moments and the K-Means Algorithm
by Roberto Baeza-Serrato
Appl. Sci. 2025, 15(15), 8550; https://doi.org/10.3390/app15158550 - 1 Aug 2025
Viewed by 723
Abstract
Control charts (CCs) are one of the most important techniques in statistical process control (SPC) used to monitor the behavior of critical variables. SPC is based on the averages of the samples taken. In this way, not every measurement is observed, and errors [...] Read more.
Control charts (CCs) are one of the most important techniques in statistical process control (SPC) used to monitor the behavior of critical variables. SPC is based on the averages of the samples taken. In this way, not every measurement is observed, and errors in measurements or out-of-control behaviors that are not shown graphically can be hidden. This research proposes a novel segmented control chart (SCC) that considers each measurement of the samples, expressed in matrix form. The vision system technique is used to segment measurements by shading and segmenting into binary values based on the control limits of SPC. Once the matrix is segmented, the seven main features of the matrix are extracted using the translation-, scale-, and rotation-invariant Hu moments of the segmented matrices. Finally, a grouping is made to classify the samples in clear and simple language as excellent, good, or regular using the k-means algorithm. The results visually display the total pattern behavior of the samples and their interpretation when they are classified intelligently. The proposal can be replicated in any production sector and strengthen the control of the sampling process. Full article
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