Multivariate Statistical Control Research Articles

Integration of the multivariate statistical control chart and machine learning to identify faults in the quality characteristics for polylactic acid with glass fiber composites in injection molding

Complex processing parameters need to be adjusted for expected qualities in injection molding processing. Once the process is abnormal, it is essential to spend time and human work on fault diagnosis. In this study, we focus on fault diagnosis of injection molding processing parameters for polylactic acid/glass fiber composites. The injection molding processing parameters include the melt temperature, injection speed, packing pressure, packing time, and cooling time. The qualities include tensile strength, hardness, impact strength, and flexure strength. When processing parameters deviate from the optimal process condition, the multivariate statistical control chart monitors downgraded qualities. The machine is operated at the optimal process conditions to generate normal samples and the corresponding four qualities of data are chosen as the historical data. Hotelling’s T2 is used to calculate the upper control limit (UCL) from the historical data to detect abnormal samples. If the T2 value exceeds the UCL, the corresponding sample is considered abnormal. Then, the residuals of qualities for abnormal samples are obtained by a residual control chart. They are chosen as the feature values for the backpropagation neural network (BPNN) to identify the abnormal processing parameters. The experimental results proved that the BPNN can achieve a 100% recognition rate for single-factor abnormal samples. For the single-/double-factor mixture, the accuracy rate of double-factor classification can reach 97.44%. This proposed study has the advantage of high stability, being non-destructive, high precision, and low cost, and can be widely promoted in injection molding industries.

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.

Rapid assessment of surface water quality using statistical multivariate analysis approach: Oder River system case study

Many physicochemical and biological monitored parameters must be taken into consideration to fully evaluate the surface water environmental condition. However, there are situations where a simple and rapid assessment of the poor water quality situations is critically important. This work presents a universal methodology for monitoring of many parameters simultaneously and early detection out-of-control samples in a real-time mode. The approach uses multivariate statistical quality control chart based on Principal Component Analysis (PCA) model with two well-known measures of abnormal behaviour in a process or system: Hoteling's T2 statistics and Q-statistic. The proposed TQ_PCA quality index provides on-line assessment of the water sample quality, with no specific knowledge and assumptions about control limits for monitored parameters required. A water sample is assessed through the simple control chart using the PCA model established for training/reference samples. The power of the proposed index has been tested using water quality data from the Oder River, including the time of the largest ecological disaster in recent European river history. The proposed index showed excellent analysis performance for physicochemical water quality dataset from Polish stations and physicochemical and biological water quality dataset from German/Frankfurt station, confirming earlier reports. There were consecutive number of alarms reported by the statistical index, a month prior to the disaster when there were no evident changes in the individual parameters. The method presented in this study demonstrated capability of assessment of the major water quality parameters, whose changes preempt the uncommon event. The presented TQ_PCA index could be easily extended to any research involving a large dataset of monitoring parameters from any industrial chemical process.

Integration of Multivariate Statistical Control Chart and Machine Learning to Identify the Abnormal Process Parameters for Polylactide with Glass Fiber Composites in Injection Molding; Part I: The Processing Parameter Optimization for Multiple Qualities of Polylactide/Glass Fiber Composites in Injection Molding.

This paper discusses the mixing of polylactide (PLA) and glass fiber which use injection molding to produce a functional composite material with glass fiber properties. The injection molding process explores the influence of glass fiber ratio, melt temperature, injection speed, packing pressure, packing time and cooling time on the mechanical properties of composite. Using the orthogonal table planning experiment of the Taguchi method, the optimal parameter level combination of a single quality process is obtained through main effect analysis (MEA) and Analysis of variance (ANOVA). Then, the optimal parameter level combination of multiple qualities is obtained through principal component analysis (PCA) and data envelopment analysis (DEA), respectively. It is observed that if all the quality characteristics of tensile strength, hardness, impact strength and bending strength are considered at the same time, the optimal process conditions are glass fiber addition 20 wt %, melt temperature 185 °C, injection speed 80 mm/s, holding pressure 60 MPa, holding time 1 s and cooling time 15 s, and the corresponding mechanical properties are tensile strength 95.04 MPa, hardness 86.52 Shore D, impact strength 4.4408 J/cm2, bending strength 119.89 MPa. This study effectively enhances multiple qualities of PLA/GF composite.

SSMSPC: self-supervised multivariate statistical in-process control in discrete manufacturing processes

Self-supervised learning has demonstrated state-of-the-art performance on various anomaly detection tasks. Learning effective representations by solving a supervised pretext task with pseudo-labels generated from unlabeled data provides a promising concept for industrial downstream tasks such as process monitoring. In this paper, we present SSMSPC a novel approach for multivariate statistical in-process control (MSPC) based on self-supervised learning. Our motivation for SSMSPC is to leverage the potential of unsupervised representation learning by incorporating self-supervised learning into the general statistical process control (SPC) framework to develop a holistic approach for the detection and localization of anomalous process behavior in discrete manufacturing processes. We propose a pretext task called Location + Transformation prediction, where the objective is to classify both, the type and the location of a randomly applied augmentation on a given time series input. In the downstream task, we follow the one-class classification setting and apply the Hotelling’s T2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T^2$$\\end{document} statistic on the learned representations. We further propose an extension to the control chart view that combines metadata with the learned representations to visualize the anomalous time steps in the process data which supports a machine operator in the root cause analysis. We evaluate the effectiveness of SSMSPC with two real-world CNC-milling datasets and show that it outperforms state-of-the-art anomaly detection approaches, achieving 100%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$100\\%$$\\end{document} and 99.6%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$99.6\\%$$\\end{document} AUROC, respectively. Lastly, we deploy SSMSPC at a CNC-milling machine to demonstrate its practical applicability when used as a process monitoring tool in a running process.

Deep learning for multivariate statistical in-process control in discrete manufacturing: A case study in a sheet metal forming process

Detecting abnormal conditions in manufacturing processes is a crucial task to avoid unplanned downtimes and prevent quality issues. The increasing amount of available high-frequency process data combined with advances in the field of deep autoencoder-based monitoring offers huge potential in enhancing the performance of existing Multivariate Statistical Process Control approaches. We investigate the application of deep auto encoder-based monitoring approaches and experiment with the reconstruction error and the latent representation of the input data to compute Hotelling’s T2 and Squared Prediction Error monitoring statistics. The investigated approaches are validated using a real-world sheet metal forming process and show promising results.

ОПТИМИЗАЦИЯ ПАРАМЕТРОВ АЛГОРИТМА ОБОБЩЕННОЙ ДИСПЕРСИИ ПРИ СТАТИСТИЧЕСКОМ КОНТРОЛЕ ПРОЦЕССА

When monitoring a real production process using statistical methods, the question of early detection of violations arises. In most cases, several indicators are monitored simultaneously in the production process, and a change in the values of some indicators leads to a change in others. If there is a dependence of indicators for their monitoring, multivariate statistical control tools are used, in particular generalized variance chart. By varying the parameters of the chart, its efficiency can be significantly increased, this allows minimizing the time the process is in an unstable state.Applying the approach of A. Duncan, which he developed for Shewhart charts, a formula for the expectation of the duration of an unstable state of a process was obtained and a Python program was developed to minimize it. To test the set optimization problem, the calculation of the data of two process indicators is given and the optimal parameters of the generalized variance chart are obtained, at which the duration of the process in an unstable state is minimal.

Development of dietary fibre incorporated tuna sausage employing response surface methodology and quality evaluation during chilled storage using multivariate control charts

In the present study, dietary fibre incorporated functional sausage was prepared by optimising the ingredients viz. tuna mince, wheat and oats dietary fibre using response surface methodology. D-optimal mixture response surface experimental design with 13 runs was formulated for the development of dietary fibre incorporated tuna sausage. The optimum combinations of sausage were found to be 62.5% fish mince, 2.5% wheat and 5% oats fibre and 66.8% fish mince and 1.6% of oats and wheat fibre each. The quality evaluation of combination sausage prepared at optimum conditions along with control sample was carried out based on biochemical, physical and sensory parameters during storage in chilled condition at 2°C. Storage stability studies of the optimised sausage samples indicated a shelf life of 14 days under chilled conditions. Multivariate statistical control charts based on T2 and PSE statistics were developed to monitor quality variations during storage.

Statistical Control of Multivariant Processes through the Artificial Neural Network Multilayer Perceptron and the MEWMA Graphic Analysis

Nowadays the supervision of the quality in the production systems is a very important task. In order to reach this goal, it is necessary that quality of the products is supervised from a global approach where all the quality characteristics are considered. In addition, it is necessary to apply multivariate statistical process control techniques to guarantee a correct control of the manufacturing systems. An important disadvantage of multivariate statistical control is the lack of a complementary analysis that identify the presence of variations or out of control signals that allow locate the source of the instability in the manufacturing process. In order to solve this problem, this research proposes using a multilayer perceptron artificial neural network as an analysis mechanism for each out-of-control signal detected by the multivariate exponentially weighted moving average control chart which is able to identify small changes in the quality of any process. The monitoring and control procedure were used in a process of bearings manufactured for the automotive industry, the results show that the mechanism detected and interpreted small variations and significant changes successfully, identifying the origin of the variation generated in the productive system with an accuracy of 99.85%.

Multivariate analyses to determine fungicide efficacy on Ecuadorian bananas for consumption

Half maximal effective concentration EC 50 is considered the main reference for evaluating the efficacy of the products in any plantation using doses and inhibition percentages from laboratory data. However, EC 50 is not the best representation when other relevant variables and their relationships could be involved. As an agricultural case study, fungicide sensitivity of Pseudocercospora fijiensis , the causal agent of black sigatoka, was evaluated on bananas’ plantations in three provinces of Ecuador. In this study, multivariate statistical process control was adjusted to a fungicide efficacy evaluation case considering multiple data tables from different locations and years at the same time. The threshold conveyed by inhibition percentages, related to the EC , along with locations and years allowed the multivariate analyses carried out in the proposal. The multivariate statistical control techniques applied were Multilinear Principal Component Analysis (MPCA) and Dual STATIS-Parallel Coordinates approach (DS-PC). A comparison was developed and showed that both methods discriminate correctly between the normal and anomalous conditions within plantations along years, validating the ability of the novel method DS-PC for exhibiting better signaling of anomalous plantations and performing variable-wise analysis to find out possible causes of this behavior in an easier time-saving graphical framework.

Multivariate statistical monitoring strategy for an automotive manufacturing part facility

In this article an attempt has been made to devise a statistical monitoring strategy based on multivariate projection based method. The projection based method that was employed for development for the strategy was Principle Component Analysis (PCA) which is primarily used as a dimension reduction technique. The strategy thus devised was applied to a connecting rod manufacturing facility. Connecting rods are primarily produced via hot forging process accompanied by a litany of other finishing processes. Each process in turn is characterized by their own set of process characteristics which requires simultaneous monitoring so as to produce good quality end product. Simultaneous monitoring of characteristics and moreover correlated characteristics can be achieved via the employment of multivariate statistical control technique. Projection based techniques viz., PCA and partial least squares regression fall under special category MSPC techniques owning to their ability to deal with highly correlated and ill-conditioned data. The PCA based monitoring strategy thus devised in this article was found to be efficient in detection of faults indicated by out-of-control observations and thus aiding in producing good quality connecting rods.

Sensor-Based Recurrence Analysis of Energy Efficiency in Machining Processes

Manufacturing industry incurs a large portion of energy consumption and carbon emission in the economy. Traditionally, smart energy management depends on aggregated measures from billing information, as well as physics-based models, empirical results derived from extensive experiments, which tend to be limited in the ability for real-time monitoring of energy efficiency. There is an urgent need to develop energy monitoring solutions for more transparency about energy use. This paper presents a new sensor-based approach for recurrence analysis of continuous power signals and multi-state modeling of energy efficiency in the machining process. First, we leverage the recurrence plot to characterize the nonlinear variations in power signals and further help delineate different states in the machining process, thereby providing statistics of energy consumption in each state. Second, we compute the composite index of energy efficiency for each workpiece and then develop multivariate statistical control charts for process monitoring of continuous production of workpieces. Third, after an anomaly is detected, we propose the orthogonal decomposition approach to diagnose the root cause of abnormal states in the energy use. The proposed methodology is evaluated and validated on real-world manufacturing of shaft-like parts in a machine shop. Experimental results show that the prediction error of energy efficiency from sensor-based models is within 5% from the ground truth, which show great potentials to implement sensor-based monitoring and analysis of real-time energy efficiency in the manufacturing process.

A Comparative Analysis of Bootstrap Multivariate Exponentially-Weighted Moving Average (BMEWMA) Control Limits

In the manufacturing and service industries, multivariate statistical quality control charts are mostly used to determine whether a process is performing as intended or if there are some special causes resulting in the variation of an overall statistics. Normally, control charts are obtained under the assumption that the variable under study follows some form of parametric distribution. When this assumption is violated, the performance of such control chart often gives false alarm signals. To address this problem, the Multivariate Exponential Weighted Moving Average (MEWMA) control limits have been proposed in existing literature. This article focuses on reviewing this existing method with a view to developing a novel approach based on the use of bootstrap. Results from a performance study shows that the proposed method enables the setting of control limits that can enhance the easy detection of out of control signals.

MONITORING VARIABILITAS PROSES BERDASARKAN STATISTIK WILKS

In a manufacturing industry quality problems often occur. One of the main cause is due to variability process. Variability process is a variation that occurs in the process, both in manufacturing and non-manufacturing processes. One method for monitoring variabiliti process is by using Wilks Statistics. Wilks statistics is a method that is used based on individual observations. This study aims to monitor the variability of the process and apply it to Electric Resistance Welded (ERW) pipes with the Wilks statistical method. In addition, a capability process analysis is also carried out when the Wilks control chart has been controlled. The result showed that all observations carried out individually were in control limit with a capability process of 2.5386, which means the process capability of ERW pipe production using a multivariate Wilks statistical control chart was capable and match with the specifications limit specified by company.

Monitoring of Multivariate Processes Through the Regression Adjustment Procedure Based on Artificial Neural Networks

In current production systems, organizations must control the total of the variables that have a correlated influence on the final quality of the products. For this task, multivariate statistical control is used. One of the most used multivariate control methods is the so-called regression adjustment whose scheme proposes that to monitor a final quality characteristic in a product, a multiple regression should be applied on the previous variables that define it in the process and the resulting residue will be controlled from a univariate control chart to detect changes in the variations, however, the utility of the procedure is directly related to the efficiency of the method used to perform the adjustment task between the dependent and independent variables. The present work proposed to use an artificial neural network to carry out the adjustment operation, the results showed a remarkable superiority of the proposed scheme in comparison with the current scheme (Least Squares) and adjustment methods proposed in the literature (LAD and M). The proposed multivariate control approach allows the evolution of the regression adjustment method with the incorporation of artificial intelligence.

Tracing recombinant bovine somatotropin ab(use) through transcriptomics: the potential of bovine somatic cells in a multi-dose longitudinal study

In the European Union, the use of recombinant bovine somatotropin (rbST) in dairy cattle is forbidden. Monitoring rbST (ab)use by its direct detection in animal matrices still remains a challenging task. New monitoring methods based on indirect detection of the substance are necessary. A new transcriptomic system based on the use of high-throughput real-time PCR in combination with somatic cells was developed to control rbST administration in dairy animals. A total of nine cows, separated into control and rbST-treated groups, were included in the study. A subcutaneous injection containing 500 mg of rbST was administered to the treated group every 14 days, up to a total of 12 doses. Milk somatic cells (MSCs) were sampled from each animal at different time points throughout 8 months of study. It was possible to obtain the transcriptomic profile of 18 genes in MSCs of rbST-treated and control groups, and using univariate and multivariate statistical analysis control and treated animals were discriminated. The transcription of CCND1, IGF-1R, TNF and IL-1β genes resulted strongly influenced by rbST treatment. The combination of MSCs, transcriptomic tools and statistical analysis has allowed the selection of four genes as potential biomarkers that could be used in a transcriptomic panel for monitoring rbST administration in cows.

Multivariate statistical control chart and process capability indices for simultaneous monitoring of project duration and cost

Statistical process control (SPC) techniques have been implemented in a few studies in order to determine action limits on the earned value management (EVM) indices to assist project managers in monitoring project performance. Nevertheless, these indices are correlated, reliance on univariate control charts when more than one variable are involved and they are correlated may lead to unsatisfactory results such as increasing the rate of false alarms. This study presented an approach to overcome this limitation by applying multivariate Hotelling's T2 control chart to take into account possible correlations between EVM indicators and describe the entire capability of the project performance more accurately. Furthermore, in order to quantify how well a project can meet its requirements, some practical multivariate process capability indices (PCIs) are introduced. This approach provides management with more reliable information about the deviations between planned and actual performance both in terms of time and cost simultaneously.

FUNCTION AND DEVELOPMENT OF MULTIVARIATE CONTROL GRAPHS

In the present work, it is intended to highlight in a specific way the utility and advances of multivariate control graphics for the control of quality in modern production systems. The synthesis addresses the development of the most commonly used multivariate control charts as well as identifying their scope and limitations. Once the restrictions to carry out a statistical quality control through multivariate charts have been identified, the study of different techniques that complement the quality analysis in the production systems monitored under said control techniques is addressed. Keywords: Multivariate statistical control charts

The distance standard deviation

The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption of finite second moments. Applications are provided to hypothesis testing on a data set from materials science and to multivariate statistical quality control. The distance standard deviation is compared to classical scale measures for inference on the spread of heavy-tailed distributions. Inequalities for the distance variance are derived, proving that the distance standard deviation is bounded above by the classical standard deviation and by Gini’s mean difference. New expressions for the distance standard deviation are obtained in terms of Gini’s mean difference and the moments of spacings of order statistics. It is also shown that the distance standard deviation satisfies the axiomatic properties of a measure of spread.

Fault Detection and Diagnosis In Hall–Héroult Cells Based on Individual Anode Current Measurements Using Dynamic Kernel PCA

Individual anode current signals in aluminum reduction cells provide localized cell conditions in the vicinity of each anode, which contain more information than the conventionally measured cell voltage and line current. One common use of this measurement is to identify process faults that can cause significant changes in the anode current signals. While this method is simple and direct, it ignores the interactions between anode currents and other important process variables. This paper presents an approach that applies multivariate statistical analysis techniques to individual anode currents and other process operating data, for the detection and diagnosis of local process abnormalities in aluminum reduction cells. Specifically, since the Hall–Heroult process is time-varying with its process variables dynamically and nonlinearly correlated, dynamic kernel principal component analysis with moving windows is used. The cell is discretized into a number of subsystems, with each subsystem representing one anode and cell conditions in its vicinity. The fault associated with each subsystem is identified based on multivariate statistical control charts. The results show that the proposed approach is able to not only effectively pinpoint the problematic areas in the cell, but also assess the effect of the fault on different parts of the cell.