An integrated approach for multivariate statistical process control using Mahalanobis-Taguchi System and Andrews function

Multivariate process control has recently gained significant attention because it takes into account the correlation between process variables and offers a more comprehensive understanding of the overall process behavior. In line with this phenomenon, this paper proposes the multivariate triple sampling Hotelling’s T 2 (MTS) control chart as an efficient process monitoring method in multivariate statistical process control. The mathematical properties of the MTS chart are also derived. The performance of the MTS chart is assessed using key performance metrics, such as average run length (ARL), average number of observations to signal (ANOS) and expected average number of observations to signal (EANOS). The performance of the MTS chart is compared with that of the existing multivariate double sampling Hotelling’s T 2 (MDS) chart. The findings indicate that the MTS chart consistently surpasses the MDS chart across all performance metrics, demonstrating its superior capability in detecting shifts for a multivariate process. Notably, the MTS chart exhibits lower ARL, ANOS and EANOS values, emphasizing its effectiveness in promptly identifying process shifts. In terms of practical application, an example is given to elucidate the execution of the MTS chart.

Process modeling and control applied to real-time monitoring of distillation processes by near-infrared spectroscopy

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.

Multivariate monitoring and control schemes based on latent variable methods have been receiving increasing attention by industrial practitioners in the last 15 years. Several companies have enthusiastically adopted the methods and have reported many success stories. Applications have been reported where multivariate statistical process control, fault detection and diagnosis is achieved by utilizing the latent variable space, for continuous and batch processes, as well as, for process transitions as for example start ups and re‐starts. This paper gives an overview of the latest developments in multivariate statistical process control (MSPC) and its application for fault detection and isolation (FDI) in industrial processes. It provides a critical review of the methodology and describes how it is transferred to the industrial environment. Recent applications of latent variable methods to process control as well as to image analysis for monitoring and feedback control are discussed. Finally it is emphasized that the multivariate nature of the data should be preserved when data compression and data preprocessing is applied. It is shown that univariate data compression and reconstruction may hinder the validity of multivariate analysis by introducing spurious correlations. Copyright © 2005 John Wiley & Sons, Ltd.

Statistical process control (SPC) charts are powerful tools that are used to improve quality, increase uniformity and minimize production costs in manufacturing. Neural networks (NNs) have been successfully applied to interpret univariate SPC charts. Despite the growing importance and popularity of multivariate SPC (MSPC), the published literature on the application of NNs to SPC has not adequately discussed the issues related to application of NNs to MSPC for pattern recognition. This paper uses the chi-squared ( x2) statistic as a compact format for representing the input to NNs specialized in positive identification of selected subclasses of multivariate non-random patterns. It is imperative to maintain the reliability of decisions by such specialist NNs in order to convince process operators of their benefits. Therefore, to address the above requirement, this report also shows how novelty detection (ND) can be used as a filter to allow only relevant abnormal patterns to be processed by appropriate specialist NNs. Finally, a new framework within which specialist NNs can complement the decisions of ND and other MSPC techniques is outlined.

In multivariate statistical process control (MSPC), regular multivariate control charts (eg, T2) are shown to be effective in detecting out‐of‐control signals based upon an overall statistic. But these charts do not relieve the need for multivariate process pattern recognition (MPPR). MPPR would be very useful for quality operators to locate the assignable causes that give rise to out‐of‐control situation in multivariate manufacturing process. Deep learning has been widely applied and obtained many successes in image and visual analysis. This paper presents an effective and reliable deep learning method known as stacked denoising autoencoder (SDAE) for MPPR in manufacturing processes. This study will concentrate on developing a SDAE model to learn effective discriminative features from the process signals through deep network architectures. Feature visualization is performed to explicitly present feature representations of the proposed SDAE model. The experimental results illustrate that the proposed SDAE model is capable of implementing detection and recognition of various process patterns in complicated multivariate processes. Analysis from this study provides the guideline in developing deep learning‐based MSPC systems.

In this paper, we propose an ensemble method based on bagging and decision tree to resolve the problem of diagnosing out-of-control signals in multivariate statistical process control. To classify the out-of-control signals, we obtain a series of classifiers through ensemble learning on decision tree. Then we will integrate the classification results of multiple classifiers to determine the final classification. The experimental results show that our method could improve the accuracy of classification and is superior to other methods in terms of diagnosing out-of-control signals in multivariate statistical process control.

In this paper, we propose an ensemble method based on bagging and decision tree to resolve the problem of diagnosing out-of-control signals in multivariate statistical process control. To classify the out-of-control signals, we obtain a series of classifiers through ensemble learning on decision tree. Then we will integrate the classification results of multiple classifiers to determine the final classification. The experimental results show that our method could improve the accuracy of classification and is superior to other methods in terms of diagnosing out-of-control signals in multivariate statistical process control.

Many high quality products are produced in a batch wise manner. One of the characteristics of a batch process is the recipe driven nature. By repeating the recipe in an identical manner a desired end-product is obtained. However, in spite of repeating the recipe in an identical manner, process differences occur. These differences can be caused by a change of feed stock supplier or impurities in the process. Because of this, differences might occur in the end-product quality or unsafe process situations arise. Therefore, the need to monitor an industrial batch process exists. An industrial process is usually monitored by process measurements such as pressures and temperatures. Nowadays, due to technical developments, spectroscopy is more and more used for process monitoring. Spectroscopic measurements have the advantage of giving a direct chemical insight in the process. Multivariate statistical process control (MSPC) is a statistical way of monitoring the behaviour of a process. Combining spectroscopic measurements with MSPC will notice process perturbations or process deviations from normal operating conditions in a very simple manner. In the following an application is given of batch process monitoring. It is shown how a calibration model is developed and used with the principles of MSPC. Statistical control charts are developed and used to detect batches with a process upset.

A multivariate control region can be considered to be a pattern that represents the normal operating conditions of a process. Reference data can then be generated and used to learn the difference between this region and random noise. Then multivariate statistical process control can be converted to a supervised learning task. This can dramatically reshape the control region and open the control problem to a rich collection of supervised learning tools. Such tools provide generalization error estimates that can be used to specify error rates. The effectiveness of such an approach is shown here. Such a computational approach is now easily accomplished with modern computing resources. Examples use random forests and a regularized least squares classifier as the learners.

This article develops a new multivariate statistical process control (SPC) methodology based on adapting the LASSO variable selection method to the SPC problem. The LASSO method has the sparsity property of being able to select exactly the set of nonzero regression coefficients in multivariate regression modeling, which is especially useful in cases where the number of nonzero coefficients is small. In multivariate SPC applications, process mean vectors often shift in a small number of components. Our primary goals are to detect such a shift as soon as it occurs and to identify the shifted mean components. Using this connection between the two problems, we propose a LASSO-based multivariate test statistic, and then integrate this statistic into the multivariate EWMA charting scheme for Phase II multivariate process monitoring. We show that this approach balances protection against various shift levels and shift directions, and thus provides an effective tool for multivariate SPC applications. This article has supplementary material online.

Statistical process control charts are important tools for monitoring process stability in manufacturing and service industries. Using multivariate control charts to monitor two or more related quality characteristic has become increasingly popular in today’s environment. Out-of-control signals in multivariate control charts may be caused by one or more variables or a set of variables. In the practice of quality control, in addition to the quick detection of process change, it is also critical to diagnose the change and identify which variable(s) has changed after an out-of-control signal occurred. In this paper, we propose a decision tree (DT)-based ensemble classifier to approach the problem of diagnosing out-of-control signal. The focus of this paper is on the variance shifts of a multivariate process. Simulation studies indicate that the proposed ensemble classification model is a successful method in identifying the source of variance change. A comparative study also reveals that DT using extracted features as input vector has slightly better classification performance than using raw data as input. The proposed method could be a useful diagnostic aid in monitoring shifts in process dispersion.

The output of a manufacturing process is typically evaluated based on multiple quality characteristics or responses, which are often correlated and non-normally distributed. Monitoring such processes with multiple quality characteristics is challenging, especially across varying response dimensionalities. The Mahalanobis-Taguchi System (MTS) is a prominent approach for such multivariate process control, yet research on its effectiveness remains fragmented. This study proposes an integrated MTS-based framework to address both low and high-dimensional response scenarios. While traditional MTS uses orthogonal array design for variable selection, hybrid MTS approaches employ metaheuristics such as Binary Particle Swarm Optimization (BPSO), Binary Whale Optimization Algorithm (BWOA), and Hybrid Binary Particle Swarm Optimization (HBPSO). The proposed framework incorporates a desirability function and ANOVA analysis to evaluate monitoring performance for the appropriate selection of useful variables and threshold determination for a specific data set. Comparative analysis, using literature benchmarks and real-world manufacturing data, reveals that BPSO-based MTS generally outperforms others, with HBPSO excelling in high-dimensional contexts. Notably, the method for threshold determination in MTS shows insignificant influence on overall performance, considering all datasets. This study provides practical insights into selecting effective MTS-based monitoring strategies across varying dimensionalities.

Process Fault Diagnosis Method Based on MSPC and LiNGAM and its Application to Tennessee Eastman Process

PCA-based multivariate statistical network monitoring for anomaly detection