Multivariate Statistical Process Control Research Articles

Online Nonparametric Process Monitoring for IoT Systems Using Edge Computing

Facilitated by modern sensing and integrated circuit technology, Internet of Things (IoT) systems now have the ability to intelligently and automatically collect data, perform computational tasks on edge, and efficiently make decisions locally or remotely. However, existing multivariate statistical process control (MSPC) methods commonly assume that sensors directly transmit the raw measurements to the central server, and thus the edge computing capability of the IoT systems is not effectively harnessed. To fill this literature gap, we propose a monitoring scheme tailored for IoT systems by leveraging their edge computational power. In particular, inspired by the inherent hierarchical structure of the IoT system, we construct the monitoring statistics hierarchically. At each edge device, we first construct a nonparametric stream-level statistic for each data stream and aggregate them to derive the device-level statistics. To eliminate the inconsistency in device-level statistics across different edge devices, the device-level statistics are transformed into time-related statistics, which are then sent to the central server. At the central server, a system-level monitoring statistic is constructed, and the most informative edge devices that should transmit statistics are intelligently determined. Theoretical analyses are carried out to justify the effectiveness of the data transmission strategy. Both simulations and a case study, which is based on an IoT system we built, are conducted to evaluate the performance and validate the superiority of the proposed monitoring scheme.

Portable spectroscopy, digital imaging colorimetry and multivariate statistical tools in contaminant identification: A case study of mint (Mentha) and basil (Ocimum basilicum)

The advent of portable Fourier-Transform Infrared (FTIR) and Raman spectrometers has revolutionized analysis capabilities, presenting the possibility of on-site contaminant identification without the need for specialized laboratory settings. Compared to laboratory instrumentation, portable spectroscopy is more prone to noise, and appropriate spectral processing procedures need to be established. This paper introduces a comprehensive methodology that integrates acquisition techniques, spectral analysis, and mathematical tools necessary for utilizing handheld spectrometers to diagnose plant contamination. It focuses on determining the efficacy of handheld FTIR, Raman spectroscopy, and digital imaging for detecting contaminants in two food plants, Basil (Ocimum basilicum) and Mint (Mentha). The study examines the impact of three pollutants: iron (II) sulphate (FeSO4), zinc (II) sulphate (ZnSO4), and copper (II) sulphate (CuSO4), on these plants, but also the necessary amount of measurements to spot the pollutants' effects. Measurements were conducted at the start, after 24 hours, and after 48 hours of exposure, on both fresh and dried plant leaves, as well as in solution. Spectral effects of each of the pollutants were identified with the use of multivariate statistical process control techniques. With the help of the developed methodologies, researchers can identify in-situ contaminant effects, exposure times and run diagnostics directly on the leaf both in alive and dried plants.

A novel hybrid ICA-SVM method for detection and identification of shift in multivariate processes

Detecting shifts in the mean vector of a multivariate statistical process control is crucial, and equally important is identifying the source of such a signal. This study introduces a novel approach that combines independent components analysis with support vector machines to address the challenge of multivariate process monitoring. In this hybrid independent components analysis-support vector machines method, statistical metrics $I^2$ derived from the independent components extracted through independent components analysis from observed data serve as input variables for the support vector machines. The probabilistic outputs generated by the support vector machines model are utilized as monitoring statistics for the proposed control chart, referred to as $I^2-\text{PoC}$. Simulation results validate the effectiveness of the independent components analysis with support vector machines approach in both detecting and identifying shifts in multivariate control processes, whether they follow a normal or non-normal distribution. Furthermore, the results demonstrate the robustness of this method in handling various challenges, including complex relationships between process variables, shifts of varying sizes, and different distribution shapes, when compared to existing approaches in the literature.

Data fusion of Raman spectra in MSPC for fault detection and diagnosis in pharmaceutical manufacturing

This study investigates the use of Raman spectroscopy fused with other types of data (e.g., pH, temperature and turbidity) for multivariate statistical process control of two pharmaceutical case studies: one simulated industrial-scale fed-batch process for the production of penicillin and one real lab-scale crystallization process. The monitoring schemes are built on local principal component analysis models and hyper-parameters are tuned with regards to highest accuracy in fault detection. Accuracies above 90% are obtained for all types of data and level of DF. Furthermore, for the first case study the model built solely on spectra achieves higher fault detection rates, when only considering faults that also result in off-specification quality. This is supported by the fact that the fault is not necessarily detected when it occurs, but rather when it starts to affect quality variables as measured by the spectra.

Improved Fault Detection Method based on HSMM

This paper proposes a fault detection method for multivariate statistical process control. The proposed method combines the Forward-Backward Hidden Semi-Markov Model (HSMM) and Principal Component Analysis (PCA). A stochastic automaton was used for multi-mode detection with many observation sequences. We used agglomerative clusters to find the initial parameters of HSMM. We allocated an adaptive threshold and a fixed threshold in each mode for fault detection with PCA, including Hotelling T2 statistic and squared predictive error (Q statistic). We simulated this method on the Tennessee Eastman Process (TEP). Some faults were designed with various runs and times of occurrence. The experimental results were compared with the Mixture Bayesian PCA, Hidden Markov Model (HMM), and HSMM methods. The results are robust with an efficient detection rate. This activity recommends ways to find action plans for multi-mode process monitoring in chemical plants.

Comments on the Effects of Variables’ Magnitude of Process Changes and Standard Deviations in “Adaptive Multivariate Statistical Process Control for Monitoring Time-Varying Processes”

Comments on the Effects of Variables’ Magnitude of Process Changes and Standard Deviations in “Adaptive Multivariate Statistical Process Control for Monitoring Time-Varying Processes”

A distribution-free phase II control chart for multivariate individual data with simple post signal diagnostics

Multivariate statistical process control (MSPC) charts are particularly useful when there is a need to simultaneously monitor several quality characteristics of a process. Most of the control charts in MSPC assume that the quality characteristics follow some parametric multivariate distribution, such as the normal. This assumption is almost impossible to be justified in practice. Distribution-free MSPC charts are attractive, as they can overcome this hurdle by guaranteeing a stable (or in-control (IC)) performance of the control chart without the assumption of a parametric multivariate process distribution. Utilizing an existing distribution-free multivariate tolerance interval, we propose a Phase II Shewhart-type distribution-free MSPC chart for individual observations, with control limits based on Phase I order statistics. In addition to being easy to interpret, the proposed chart preserves the original scale of measurements and can easily identify out-of-control variables after a signal. The exact in-control performance based on the conditional and unconditional perspectives is presented and examined along with the control limits determination. The out-of-control performance of the chart is studied by simulation for data from a number of multivariate distributions. Illustrative examples are provided for chart implementation, using both real and simulated data, along with a summary and conclusions.

Online nonparametric monitoring for asynchronous processes with serial correlation

Existing multivariate statistical process control methods commonly require all data streams have the same sampling interval. In practice, this assumption may not be valid, as different sensors can have different sampling intervals. In this article, we first propose a generic nonparametric monitoring scheme to online monitor the asynchronous data streams without considering serial correlation. Then the proposed scheme is extended such that it can handle serially correlated data streams. Specifically, we construct a nonparametric local statistic for each data stream, which is sensitive to mean shifts. To eliminate the influence of different sampling intervals, our innovative idea is to transform the local statistics into time-related statistics according to the sampling intervals. A global monitoring scheme is then constructed based on the sum of top- r time-related statistics. To extend the proposed method for serially correlated data streams, we further propose a novel estimation method for the pairwise covariance functions and the data streams can be decorrelated accordingly. Numerical simulations and a case study are conducted, showing the effectiveness of the proposed method in handling asynchronous data streams with serial correlation.

Use of ultrasound and NIRs as tools for monitoring ice formation in superchilled meat

This study aimed to gain a deeper understanding of the ice crystal formation during the superchilling process (SC) of meat by using non-destructive methods. Ultrasound inspection was performed considering the ultrasonic pulse velocity (UPV), while Near Infrared Spectroscopy (NIR) measurements were carried out with a spectral range of 950–1650 nm. Signals from both methodologies were periodically taken during the controlled freezing of 8 beef cubic samples of (6 cm3). Obtained results revealed that both methods have the ability to detect the ice crystal formation during the SC process, and particularly during the period of thermal arrest. Hence, these results evidence that ultrasound inspection and NIR, combined with Multivariate Statistical Process Control charts, could be implemented as quality control procedures during the SC process of muscle foods, allowing a more accurate control of the process and thus, minimizing the potential deleterious effects of ice crystals formation in meat.

Novel predictive approaches for drug-induced convulsions in non-human primates using machine learning and heart rate variability analysis.

Drug-induced convulsions are a major challenge to drug development because of the lack of reliable biomarkers. Using machine learning, our previous research indicated the potential use of an index derived from heart rate variability (HRV) analysis in non-human primates as a biomarker for convulsions induced by GABAA receptor antagonists. The present study aimed to explore the application of this methodology to other convulsants and evaluate its specificity by testing non-convulsants that affect the autonomic nervous system. Telemetry-implanted males were administered various convulsants (4-aminopyridine, bupropion, kainic acid, and ranolazine) at different doses. Electrocardiogram data gathered during the pre-dose period were employed as training data, and the convulsive potential was evaluated using HRV and multivariate statistical process control. Our findings show that the Q-statistic-derived convulsive index for 4-aminopyridine increased at doses lower than that of the convulsive dose. Increases were also observed for kainic acid and ranolazine at convulsive doses, whereas bupropion did not change the index up to the highest dose (1/3 of the convulsive dose). When the same analysis was applied to non-convulsants (atropine, atenolol, and clonidine), an increase in the index was noted. Thus, the index elevation appeared to correlate with or even predict alterations in autonomic nerve activity indices, implying that this method might be regarded as a sensitive index to fluctuations within the autonomic nervous system. Despite potential false positives, this methodology offers valuable insights into predicting drug-induced convulsions when the pharmacological profile is used to carefully choose a compound.

Measuring the quality of the learning process in basic courses using the multivariate statistical process control method

The quality of learning is the key to being able to compete in the world of education. This research aims to measure the quality of the learning process in basic courses at the University of Logistics and International Business. The method used is Multivariate Statistical Control Process with subgroups whose size is not constant. In this method, multivariate control of the target process is carried out using the T2 Hotelling control diagram. Meanwhile, control of multivariate process variability is carried out using a generalized variance control chart. The sample data used in this research was taken from grades in English courses and introductory logistics courses from 20 classes with a total of 498 students. Data collection was carried out randomly from 2019-2022. The results obtained were that in the Multivariate Process Target (MPT) calculation using the T2 Hotelling control diagram it was found that class 1 was out of control. Meanwhile, in calculating Multivariate Process Variability (MPV) using a Generalized Variance (GV) based control diagram, it was found that classes 5 and 20 were out of control. Investigating the cause of the class being out of control is a part that must be explored by study program and university leaders in an effort to improve the teaching and learning process.

A New Index to Detect Process Deviations Using IR Spectroscopy and Chemometrics Process Tools

AbstractProcess analytical technologies (PATs) have transformed the beverage production management by providing real-time monitoring and control of critical process parameters through non-destructive measurements, such as those obtained with infrared (IR) spectroscopy and enabling process readjustment if necessary. New requirements in the analysis of beverages call for new methods, so in this article, we propose a method based on the construction of multivariate statistical process control (MSPC) charts from a new dissimilarity index (the evolving window dissimilarity index, EWDI) to monitor fermentation processes. The EWDI was applied to monitor wine alcoholic fermentation, the biochemical transformation of sugars into ethanol. Small-scale fermentations were carried out and analyzed using a portable mid-infrared spectrometer. In some of them, process deviations due to nitrogen deficiency or temperature changes were intentionally promoted to evaluate the performance of the EWDI. The MSPC charts build by using the fermentations carried out under normal operating conditions allowed identifying deviations of the fermentation in its early stages. Furthermore, the shape of the EWDI curve over time provides insights about the specific type of deviation occurring. These results show the potential of this new approach to improve the monitoring and control of key process stages in biochemical processes in the food industry, which allows maximizing quality and minimizing losses. Graphical Abstract

Detecting mean changes in experience sampling data in real time: A comparison of univariate and multivariate statistical process control methods.

Detecting early warning signals of developing mood disorders in continuously collected affective experience sampling (ESM) data would pave the way for timely intervention and prevention of a mood disorder from occurring or to mitigate its severity. However, there is an urgent need for online statistical methods tailored to the specifics of ESM data. Statistical process control (SPC) procedures, originally developed for monitoring industrial processes, seem promising tools. However, affective ESM data violate major assumptions of the SPC procedures: The observations are not independent across time, often skewed distributed, and characterized by missingness. Therefore, evaluating SPC performance on simulated data with typical ESM features is a crucial step. In this article, we didactically introduce six univariate and multivariate SPC procedures: Shewhart, Hotelling's T², EWMA, MEWMA, CUSUM and MCUSUM. Their behavior is illustrated on publicly available affective ESM data of a patient that relapsed into depression. To deal with the missingness, autocorrelation, and skewness in these data, we compute and monitor the day averages rather than the individual measurement occasions. Moreover, we apply all procedures on simulated data with typical affective ESM features, and evaluate their performance at detecting small to moderate mean changes. The simulation results indicate that the (M)EWMA and (M)CUSUM procedures clearly outperform the Shewhart and Hotelling's T² procedures and support using day averages rather than the original data. Based on these results, we provide some recommendations for optimizing SPC performance when monitoring ESM data as well as a wide range of directions for future research. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Heat illness detection with heart rate variability analysis and anomaly detection algorithm

Objective:Incidence of heat illness has been increasing dramatically due to the progression of global warming. Preventing severe heat illness, called heatstroke, is crucial because it can lead to long-term multiple organ damage, including the brain, and results in more than 600 deaths per year in the United States. It has been reported that heat stress affects heart rate variability (HRV), which is the fluctuations of the R-R interval (RRI) on an electrocardiogram (ECG). We propose a method for detecting symptoms of heat illness based on HRV analysis in order to prevent exacerbation of heat illness. Methods:In the proposed method, monitoring abnormal changes in HRV caused by heat stress is monitored. Multivariate statistical process control (MSPC), a commonly used anomaly detection method in machine learning, is adopted for training the heat illness detection method. To validate the proposed method, we recruited 103 healthy volunteers with risks of heat illness development: employees working in hot environments, athletes, and amateur marathon runners. Data collection was performed using our wearable heart rate sensor and smartphone app. Results:The result of applying the proposed method showed that a sensitivity of 75% (21 out of 28 cases) and a false-positive rate of 1.02 times per hour were achieved. Conclusion:The proposed heat illness detection method will be used in daily life because RRI data can be easily measured by a wearable sensor. Significance:The proposed method will contribute to receiving appropriate treatment for heat illness before exacerbation, which contributes to protecting people’s health.

Single and multiple fault diagnosis based on PCA with relative variation of contribution strategy

Data-driven methods have been recognized as an efficient tool for multivariate statistical process control. Contribution plots are also well known as a popular tool in principal component analysis, which is used for isolating sensor faults without the need for any prior information. However, studies carried out in the literature have unified contribution plots in three general approaches. Furthermore, they demonstrated that correct diagnosis based on contribution plots is not guaranteed for either single or multiple sensor faults. Therefore, to deal with this issue, the present paper highlights a new contribution formula called relative variation of contribution. Simulation results show that the proposed method of contribution can successfully perform the fault isolation task, in comparison with partial decomposition contribution and its relative version (rPDC) based on their fault isolation rate.

New approach to multivariate statistical process control and its application to wastewater treatment process monitoring

This paper presents a new process monitoring and fault diagnosis approach based on a modified Multivariate Statistical Process Control (MSPC) and evaluates its applicability to municipal wastewater treatment process monitoring. A conventional MSPC based on Principal Component Analysis (PCA) is firstly adjusted to have an easy-to-understand user interface and then a new yet simplified decomposable diagnostic model is introduced. The developed user interface is designed to seamlessly connect MSPC to existing process monitoring system adopting the so-called trend graphs. The proposed diagnostic model is derived in a constructive way by aggregating small size models with one input or two inputs to improve tractability of the diagnostic model. The effectiveness of the modified MSPC is illustrated through some offline and on-line experiments by using a set of real multivariate process data at a municipal wastewater treatment plant.

Design of Hotelling T2 control chart using various covariance structures

The objective of this research is to evaluate different serial correlated structures in Hotelling T2 and Shewhart control charts in monitoring multivariate statistical process control. For this purpose, the false alarm rate and shift detection performance were calculated by considering different autocorrelations in the presence of three covariance matrices for the errors. Both simulated data and real data are used for validating the analysis. The result of the simulation shows that the false alarm rate decreases with the increase in the magnitude of autocorrelation in all three low, moderate, and high error covariance structures. In real data, two quality variables of the production process are used. By ignoring autocorrelation in real data, it is concluded that ARL0 shows the process in controlling on the average for nominal value. The performance of varies as the shift changes only in x1 otherwise ARL1 have small values as compared to the individual Shewhart chart by increasing shifts in both variables.

New Anomaly Detection Method based on the Multivariate Generalized Pareto Distributions

The extreme events of floods, rainfalls, waves, and wind often cause serious damage. The observed data can be used to detect the sign of abnormal phenomena and can prevent the crucial damage. Anomaly detection techniques, the techniques of distinguishing between normal and abnormal cases from the data, have been one of the most used methods for detecting suspicious events from the collected data. Although many methods of the anomaly detection have appeared in the literature, almost all of them are based on multivariate statistical process control techniques and machine learning techniques. Recently, under the idea that information for suspicious and critical events is more likely to be involved in the largest or smallest values than values around the mean or median, the anomaly detection methods are based on the “Extreme Value Theory” (EVT), which is the statistical theory dealing with the largest or smallest data, attract the variety of areas. However, they can be applied to only univariate data since they have been based on the EVT for univariate data, and hence there has been little work for the multivariate anomaly detection based on the EVT. The multivariate anomaly detection method is important in applications because almost all data for anomaly detection are multivariate and can be misleading by applying univariate methods to multivariate data independently. In this paper, we propose the new anomaly detection method based on the multivariate EVT. The performance of the proposed methods is evaluated by the Monte Carlo simulation. To illustrate all the proposed methods of anomaly detection for multivariate data, we apply them to analyze the new real data of precipitation events in 2021. The numerical results show that the proposed method outperforms the existing methods.

Control Chart T2Qv for Statistical Control of Multivariate Processes with Qualitative Variables

The scientific literature is abundant regarding control charts in multivariate environments for numerical and mixed data; however, there are few publications for qualitative data. Qualitative variables provide valuable information on processes in various industrial, productive, technological, and health contexts. Social processes are no exception. There are multiple nominal and ordinal categorical variables used in economics, psychology, law, sociology, and education, whose analysis adds value to decision-making; therefore, their representation in control charts would be useful. When there are many variables, there is a risk of redundant or excessive information, so the application of multivariate methods for dimension reduction to retain a few latent variables, i.e., a recombination of the original and synthesizing of most of the information, is viable. In this context, the T2Qv control chart is presented as a multivariate statistical process control technique that performs an analysis of qualitative data through Multiple Correspondence Analysis (MCA), and the Hotelling T2 chart. The interpretation of out-of-control points is carried out by comparing MCA charts and analyzing the χ2 distance between the categories of the concatenated table and those that represent out-of-control points. Sensitivity analysis determined that the T2Qv control chart performs well when working with high dimensions. To test the methodology, an analysis was performed with simulated data and with a real case applied to the graduate follow-up process in the context of higher education. To facilitate the dissemination and application of the proposal, a reproducible computational package was developed in R, called T2Qv, and is available on the Comprehensive R Archive Network (CRAN).

Multivariate Statistical Process Control and Classification Applied on Prostate Cancer Screening

Introduction: We report in this study the results of analyzing biomarkers in blood samples with two objectives; i) as an approach for screening patients by use of Multivariate Statistical Process Control (MSPC); ii) Compare various classification methods with the purpose of diagnosing prostate cancer. Methods: We applied Principal Component Analysis (PCA) with statistical limits for outlier detection. Various splits of the data into training and test sets were chosen to evaluate the performance of classification methods as a function of the training/test sample ratio. Results: MSPC based on 12 analytes in blood samples was shown to outperform the traditional biomarker criterion: the level of the analyte Prostate-Specific Antigen (PSA), in screening for prostate cancer. The performance of different multivariate classification techniques for classifying which of the patients in a clinical pathway for prostate cancer have malignant tumors showed that the basic method Linear Discriminant Analysis (LDA) and classification trees gave similar results, whereas adaboost gave a higher specificity but lower sensitivity. Conclusion: The accuracy, especially the sensitivity, does not justify any clinical use of the applied classification methods with the available biomarkers. Additional medical information about the patients might enhance the accuracy with the purpose of identifying benign and malignant tumors.