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Advances in Statistical Process Control and Their Applications
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Advances in Statistical Process Control and Their Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: closed (22 February 2022) | Viewed by 35691

Special Issue Editors

Prof. Dr. Timothy M. Young

E-Mail Website
Guest Editor
Center for Renewable Carbon, University of Tennessee, , Knoxville, TN 37996, USA
Interests: statistical process control; predictive modeling; data mining; reliability; data fusion
Prof. Dr. Ampalavanar Nanthakumar

E-Mail Website
Guest Editor
Department of Mathematics, State University of New Yorkat Oswego, Oswego, NY 13126, USA
Interests: discriminant analysis; statistical genetics; bio-assay; copula models; sequential analysis

Special Issue Information

Dear Colleagues,

Applications of applied mathematics and statistics have rapidly evolved during the last decade with the advent of big data, data mining, business analytics, and ‘Industry 4.0’. Fundamental to applied techniques is statistical process control or SPC. Engineers and scientists require robust real-time methodologies that support rapid assessment of process variation and the detection of ‘events’. New SPC and related methodologies that solve the numerous problems associated with rapid data collection from a vast array of sources are required. Univariate and multivariate SPC methodologies that are robust to autocorrelation are also required. Many online sensors produce data that are signatures or footprints of material attributes, and such data signatures require new SPC methods that can assist the practitioner with process decision making, e.g., statistical intervals for data signatures, or control bands. Rapid assessment of data quality and treatment of poor data quality is fundamental to successful applications of SPC, e.g., imputation for real-time applications. Papers involving statistical process control (SPC), multivariate SPC, SPC for data signatures, predictive analytics, data quality assessment, data quality treatment, and other related topics that will allow researchers and practitioners an opportunity to communicate their ideas are sought.

Prof. Timothy M. Young
Prof. Dr. Ampalavanar Nanthakumar
Guest Editors

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Keywords

  • Statistical process control (SPC)
  • Rapid data collection
  • Multivariate SPC
  • Data signatures

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Published Papers (11 papers)

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Research

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15 pages, 2242 KiB  
Article
Estimating X¯ Statistical Control Limits for Any Arbitrary Probability Distribution Using Re-Expressed Truncated Cumulants
by Paul Braden, Timothy Matis, James C. Benneyan and Binchao Chen
Mathematics 2022, 10(7), 1044; https://doi.org/10.3390/math10071044 - 24 Mar 2022
Cited by 2 | Viewed by 1647
Abstract
Shewhart X¯ control charts commonly used for monitoring the mean of a process may be inaccurate or perform poorly when the subgroup size is small or the distribution of the process variable is skewed. Truncated saddlepoint distributions can increase the accuracy of [...] Read more.
Shewhart X¯ control charts commonly used for monitoring the mean of a process may be inaccurate or perform poorly when the subgroup size is small or the distribution of the process variable is skewed. Truncated saddlepoint distributions can increase the accuracy of estimated control limits by including higher order moments/cumulants in their approximation, yet this distribution may not exist in the lower tail, and thus the lower control limit may not exist. We introduce a novel modification in which some usually truncated higher-order cumulants are re-expressed as functions of lower-order cumulants estimated from data in a manner that ensures the existence of the truncated saddlepoint distribution over the complete domain of the random variable. The accuracy of this approach is tested in cases where the cumulants are assumed either known or estimated from sample data, and demonstrated in a healthcare application. Full article
(This article belongs to the Special Issue Advances in Statistical Process Control and Their Applications)
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18 pages, 398 KiB  
Article
A New Robust Multivariate EWMA Dispersion Control Chart for Individual Observations
by Jimoh Olawale Ajadi, Inez Maria Zwetsloot and Kwok-Leung Tsui
Mathematics 2021, 9(9), 1038; https://doi.org/10.3390/math9091038 - 3 May 2021
Cited by 8 | Viewed by 2667
Abstract
A multivariate control chart is proposed to detect changes in the process dispersion of multiple correlated quality characteristics. We focus on individual observations, where we monitor the data vector-by-vector rather than in (rational) subgroups. The proposed control chart is developed by applying the [...] Read more.
A multivariate control chart is proposed to detect changes in the process dispersion of multiple correlated quality characteristics. We focus on individual observations, where we monitor the data vector-by-vector rather than in (rational) subgroups. The proposed control chart is developed by applying the logarithm to the diagonal elements of the estimated covariance matrix. Then, this vector is incorporated in an exponentially weighted moving average (EWMA) statistic. This design makes the chart robust to non-normality in the underlying data. We compare the performance of the proposed control chart with popular alternatives. The simulation studies show that the proposed control chart outperforms the existing procedures when there is an overall decrease in the covariance matrix. In addition, the proposed chart is the most robust to changes in the data distribution, where we focus on small deviations which are difficult to detect. Finally, the compared control charts are applied to two case studies. Full article
(This article belongs to the Special Issue Advances in Statistical Process Control and Their Applications)
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14 pages, 1178 KiB  
Article
Out-of-Control Multivariate Patterns Recognition Using D2 and SVM: A Study Case for GMAW
by Pamela Chiñas-Sanchez, Ismael Lopez-Juarez, Jose Antonio Vazquez-Lopez, Jose Luis Navarro-Gonzalez and Aidee Hernandez-Lopez
Mathematics 2021, 9(5), 467; https://doi.org/10.3390/math9050467 - 25 Feb 2021
Cited by 4 | Viewed by 1916
Abstract
Industrial processes seek to improve their quality control, including new technologies and satisfying requirements for globalised markets. In this paper, we present an innovative method based on Multivariate Pattern Recognition (MVPR) and process monitoring in a real-world study case. By identifying a distinctive [...] Read more.
Industrial processes seek to improve their quality control, including new technologies and satisfying requirements for globalised markets. In this paper, we present an innovative method based on Multivariate Pattern Recognition (MVPR) and process monitoring in a real-world study case. By identifying a distinctive out-of-control multivariate pattern using the Support Vector Machines (SVM) and the Mahalanobis Distance D2 it is possible to infer the variables that disturbed the process; hence, possible faults can be predicted knowing the state of the process. The method is based on our previous work, and in this paper we present the method application for an automated process, namely, the robotic Gas Metal Arc Welding (GMAW). Results from the application indicate an overall accuracy up to 88.8%, which demonstrates the effectiveness of the method, which can also be used in other MVPR tasks. Full article
(This article belongs to the Special Issue Advances in Statistical Process Control and Their Applications)
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14 pages, 3221 KiB  
Article
A New HWMA Dispersion Control Chart with an Application to Wind Farm Data
by Muhammad Riaz, Saddam Akber Abbasi, Muhammad Abid and Abdulhammed K. Hamzat
Mathematics 2020, 8(12), 2136; https://doi.org/10.3390/math8122136 - 1 Dec 2020
Cited by 21 | Viewed by 2492
Abstract
Recently, a homogeneously weighted moving average (HWMA) chart has been suggested for the efficient detection of small shifts in the process mean. In this study, we have proposed a new one-sided HWMA chart to effectively detect small changes in the process dispersion. The [...] Read more.
Recently, a homogeneously weighted moving average (HWMA) chart has been suggested for the efficient detection of small shifts in the process mean. In this study, we have proposed a new one-sided HWMA chart to effectively detect small changes in the process dispersion. The run-length (RL) profiles like the average RL, the standard deviation RL, and the median RL are used as the performance measures. The RL profile comparisons indicate that the proposed chart has a better performance than its existing counterpart’s charts for detecting small shifts in the process dispersion. An application related to the Dhahran wind farm data is also part of this study. Full article
(This article belongs to the Special Issue Advances in Statistical Process Control and Their Applications)
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17 pages, 376 KiB  
Article
Multivariate Control Chart and Lee–Carter Models to Study Mortality Changes
by Gisou Díaz-Rojo, Ana Debón and Jaime Mosquera
Mathematics 2020, 8(11), 2093; https://doi.org/10.3390/math8112093 - 23 Nov 2020
Cited by 6 | Viewed by 2615
Abstract
The mortality structure of a population usually reflects the economic and social development of the country. The purpose of this study was to identify moments in time and age intervals at which the observed probability of death is substantially different from the pattern [...] Read more.
The mortality structure of a population usually reflects the economic and social development of the country. The purpose of this study was to identify moments in time and age intervals at which the observed probability of death is substantially different from the pattern of mortality for a studied period. Therefore, a mortality model was fitted to decompose the historical pattern of mortality. The model residuals were monitored by the T2 multivariate control chart to detect substantial changes in mortality that were not identified by the model. The abridged life tables for Colombia in the period 1973–2005 were used as a case study. The Lee–Carter model collects information regarding violence in Colombia. Therefore, the years identified as out-of-control in the charts are associated with very early or quite advanced ages of death and are inversely related to the violence that did not claim as many victims at those ages. The mortality changes identified in the control charts pertain to changes in the population’s health conditions or new causes of death such as COVID-19 in the coming years. The proposed methodology is generalizable to other countries, especially developing countries. Full article
(This article belongs to the Special Issue Advances in Statistical Process Control and Their Applications)
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10 pages, 7610 KiB  
Article
Matching Score Models for Hyperspectral Range Analysis to Improve Wood Log Traceability by Fingerprint Methods
by Rudolf Schraml, Karl Entacher, Alexander Petutschnigg, Timothy Young and Andreas Uhl
Mathematics 2020, 8(7), 1071; https://doi.org/10.3390/math8071071 - 2 Jul 2020
Cited by 13 | Viewed by 3561
Abstract
Traceability of natural resources, from the cradle to the final product is a crucial issue to secure sustainable material usage as well as to optimize and control processes over the whole supply chain. In the forest products industries the material can be tracked [...] Read more.
Traceability of natural resources, from the cradle to the final product is a crucial issue to secure sustainable material usage as well as to optimize and control processes over the whole supply chain. In the forest products industries the material can be tracked by different technologies, but for the first step of material flow, from the forest to the industry, no systematic and complete technology has been developed. On the way to close this data gap the fingerprint technology for wooden logs looks promising. It uses inherent properties of a wood stem for identification. In this paper hyperspectral cameras are applied to gain images of Norway spruce (Picea abies [L.] Karst.) log end faces in different spectral ranges. The images are converted to a biometric template of feature vectors and a matching algorithm is used to evaluate if the biometric templates are similar or not. Based on this, matching scores specific spectral ranges which contain information to distinguish between different log end faces are identified. The method developed in this paper is a necessary and successful step to define scanning system parameters for fingerprint recognition systems for wood log traceability from the forest. Full article
(This article belongs to the Special Issue Advances in Statistical Process Control and Their Applications)
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15 pages, 5216 KiB  
Article
Simulating the Gluing of Wood Particles by Lattice Gas Cellular Automata and Random Walk
by Carina Rößler, Felix Breitenecker and Martin Riegler
Mathematics 2020, 8(6), 988; https://doi.org/10.3390/math8060988 - 16 Jun 2020
Cited by 4 | Viewed by 2830
Abstract
In this work a mathematical model and simulation for the gluing of wood particles designated for particleboards is presented. The aim is to obtain a better understanding of the gluing process. Thus, the behaviour of wood particles during gluing is investigated and the [...] Read more.
In this work a mathematical model and simulation for the gluing of wood particles designated for particleboards is presented. The aim is to obtain a better understanding of the gluing process. Thus, the behaviour of wood particles during gluing is investigated and the resulting adhesive distribution across the surface of the wood particles is analysed. For developing a mathematical model, the modelling methods “lattice gas cellular automata” and “random walk” were used. The model was implemented in MATLAB and different scenarios were simulated for answering the main questions of the behaviour during gluing. The influences of different parameters on the adhesive distribution were investigated and quantitatively determined by several key figures. Based on these key figures, the effects of the mixing arm, realistic size distributions of wood particles and adhesive droplets, the transfer of adhesive, and the total mass of adhesive are discussed. Furthermore the results are compared with experimental measurements. The simulation results show that the model can feasibly be used for studying the gluing of wood particles. For a possible industrial application, additional research for developing a three-dimensional model is needed. Full article
(This article belongs to the Special Issue Advances in Statistical Process Control and Their Applications)
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20 pages, 2485 KiB  
Article
An Investigation on a Closed-Loop Supply Chain of Product Recycling Using a Multi-Agent and Priority Based Genetic Algorithm Approach
by Yong-Tong Chen and Zhong-Chen Cao
Mathematics 2020, 8(6), 888; https://doi.org/10.3390/math8060888 - 2 Jun 2020
Cited by 6 | Viewed by 2744
Abstract
Product recycling issues have gained increasing attention in many industries in the last decade due to a variety of reasons driven by environmental, governmental and economic factors. Closed-loop supply chain (CLSC) models integrate the forward and reverse flow of products. Since the optimization [...] Read more.
Product recycling issues have gained increasing attention in many industries in the last decade due to a variety of reasons driven by environmental, governmental and economic factors. Closed-loop supply chain (CLSC) models integrate the forward and reverse flow of products. Since the optimization of these CLSC models is known to be NP-Hard, competition on optimization quality in terms of solution quality and computational time becomes one of the main focuses in the literature in this area. A typical six-level closed-loop supply chain network is examined in this paper, which has great complexity due to the high level of echelons. The proposed solution uses a multi-agent and priority based approach which is embedded within a two-stage Genetic Algorithm (GA), decomposing the problem into (i) product flow, (ii) demand allocation and (iii) pricing bidding process. To test and demonstrate the optimization quality of the proposed algorithm, numerical experiments have been carried out based on the well-known benchmarking network. The results prove the reliability and efficiency of the proposed approach compared to LINGO and the benchmarking algorithm discussed in the literature. Full article
(This article belongs to the Special Issue Advances in Statistical Process Control and Their Applications)
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32 pages, 7286 KiB  
Article
On the Efficient Monitoring of Multivariate Processes with Unknown Parameters
by Nasir Abbas, Muhammad Riaz, Shabbir Ahmad, Muhammad Abid and Babar Zaman
Mathematics 2020, 8(5), 823; https://doi.org/10.3390/math8050823 - 19 May 2020
Cited by 16 | Viewed by 3177
Abstract
Control charts are commonly used tools that deal with monitoring of process parameters in an efficient manner. Multivariate control charts are more practical and are of greater importance for timely detection of assignable causes in multiple quality characteristics. This study deals with multivariate [...] Read more.
Control charts are commonly used tools that deal with monitoring of process parameters in an efficient manner. Multivariate control charts are more practical and are of greater importance for timely detection of assignable causes in multiple quality characteristics. This study deals with multivariate memory control charts to address smaller shifts in process mean vector. By adopting a new homogeneous weighting scheme, we have designed an efficient structure for multivariate process monitoring. We have also investigated the effect of an estimated variance covariance matrix on the proposed chart by considering different numbers and sizes of subgroups. We have evaluated the performance of the newly proposed multivariate chart under different numbers of quality characteristics and varying sample sizes. The performance measures used in this study include average run length, standard deviation run length, extra quadratic loss, and relative average run length. The performance analysis revealed that the proposed control chart outperforms the usual scheme under both known and estimated parameters. An application of the study proposal is also presented using a data set related to Olympic archery, for the monitoring of the location of arrows over the concentric rings on the archery board. Full article
(This article belongs to the Special Issue Advances in Statistical Process Control and Their Applications)
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21 pages, 2519 KiB  
Article
On Phase-I Monitoring of Process Location Parameter with Auxiliary Information-Based Median Control Charts
by Shahid Hussain, Sun Mei, Muhammad Riaz and Saddam Akber Abbasi
Mathematics 2020, 8(5), 706; https://doi.org/10.3390/math8050706 - 2 May 2020
Cited by 5 | Viewed by 2954
Abstract
A control chart is often used to monitor the industrial or services processes to improve the quality of the products. Mostly, the monitoring of location parameters, both in Phase I and Phase II, is done using a mean control chart with the assumption [...] Read more.
A control chart is often used to monitor the industrial or services processes to improve the quality of the products. Mostly, the monitoring of location parameters, both in Phase I and Phase II, is done using a mean control chart with the assumption that the process is free from outliers or the estimators are correctly estimated from in-control samples. Generally, there are question marks about such kind of narratives. The performance of the mean chart is highly affected in the presence of outliers. Therefore, the median chart is an attractive alternative to the mean chart in this situation. The control charts are usually implemented in two phases: Phase I (retrospective) and Phase II (prospective/monitoring). The efficiency of any control chart in Phase II depends on the accuracy of control limits obtained from Phase I. The current study focuses on the Phase I analysis of location parameters using median control charts. We examined the performance of different auxiliary information-based median control charts and compared the results with the usual median chart. Standardized variance and relative efficacy are used as performance measures to evaluate the efficiency of median estimators. Moreover, the probability to signal measure is used to evaluate the performance of proposed control charts to detect any potential changes in the process. The results revealed that the proposed auxiliary information based median control charts perform better in Phase I analysis. In addition, a practical illustration of an industrial scenario demonstrated the significance of the proposed control charts, in which the monitoring of concrete compressive strength is emphasized. Full article
(This article belongs to the Special Issue Advances in Statistical Process Control and Their Applications)
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Review

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31 pages, 20411 KiB  
Review
Concurrent Control Chart Pattern  Recognition: A Systematic Review
by Ethel García, Rita Peñabaena-Niebles, Maria Jubiz-Diaz and Angie Perez-Tafur
Mathematics 2022, 10(6), 934; https://doi.org/10.3390/math10060934 - 15 Mar 2022
Cited by 14 | Viewed by 6452
Abstract
The application of statistical methods to monitor a process is critical to ensure its stability. Statistical process control aims to detect and identify abnormal patterns that disrupt the natural behaviour of a process. Most studies in the literature are focused on recognising single [...] Read more.
The application of statistical methods to monitor a process is critical to ensure its stability. Statistical process control aims to detect and identify abnormal patterns that disrupt the natural behaviour of a process. Most studies in the literature are focused on recognising single abnormal patterns. However, in many industrial processes, more than one unusual control chart pattern may appear simultaneously, i.e., concurrent control chart patterns (CCP). Therefore, this paper aims to present a classification framework based on categories to systematically organise and analyse the existing literature regarding concurrent CCP recognition to provide a concise summary of the developments performed so far and a helpful guide for future research. The search only included journal articles and proceedings in the area. The literature search was conducted using Web of Science and Scopus databases. As a result, 41 studies were considered for the proposed classification scheme. It consists of categories designed to assure an in-depth analysis of the most relevant topics in this research area. Results concluded a lack of research in this research field. The main findings include the use of machine learning methods; the study of non-normally distributed processes; and the consideration of abnormal patterns different from the shift, trend, and cycle behaviours. Full article
(This article belongs to the Special Issue Advances in Statistical Process Control and Their Applications)
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