Multivariate Statistical Process Control Methods 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.

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.

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.

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).

Study on robust model construction method of multi-batch fruit online sorting by near-infrared spectroscopy

In the online detection of fruit samples by near-infrared spectroscopy (NIRS), the natural change of sample states or the variations of instruments will often cause a large error in predicting different batches of samples. In this study, a total of 440 tomato samples were collected in four batches with each batch of 110 samples. The Spectral and soluble solids content (SSC) of single batch were collected every other day in batch order. The multivariate statistical process control (MSPC) method was adopted to establish a stability monitor model. The robustness regression (Rob-Reg) and partial least squares regression (PLSR) were used for mixed modeling of multiple batches of samples to eliminate the variability influence of sample and instrument states. The results show that MSPC can effectively monitor the consistency of the same batch samples measured at different times or different batches. The variation of sample attributes with spectral acquisition time has dramatically damaged the adaptation of PLSR models. The Rob-Reg method can predict the SSC of the different batches of samples at different collection times. Compared with the PLSR method, the correlation coefficient of prediction (Rp) was improved from 0.61 to 0.66, and the root mean square error of prediction (RMSEP) was decreased from 0.55 to 0.44 for Rob-Reg method. The RPD of 3.85 indicated that the model is excellent. The Robust modeling method can be well applied to fruit near-infrared online detection system.

Improved neural component analysis for monitoring nonlinear and Non-Gaussian processes

Neural component analysis (NCA) is one of the latest nonlinear multivariate statistical process control (MSPC) methods, which consists in combining artificial neural networks (ANNs) with principal component analysis (PCA). However, NCA cannot handle the non-Gaussian feature and the extracted principal components (PCs) in NCA may not be the key information in the process data. Herein, we propose an improved NCA (INCA) which introduces a new cost function based on kurtosis to restrict the Gaussianity of PCs. We also propose a novel PC selection mechanism based on the information of PCs in the original data space rather than in the PC data space. INCA achieves almost 100% detection rates in three different types of faults in a simulation model test, and it can detect the fault in the thermal power plant process more than 1 min ahead of orthogonal nonlinear PCA (O-NLPCA) and NCA.

Detection and identification of mean shift using independent component analysis in multivariate processes

Multivariate Statistical Process Control (MSPC) methods are used commonly to detect and identify shifts in multivariate industrial processes. However, these methods are limited by assumptions and complexities. In this study, a new two-stage MSPC approach based on independent component analysis is proposed. The proposed method aims to provide solutions to both the determination and the identification of the shift in the mean vector of a multivariate process. In the first step of this new method, independent components extracted by ICA were used as monitoring statistics in the MSPC chart to detect the shift in the process. The second step of the method started to deal with the problem of identifying the source of this shift by decomposing the monitoring statistics. The simulation results show the superiority of the new method over traditional methods in both determining and identifying the shift in the process mean vector.

Critical quality attribute assessment of big brand traditional Chinese medicine: quality control method of Huangjing Zanyu Capsules based on chemical properties of characteristic components

The chemical properties of characteristic components are significant to the manufacturing quality control of big brand traditional Chinese medicine. In this study, the Huangjing Zanyu Capsules were used as the research carrier to determine the content of five characteristic components including icraiin, emodin, schisandrin A, 2,3,5,4'-tetrahydroxystilbene-2-O-β-D-glucoside, and osthole simultaneously by high-performance liquid chromatography(HPLC). The results showed that the chemical properties of five cha-racteristic components had a good linear relationship(r>0.999 9) within the quantitative range; the relative standard deviations(RSD) was 0.11%-2.0% and 0.25%-2.8% respectively for intra-day and inter-day precision; the RSD of repeatability was 1.8%-2.6%; the RSD of stability within 48 hours was 0.19%-2.8%, and the average recovery rate was 95.52%-100.1%, all meeting the requirements of pharmaceutical quantitative analysis. Additionally, the interval estimation method was used to directly reflect the distribution of samples with abnormal chemical properties of characteristic components, and the results showed ten samples were detected beyound the 95% control line of confidence level. Multivariate statistical process control(MSPC) method was used to monitor the abnormal samples of Huangjing Zanyu Capsules collectively, and the results showed that two samples were beyond the 95% control line of Hotelling's T~2 and three samples beyond the 95% control line of squared prediction error(SPE), indicating consistent quality control of Huangjing Zanyu Capsules. In conclusion, the proposed method is not only accurate and efficient but also a compensation for the traditional single-component quality control method, providing a scientific basis for the quality control in manufacturing process of Huangjing Zanyu Capsules. Furthermore, it could also serve as a reference method for the quality control in manufacturing big brand traditional Chinese medicine.

Multivariate statistical process control methods for batch production: a review focused on applications

ABSTRACT In this paper, we highlight the basic techniques of multivariate statistical process control (MSPC) under the dimensionality criteria, such as Multiway Principal Component Analysis, Multiway Partial Squares, Structuration à Trois Indices de la Statistique, Tucker3, Parallel Factors, Multiway Independent Component Analysis, Multiset Canonical Correlation Analysis, Slow Features Analysis, and Parallel Coordinates. Furthermore, we summarize the procedures of each statistical technique and the usage of multivariate control charts. In addition, we review the most significant proposals and applications in practical cases. Finally, we compare and discuss the benefits and limitations within methods.

Fault Detection for Rolling-Element Bearings Using Multivariate Statistical Process Control Methods

This paper proposes a new bearing fault detection framework that is based on multivariate statistical process control methods. In this framework, historical offline normal data are used to train the models and calculate the control limits of the monitored metrics. Then, bearings’ new online data are the input to the trained models to obtain their monitoring metrics, which are compared with the control limits to determine the healthy status of bearings. Unlike most conventional methods, the proposed framework does not need any faulty data at the training stage. Therefore, the proposed framework is flexible and applicable to most practical cases in which few or even no faulty data are available at the training stage. Two bearings’ life data sets are used to validate the proposed fault detection approach. Results show that the higher order cumulants analysis-based approach exhibits better performance in bearing fault detection when compared with principal component analysis-based and independent component analysis-based approach.

Sparse abnormality detection based on variable selection for spatially correlated multivariate process

Monitoring the manufacturing process becomes a challenging task with a huge number of variables in traditional multivariate statistical process control (MSPC) methods. However, the rich information is often loaded with some rare suspicious variables, which should be screened out and monitored. Even though some control charts based on variable selection algorithms were proven effective for dealing with such issues, charting algorithms for the sparse mean shift with some spatially correlated features are scarce. This article proposes an advanced MSPC chart based on fused penalty-based variable selection algorithm. First, a fused penalised likelihood is developed for selecting the suspicious variables. Then, a charting statistic is employed to detect potential shifts among the variables monitored. Simulation experiments demonstrate that the proposed scheme can detect abnormal observation efficiently and provide root causes reasonably. It is shown that the fused penalty can capture the spatial information and improve the robustness of a variables selection algorithm for spatially correlated process.

A combined monitoring scheme with fuzzy logic filter for plant-wide Tennessee Eastman Process fault detection

Principal Component Analysis (PCA) is the most common Multivariate Statistical Process Control (MSPC) method that is widely used for Fault Detection and Diagnosis (FDD). Since early abnormality detection with high accuracy is required for safe and reliable process operation, False Alarms Rate (FAR), Missed Detection Rate (MDR) and the detection time delay are the major factors that must be taken into consideration when developing any process monitoring scheme. Unfortunately, the PCA performance, with fixed limits, is weak in terms of the stated factors. In contrast, conventional Moving Window PCA (MWPCA) is an adaptive technique which updates both the PCA model and the thresholds once a new normal observation is available. Yet, MWPCA methodology still does not reduce the MDR and the detection delay. In this paper, a Modified MWPCA (MMWPCA) with Fuzzy Logic Filter (FLF) is proposed to enhance the monitoring performance of PCA. It is an adaptive approach with a fixed model that combines both aforementioned techniques. The aim of using FLF is to ensure robustness to false alarms without affecting the Fault Detection (FD) performance. The application of the proposed method has been carried out on the Tennessee Eastman Process (TEP). Hold-one and hold-five MMWPCA with FLF are applied and compared to recent FDD work in the literature. The obtained results demonstrate the superiority of the proposed technique in detecting different types of faults with high accuracy and with shorter time delay.

Dynamic mutual information similarity based transient process identification and fault detection

Industrial process status can be modified according to continuous operations, which are required by different production specifications. Commonly, in a multimode process, attention was always paid to stable modes, while transitions were neglected. In a transition process, the process may be externally time varying or nonstationary so that the identification and the modelling are intractable to implement using traditional statistical methods. In this article, a transition identification and process monitoring method is proposed to handle the above problems based on a novel dynamic mutual information similarity (DMIS) analysis. Firstly, a multimode process is represented by a series of overlapping moving windows to consider the local information. In order to extract the corresponding dynamic information, each of these windows is modelled using the dynamic partial least squares (DPLS) method. Then, the mutual information algorithm is introduced to calculate the similarity between different latent variables. The hierarchical clustering method is employed to transfer the similarity information into a visualized dendrogram where the whole process, including a transition, is divided into several segments. The statistical characteristics in each segment are relatively stable and can be characterized by conventional multivariate statistical process control methods. Online identification and fault detection are then carried out for the multimode process through a series of DPLS models, established in the offline steps. The feasibility and effectiveness of the proposed method are validated by the Tennessee Eastman (TE) benchmark and a real process. The results of the proposed methods have shown superior performance compared to previous works.

Multivariate Statistical Quality Control Based on Ranked Set Sampling

The sample of the study was formed using simple random sampling, ranked set sampling, extreme ranked set sampling and median ranked set sampling. At the end of this process, the researcher created Hotelling’s T2 control charts, a multivariate statistical process control method. The performances of SRS, RSS, ERSS and MRSS sampling methods were compared to one another using these control charts. A simulation was performed to see the average run-length values for Hotelling’s T2 control charts, and these findings were also used for the comparison of the sampling performances.At the end of the study, the researcher formed a sample using median ranked set sampling and created the Hotelling’s T2 control chart. As a result of this operation, the researcher found that there was an out-of-control signal in the process, while there was no such signal in other sampling methods. When the average run-length values obtained from Hotelling’s T2 control charts were compared, it was seen that a shift in the process was detected by the ranked set sampling earlier, when compared to other sampling methods. This paper it can be said that the methods used are unique to the literature because they are applied to multivariate data.

Variable selection methods in multivariate statistical process control: A systematic literature review

Abstract Technological advances led to increasingly larger industrial quality-related datasets calling for process monitoring methods able to handle them. In such context, the application of variable selection (VS) in quality control methods emerges as a promising research topic. This review aims at presenting the current state-of-the-art of the integration of VS in multivariate statistical process control (MSPC) methods. Proposals aligned with the objective were identified, classified according to VS approach, and briefly presented. Research on the topic has considerably increased in the past five years. Thirty methods were identified and categorized in 10 clusters, according to the objective of improvement in MSPC and the step of process monitoring they were aimed to improve. The majority of the propositions were either targeted at exclusively monitoring potential out-of-control variables or improving the monitoring of in-control variables. MSPC improvements were centered in principal component analysis (PCA) projection methods, while VS was mainly carried out using the Least Absolute Shrinkage and Selection Operator (LASSO) method and genetic algorithms. Fault isolation was the most addressed step in process monitoring. We close the paper proposing five topics for future research, exploring the opportunities identified in the literature.

Quality Prediction of Refined Bleached Deodorized Palm Oil (RBDPO) Using Partial Least Square Regression Technique

Out of specification in the production of Refined Bleached Deodorized Palm Oil (RBDPO) will cause recycling in palm oil refining process as well as zero production during that period. Hence, the ability to predict the output quality variables so that appropriate adjustment can be made in the process beforehand is very useful in minimizing the production cost and time consumption. In this study, Multivariate Statistical Process Control (MSPC) is used to develop a prediction tool in order to predict the output quality variables before the process even began and eventually reduce the utility cost as compare to traditional method of using tacit knowledge which is not very practical. Knowing product quality in advance, adjustment can be made at the specific unit operation and also to identify in which standard the quality variables belongs to, be it Palm Oil Refiners Association Malaysia (PORAM) standard, China or Vietnam. The MSPC method used in this study is Partial Least Squares Regression (PLS) which capable in finding the relationships between the process and quality variables of the palm oil refining process assuming that the data are linear. In simulation, data used are obtained from Lahad Datu Edible Oil Sdn. Bhd. (LDEO) with percentage of fatty acid (FFA), moisture content, and iodine value as both the process and quality variable which undergone pre-screening and pre-processing of data. This study also considers a constant sampling time to ensure the randomness of the data as well as the residence time in determining the relationships of the quality variables corresponded to the actual process variables. Simulation results obtained from developed correlation coefficient are evaluated and compared using Mean Squared Error (MSE). MSE results shows that PLS method is capable in predicting the output quality variables.

Discriminant diffusion maps based k‐nearest‐neighbour for batch process fault detection

In this paper, a novel discriminant diffusion maps based k‐nearest‐neighbour rule (DDM‐kNN) is developed for the high‐dimensional data of batch process and nonlinear characteristics of the data, and the traditional multivariate statistical process control and monitoring methods is less effective. Firstly, a discriminant kernel parameter is applied to the framework of the diffusion maps, and the Gaussian kernel width is selected from the within‐class width and the between‐class width according to discriminating sample class labels, which can make kernel function effectively extract data correlation features and exactly describe the structure characteristics of data original space in the low‐dimensional feature. Subsequently, the adapted kNN rule is applied to the low‐dimensional manifold feature space for fault detection. The effectiveness of DDM for the performance of data dimension reduction and feature extraction is verified in 3 arm spiral test data experiments compared with other dimensionality reduction methods, and successfully shows the high‐dimensional data in the low‐dimensional space and optimally preserves the original intrinsic nonlinear structure of the dataset. In addition, DDM‐kNN is applied to penicillin fermentation process monitoring and fault detection, and results also verify the effectiveness of the proposed method by integrating discriminant diffusion maps with k‐nearest‐neighbour rule.

A sparse dissimilarity analysis algorithm for incipient fault isolation with no priori fault information

The conventional multivariate statistical process control (MSPC) methods in general quantify the distance between the new sample and the modelling samples for fault detection and diagnosis, which, however, do not check the changes of data distribution as long as monitoring statistics stay inside normal region enclosed by control limit and thus are not sensitive to incipient changes. In the present work, a sparse dissimilarity (SDISSIM) algorithm is developed which can isolate the incipient abnormal variables that change the data distribution structure and does not need any priori fault knowledge. First, the distribution dissimilarity is decomposed deeply and significant dissimilarity is extracted to integrate the critical difference of variable covariance structure between the reference normal operation distribution and the actual distribution. Second, a sparse regression-based optimization problem is formulated to isolate abnormal variables associated with changes of distribution structure. Sparse coefficients are obtained with only a small fraction of variables’ coefficients nonzeros, pointing to abnormal variables. As illustrations, SDISSIM is applied to both simulated and real industrial process data with encouraging results to figure out the slight distortions.

An on-line SAX and HMM-based anomaly detection and visualization tool for early disturbance discovery in a dynamic industrial process

In order to achieve an optimum and successful operation of an industrial process, it is important firstly to detect upsets, equipment malfunctions or other abnormal events as early as possible and secondly to identify and remove the cause of those events. Univariate and multivariate statistical process control methods have been widely applied in process industries for early fault detection and localization.The primary objective of the proposed research is the design of an anomaly detection and visualization tool that is able to present to the shift operator – and to the various levels of plant operation and company management – an early, global, accurate and consolidated presentation of the operation of major subgroups or of the whole plant, aided by a graphical form.Piecewise Aggregate Approximation (PAA) and Symbolic Aggregate Approximation (SAX) are considered as two of the most popular representations for time series data mining, including clustering, classification, pattern discovery and visualization in time series datasets. However SAX is preferred since it is able to transform a time series into a set of discrete symbols, e.g. into alphabet letters, being thus far more appropriate for a graphical representation of the corresponding information, especially for the shift operator. The methods are applied on individual time records of each process variable, as well as on entire groups of time records of process variables in combination with Hidden Markov Models. In this way, the proposed visualization tool is not only associated with a process defect, but it allows also identifying which specific abnormal situation occurred and if this has also occurred in the past. Case studies based on the benchmark Tennessee Eastman process demonstrate the effectiveness of the proposed approach. The results indicate that the proposed visualization tool captures meaningful information hidden in the observations and shows superior monitoring performance.

A feasibility research on the monitoring of traditional Chinese medicine production process using NIR-based multivariate process trajectories

Traditional Chinese medicine (TCM) products are usually manufactured through batch processes. To improve the batch-to-batch reproducibility, practical approaches for the real-time monitoring of batch evolution need to be developed. In-line near-infrared (NIR) spectroscopy combined with multivariate statistical process control (MSPC) method, as an efficient process analytical technology, is presented for the real-time batch process monitoring. Two representative TCM technical processes, the alkaline precipitation of the compound E-Jiao oral liquid and the liquid preparation process of Tanreqing injection, were taken as examples. The NIR spectra collected in-line was “variable-wise” unfolded into two-dimensional matrix, and multi-way principal component analysis (MPCA) model were developed based on the rearranged data of the normal operation condition (NOC) batches. Three kinds of multivariate control charts (PC scores, Hotelling T2 and DModX) were used to monitor the evolution of test batches with artificial batch variations, including the change of starting material quality attributes and abnormal operation conditions. As illustrated with test batches, the established model can identify NOC or AOC (abnormal operation condition) batches accurately, and detect different kinds of deviations from NOC batches using these control charts. The results indicated that the NIR-based multivariate process trajectories can reflect the batch-to-batch reproducibility effectively, and can also help for the diagnosis of the failure batches in the TCM production.