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Symmetry
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Symmetry Application in Statistical Process Control
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Symmetry Application in Statistical Process Control

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "B: Mathematics".

Deadline for manuscript submissions: 30 September 2026 | Viewed by 1117

Editors

Prof. Dr. Liu Liu

E-Mail Website
Guest Editor
Geomathematics Key Laboratory of Sichuan Province, College of Mathematical Sciences, Chengdu University of Technology, Chengdu 610059, China
Interests: statistical process control; change point detection; random effects models; quality control; big data analytics; statistics and artificial intelligence; biostatistics/biomedical statistics
Dr. Xin Lai

E-Mail Website
Guest Editor
School of Computer Science and Technology, Faculty of Electronics and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China
Interests: statistical process control; medical risk prediction and monitoring
Dr. Zhonghua Li

E-Mail Website
Guest Editor
LPMC, LEBPS and KLMDASR, School of Statistics and Data Science, Nankai University, Tianjin 300071, China
Interests: statistical process control; change point; high dimensional statistical inference; robust statistics; graphical model
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Statistical process control (SPC) and change point detection are vital for ensuring reliability in the era of complex data. As AI and big data analytics merge with statistics, understanding the underlying structural properties of data becomes essential. This Special Issue explores the intersection of quality control and bio-statistics, with a particular focus on symmetry and asymmetry in statistical modeling. We invite contributions addressing high-dimensional monitoring, machine learning integration, and robust detection. Topics of interest include handling asymmetric distributions in skewed data, optimizing decisions under symmetric versus asymmetric loss functions, and exploiting the symmetry inherent in high-dimensional covariance matrices. By bridging statistical theory with modern AI, this issue aims to advance methodology in manufacturing and healthcare, enhancing system precision and resilience through the lens of symmetry.

Prof. Dr. Liu Liu
Dr. Xin Lai
Dr. Zhonghua Li
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 250 words) can be sent to the Editorial Office for assessment.

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-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly 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 2400 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

  • statistical process control
  • change point detection
  • quality control
  • big data analytics
  • statistics and artificial intelligence
  • biostatistics/biomedical statistics

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Published Papers (2 papers)

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Research

37 pages, 2014 KB  
Article
Analysis of Average Run Length of Extended and New Extended Exponentially Weighted Moving Average Control Charts Using Markov Chain Approach Under Symmetric Distribution
by Apitad Kraichok, Yupaporn Areepong and Saowanit Sukparungsee
Symmetry 2026, 18(6), 938; https://doi.org/10.3390/sym18060938 - 29 May 2026
Viewed by 268
Abstract
Statistical Process Control (SPC) plays a crucial role in monitoring and improving manufacturing processes to ensure product quality. Control charts using exponentially weighted moving averages (EWMA) and their extensions, including Extended EWMA (EEWMA) and New Extended EWMA (NEEWMA), have been developed to increase [...] Read more.
Statistical Process Control (SPC) plays a crucial role in monitoring and improving manufacturing processes to ensure product quality. Control charts using exponentially weighted moving averages (EWMA) and their extensions, including Extended EWMA (EEWMA) and New Extended EWMA (NEEWMA), have been developed to increase the sensitivity for detecting small to medium process changes. This research proposes a method for calculating the Average Run Length (ARL) and Standard Deviation of Run Length (SDRL) of control charts under a symmetric distribution using the Markov Chain Approach (MCA). This method is based on the probability of state transitions between controlled and uncontrolled states. The MCA method is more efficient than the Monte Carlo Simulation Approach (MC) in terms of accuracy and significantly reduces processing time. This research also demonstrates the application of ARL and SDRL calculations using the MCA method in various studies. Firstly, the performance of control charts is compared using the Mean Percentage Error (MPE) and Mean Absolute Percentage Error (MAPE). Secondly, the impact of symmetrically distributed process parameters on the performance of control charts is examined. Thirdly, a practical application of the control charts is presented. This research applies the proposed method to detect changes in unemployment insurance claims (UI) using seasonally adjusted initial claims assessment (ICSA) and continuing claims assessment (CCSA) rates from 2021 to 2025. The results show that the MCA method is more efficient than the MC method in terms of accuracy and significantly reduces processing time. Full article
(This article belongs to the Special Issue Symmetry Application in Statistical Process Control)
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32 pages, 3208 KB  
Article
Integration of Unsupervised Machine Learning into Statistical Process Control: Handling Distributional Asymmetry with Poisson Mixture EWMA Charts
by Selin Saraç Güleryüz
Symmetry 2026, 18(6), 896; https://doi.org/10.3390/sym18060896 - 25 May 2026
Viewed by 343
Abstract
The Poisson exponentially weighted moving average (PEWMA) control chart rests upon the equidispersion assumption of the pure Poisson distribution, a structural symmetry condition stipulating that the process mean and variance are equal. In manufacturing environments characterized by latent process heterogeneity, this assumption is [...] Read more.
The Poisson exponentially weighted moving average (PEWMA) control chart rests upon the equidispersion assumption of the pure Poisson distribution, a structural symmetry condition stipulating that the process mean and variance are equal. In manufacturing environments characterized by latent process heterogeneity, this assumption is systematically violated: the resulting distributions are inherently asymmetric, heavily right-skewed, and overdispersed. This structural asymmetry renders standard PEWMA control limits artificially narrow, inducing a substantial inflation of false alarm rates. This paper introduces the Poisson mixture EWMA (PM-EWMA) control chart, which models the latent heterogeneous structure of count data as a finite Poisson mixture distribution, with parameters estimated via the Expectation–Maximization (EM) algorithm without requiring prior labeling of process states. The optimal number of components is determined via the Bayesian Information Criterion (BIC) as the primary criterion, supplemented by the Akaike Information Criterion (AIC), its bias-corrected variant (AICc), and the log-likelihood ratio diagnostic. The PM-EWMA chart incorporates the exact mixture variance, accounting for both within-component and between-component variability, into the EWMA control limit structure, thereby providing a theoretically justified correction under the fitted Poisson mixture assumption. A Monte Carlo simulation study comprising 495 factorial configurations benchmarks the PM-EWMA chart against both the standard PEWMA chart and the negative binomial EWMA (NB-EWMA) chart with oracle dispersion calibration, confirming stable in-control ARL performance and demonstrating improved discrimination relative to the misspecified PEWMA baseline. Empirical validation using fabric defect count data from two textile manufacturers in Türkiye, with Overdispersion Indices of 6.01 and 2.74, respectively, demonstrates false alarm reductions ranging from 40.9% to 89.2% relative to the standard PEWMA chart, depending on the smoothing parameter and degree of overdispersion. Full article
(This article belongs to the Special Issue Symmetry Application in Statistical Process Control)
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