Robust kernel distance multivariate control chart using support vector principles

It is important to monitor manufacturing processes in order to improve product quality and reduce production cost. Statistical Process Control (SPC) is the most commonly used method for process monitoring, in particular making distinctions between variations attributed to normal process variability to those caused by ‘special causes’. Most SPC and multivariate SPC (MSPC) methods are parametric in that they make assumptions about the distributional properties and autocorrelation structure of in-control process parameters, and, if satisfied, are effective in managing false alarms/-positives and false-negatives. However, when processes do not satisfy these assumptions, the effectiveness of SPC methods is compromised. Several non-parametric control charts based on sequential ranks of data depth measures have been proposed in the literature, but their development and implementation have been rather slow in industrial process control. Several non-parametric control charts based on machine learning principles have also been proposed in the literature to overcome some of these limitations. However, unlike conventional SPC methods, these non-parametric methods require event data from each out-of-control process state for effective model building. The paper presents a new non-parametric multivariate control chart based on kernel distance that overcomes these limitations by employing the notion of one-class classification based on support vector principles. The chart is non-parametric in that it makes no assumptions regarding the data probability density and only requires ‘normal’ or in-control data for effective representation of an in-control process. It does, however, make an explicit provision to incorporate any available data from out-of-control process states. Experimental evaluation on a variety of benchmarking datasets suggests that the proposed chart is effective for process monitoring.     

Kernel distance-based robust support vector methods and its application in developing a robust K-chart

Traditional statistical process control (SPC) techniques are not applicable in many process industries due to autocorrelation among data. In addition, most conventional charts are based on the assumption that quality characteristics follow a multivariate normality assumption. Therefore, the reduction in process variability obtained through the use of SPC techniques has not been realized in the industries. However, this may not be reasonable in many real-world problems and its extension poses serious limitations. Hence, it is not only desirable, but also inevitable to have some techniques that can serve the same purpose as SPC control charts used for correlated parameters. In this paper, a robust support vector method drawn from statistical learning theory was applied to develop a multivariate control chart based on kernel distance, which is a measure of the distance between the centre of a class and the sample to be monitored. The proposed robust chart takes advantage of information extracted from in-control preliminary samples. A robust support vector method-based chart aims to solve the over fitting problems when outliers exist in the training data set. The robust support vector method makes the decision function less sensitive towards the noise and outliers. The performance of the robust chart is tested on the problem taken from the literature and the results verify the effectiveness of the chart and validate that the robust chart is better than the conventional charts when the distribution of the quality characteristics is not multivariate normal. Experiments for the problem undertaken confirm the reduction in the number of support vectors and there is significant improvement in performance when compared with the standard support vector methods.     

Comprehensive control charting applied to chromatography

Multivariate statistical process control (MSPC) based for example on principal component analysis (PCA) can make use of the information contained in multiple measured signals simultaneously. This can be much more powerful in detecting variations due to special causes than conventional single variable statistical process control (SPC). Furthermore, the PCA based SPC simplifies monitoring as it limits the number of control charts to typically two charts rather than one for each signal. However, the derived MSPC statistics may suffer from lack of sensitivity if only one or a few variables deviate in a given situation. In this paper we develop a new comprehensive control (COCO) chart procedure that considers both univariate statistics and multivariate statistics derived from PCA in a single plot that allows easy visualization of the combined data from a univariate and multivariate point of view. The method is exemplified using twenty analytical chromatographic peak areas obtained for purity analysis of a biopharmaceutical drug substance. The new control chart procedure detected two different types of faulty events in this study.     

Dual multivariate CUSUM charts with auxiliary information for process mean

It is customary to increase the sensitivity of a control chart using an efficient estimator of the underlying process parameter which is being monitored. In this paper, using an auxiliary information-based (AIB) mean estimator, we propose dual multivariate CUSUM (DMCUSUM) and mixed DMCUSUM (MDMCUSUM) charts, called the AIB-DMCUSUM and AIB-MDMCUSUM charts, with and without fast initial response features for monitoring the mean vector of a multivariate normally distributed process. The DMCUSUM chart combines two similar-type multivariate CUSUM (MCUSUM) charts while the MDMCUSUM chart combines two different-type MCUSUM charts, into a single chart. The objective of two multivariate subcharts in the DMCUSUM/MDMCUSUM chart is to simultaneously detect small-to-moderate and moderate-to-large shifts in the process mean vector. Monte Carlo simulations are used to compute the run length characteristics, including the average run length (ARL), extra quadratic loss, and integral of the relative ARL. Based on detailed run length comparisons, it turns out that the AIB-DMCUSUM and AIB-MDMCUSUM charts uniformly and substantially outperform the DMCUSUM and MDMCUSUM charts when detecting different sizes of shift in the process mean vector. A real dataset is used to explain the implementation of proposed AIB multivariate charts.     

An assessment of the kernel‐distance‐based multivariate control chart through an industrial application

Traditional multivariate quality control charts assume that quality characteristics follow a multivariate normal distribution. However, in many industrial applications the process distribution is not known, implying the need to construct a flexible control chart appropriate for real applications. A promising approach is to use support vector machines in statistical process control. This paper focuses on the application of the ‘kernel‐distance‐based multivariate control chart’, also known as the ‘k‐chart’, to a real industrial process, and its assessment by comparing it to Hotelling's T² control chart, based on the number of out‐of‐control observations and on the Average Run Length. The industrial application showed that the k‐chart is sensitive to small shifts in mean vector and outperforms the T² control chart in terms of Average Run Length. Copyright © 2010 John Wiley & Sons, Ltd.     

A Phase II depth-based variable dimension EWMA control chart for monitoring process mean

Statistical process control consists of tools and techniques that are useful for improving a process or ensuring that a process is in a stable and satisfactory state. In many modern industrial applications, it is critically important to simultaneously monitor two or more correlated process quality variables, thus necessitating the development of multivariate statistical process control (MSPC) as an important area of research for the new century. Nevertheless, the existing MSPC research is mostly based on the assumption that the process data follow a multinormal distribution or a known distribution. However, it is well recognized that in many applications the underlying process distribution is unknown. In practice, among a set of correlated variables to be monitored, there is oftentimes a subset of variables that are easy and/or inexpensive to measure, whereas the remaining variables are difficult and/or expensive to measure but contain information that may help more quickly detect a shift in the process mean. We are motivated to develop a Phase II control chart to monitor variable dimension (VD) mean vector for unknown multivariate processes. The proposed chart is based on the exponentially weighted moving average (EWMA) of a depth-based statistic. The proposed chart is shown to lead to faster detection of mean shifts than the existing VDT² and VD EWMAT² charts studied in Aparisi et al. and Epprecht et al., respectively.     

Should observations be grouped for effective monitoring of multivariate process variability?

A multivariate dispersion control chart monitors changes in the process variability of multiple correlated quality characteristics. In this article, we investigate and compare the performance of charts designed to monitor variability on the basis of individual and grouped multivariate observations. We compare one of the most well-known methods for monitoring individual observations—a multivariate exponentially weighted mean squared deviation (MEWMS) chart—with various charts based on grouped observations. In addition, we compare charts based on monitoring with overlapping and nonoverlapping subgroups. We recommend using charts based on overlapping subgroups when monitoring with subgroup data. The effect of subgroup size is also investigated. Steady-state average time to signal is used as the performance measure. We show that monitoring methods based on individual observations are the quickest in detecting sustained shifts in the process variability. We use a simulation study to obtain our results and illustrated these with a case study.     

Improving the performance of the multivariate exponentially weighted moving average control chart

Multivariate statistical process control (SPC) procedures are useful in cases where several process variables are monitored simultaneously. A significant disadvantage of these techniques is that the time required to detect a process shift increases with the number of variables being monitored. We show how the shift detection capability of one popular multivariate SPC scheme, the multivariate analogue of the exponentially weighted moving average control chart, can be significantly improved by transforming the original process variables to a lower‐dimensional subspace through the use of a U‐transformation. Copyright © 1999 John Wiley & Sons, Ltd.     

基于神经网络的SPC/EPC整合过程监测方法研究

为解决统计过程控制(SPC)/工程过程调整(EPC)整合引起的传统SPC控制图监测异常扰动效率低的问题,提出了采用神经网络技术监测SPC/EPC整合过程的策略,并对神经网络模型结构和参数设置进行分析,构建过程输入、过程输出及两者的协方差为输入参数,异常扰动发生与否为输出参数的3层神经网络模型。为验证该方法的性能,进行了大量的比较实验:即对相同的样本,分别采用Shewhar图、CUSUM图和上述神经网络模型进行监测。实验结果表明:神经网络模型能准确监测幅度大于2的阶跃扰动和大于2的过程漂移,平均运行步长(ARL)为1;传统SPC监测技术只能较准确地(监测率大于90%)监测幅度大于5的阶跃扰动和大于2的过程漂移,ARL大于2。与传统监测方法相比,该方法能快速有效地监测异常扰动的发生。     

Process monitoring with ICA‐based signal extraction technique and CART approach

In order to reduce the variation in a manufacturing process, traditional statistical process control (SPC) techniques are the most frequently used tools in monitoring engineering process control (EPC)‐controlled processes for detecting assignable cause process variation. Even though application of SPC with EPC can successfully detect time points when abnormalities occur during process, their combination can also cause an increased occurrence of false alarms when autocorrelation is present in the process. In this paper, we propose an independent component analysis‐based signal extraction technique with classification and regression tree approach to identify disturbance levels in the correlated process parameters. For comparison, traditional cumulative sum (CUSUM) chart was constructed to evaluate the identifying capability of the proposed approach. The experimental results show that the proposed method outperforms CUSUM control chart in most instances. Copyright © 2008 John Wiley & Sons, Ltd.     

On-line classifying process mean shifts in multivariate control charts based on multiclass support vector machines

In multivariate statistical process control (MSPC), most multivariate control charts can effectively monitor anomalies based on overall statistic, however, they cannot provide guidelines to classify the source(s) of out-of-control signals. Classifying the source(s) of process mean shifts is critical for quality control in multivariate manufacturing process since the immediate identification of them can greatly help quality engineer to narrow down the set of possible root causes and take corrective actions. This study presents an improved particle swarm optimisation with simulated annealing-based selective multiclass support vector machines ensemble (PS-SVME) approach, in which some selective multiclass SVMs are jointly used for classifying the source(s) of process mean shifts in multivariate control charts. The performance of the proposed PS-SVME approach is evaluated by computing its classification accuracy. Simulation experiments are conducted and a real application is illustrated to validate the effectiveness of the developed approach. The analysis results indicate that the developed PS-SVME approach can perform effectively for classifying the source(s) of process mean shifts.     

Monitoring compositional data using multivariate exponentially weighted moving average scheme

Recently, the monitoring of compositional data by means of control charts has been investigated in the statistical process control literature. In this article, we develop a Phase II multivariate exponentially weighted moving average control chart, for the continuous surveillance of compositional data based on a transformation into coordinate representation. We use a Markov chain approximation to determine the performance of the proposed multivariate control chart. The optimal multivariate exponentially weighted moving average smoothing constants, control limits, and out‐of‐control average run lengths have been computed for different combinations of the in‐control average run lengths and the number of variables. Several tables are presented and enumerated to show the statistical performance of the proposed control chart. An example illustrates the use of this chart on an industrial problem from a plant in Europe.     

Monitoring multivariate process variability with individual observations via penalised likelihood estimation

Excessive variation in a manufacturing process is one of the major causes of a high defect rate and poor product quality. Therefore, quick detection of changes, especially increases in process variability, is essential for quality control. In modern manufacturing environments, most of the quality characteristics that have to be closely monitored are multivariate by the nature of the applications. In these multivariate settings, the monitoring of process variability is considerably more difficult than monitoring a univariate variance, especially if the manufacturing environment only allows for the collection of individual observations. Some recent charts, such as the MaxMEWMV chart, the MEWMS chart and the MEWMC chart, have been proposed to monitor process variability specifically when the subgroup size is equal to 1. However, these methods do not take into account the engineering and operational understanding of how the process works. That is, when the process variability goes out of control, it is often the case that changes only occur in a small number of elements of the covariance matrix or the precision matrix. In this work, we propose a control charting mechanism that enhances the existing methods via penalised likelihood estimation of the precision matrix when only individual observations are available for monitoring the process variability. The average run length of the proposed chart is compared with that of the MaxMEWMV, MEWMS and MEWMC charts. A real example is also presented in which the proposed chart and the existing charts are applied and compared.     

Stacked denoising autoencoder‐based feature learning for out‐of‐control source recognition in multivariate manufacturing process

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.     

Probabilities on Algebraic Structures

Time-between-events (TBE) charts or T charts have attracted increasing research interest in statistical process control (SPC). These charts monitor TBE or the time interval T between the events. Currently, almost all studies on T charts are focused on applications under 100% inspection. However, due to limitations in resources and working conditions, sampling inspection has to be adopted for many SPC applications, especially when testing is destructive and/or expensive. The operational characteristics of T charts under sampling inspection could be quite different from those under 100% inspection. Specifically, some highly efficient techniques or methods, such as sequential analysis, may be adopted for sampling inspection. This article studies four T charts for sampling inspection: (1) a Shewhart T chart; (2) a CUSUM T chart and its variable sample size version; (3) a SA T chart (the T chart using sequential analysis); and (4) a curtailed SA T chart. It is the first time that sequential analysis and curtailment technique are adopted for TBE control charts. It is found that these SA-type charts, especially the curtailed chart, are significantly more effective than the Shewhart T chart, CUSUM T chart, and any other charts in current literature. This article has supplementary material online.     

Optimal designs of the multivariate synthetic chart for monitoring the process mean vector based on median run length

The average run length (ARL) is usually used as a sole measure of performance of a multivariate control chart. The Hotelling's T², multivariate exponentially weighted moving average (MEWMA) and multivariate cumulative sum (MCUSUM) charts are commonly optimally designed based on the ARL. Similar to the case of univariate quality control, in multivariate quality control, the shape of the run length distribution changes in accordance to the magnitude of the shift in the mean vector, from highly skewed when the process is in‐control to nearly symmetric for large shifts. Because the shape of the run length distribution changes with the magnitude of the shift in the mean vector, the median run length (MRL) provides additional and more meaningful information about the in‐control and out‐of‐control performances of multivariate charts, not given by the ARL. This paper provides a procedure for optimal designs of the multivariate synthetic T² chart for the process mean, based on MRL, for both the zero and steady‐state modes. Two Mathematica programs, each for the zero state and steady‐state modes are given for a quick computation of the optimal parameters of the synthetic T² chart, designed based on MRL. These optimal parameters are provided in the paper, for the bivariate case with sample sizes, nin{4, 7, 10}. The MRL performances of the synthetic T², MEWMA and Hotelling's T² charts are also compared. Copyright © 2011 John Wiley & Sons, Ltd.     

Monitoring therapeutic processes using risk-adjusted multivariate Tukey's CUSUM control chart

Using control charts for monitoring therapeutic processes has become popular lately. As the application of traditional control charts in the therapeutic processes may be misleading due to the inherent differences between patients, a multifactor correlated risk measure is considered in monitoring of these processes. Therefore, using risk-adjusted control charts for monitoring the therapeutic processes is of interest to practitioners. Furthermore, in health care monitoring, statistical models should account for abnormal distributions and outlier data to minimize misinterpretations of monitoring schemes. This study proposes a risk-adjusted multivariate Tukey's cumulative sum (RA-MTCUSUM) control chart. The proposed method is a combination of the accelerated failure time (AFT) regression model, the Tukey's control chart (TCC) featuring robustness against abnormality, and the multivariate cumulative sum (MCUSUM) control chart for monitoring multivariable process. Simulation experiments are performed to evaluate the performance of the proposed control chart using the average run length (ARL) measure. Results show that the RA-MTCUSUM control chart has better performance in comparison with traditional ones for monitoring various distributions (normal and non-normal). Based on the simulation results, outlier data do not disturb the proposed control chart's performance. Moreover, applying the RA-MTCUSUM control chart to a real-world dataset related to sepsis patients of a hospital located in Tehran, Iran indicates that the control chart has more reasonable performance than the traditional control charts in the real applications due to its robustness.     

Using an MQE chart based on a self-organizing map NN to monitor out-of-control signals in manufacturing processes

Control charts are recognized as one of the most important tools for statistical process control (SPC), used for monitoring any abnormal deviations in the state of manufacturing processes. However, the effectiveness of control charts is strictly dependent on statistical assumptions that in real applications are frequently violated. In contrast, neural networks (NNs) have excellent noise tolerance in real time, requiring no hypothesis on the statistical distribution of monitored processes. This feature makes NNs promising tools for quality control. In this paper, a self-organizing map (SOM)-based monitoring approach is proposed for enhancing the monitoring of processes. It is capable of providing a comprehensive and quantitative assessment value for the current process state, achieved by minimum quantization error (MQE) calculation. Based on MQE values over time series, a novel MQE chart is developed for monitoring process changes. The aim of this research is to analyse the performance of the MQE chart under the assumption that predictable abnormal patterns are not available. To this aim, the performance of the MQE chart in manufacturing processes (including non-correlated, auto-correlated and multivariate processes) is evaluated. The results indicate that the MQE chart may be a promising tool for quality control.     

A boosting approach for understanding out-of-control signals in multivariate control charts

The most widely used tools in statistical quality control are control charts. However, the main problem of multivariate control charts, including Hotelling's T ² control chart, lies in that they indicate that a change in the process has happened, but do not show which variable or variables are the source of this shift. Although a number of methods have been proposed in the literature for tackling this problem, the most usual approach consists of decomposing the T ² statistic. In this paper, we propose an alternative method interpreting this task as a classification problem and solving it through the application of boosting with classification trees. The classifier is then used to determine which variable or variables caused the change in the process. The results prove this method to be a powerful tool for interpreting multivariate control charts.     

A comparison of multivariate moving average control charts for the process mean

Two alternatives to the multivariate exponentially weighted moving average (EWMA) chart are considered. One of these alternatives is an arithmetic moving average control chart which is the arithmetic average of the sample means for the last k periods. The other alternative is a truncated version of the EWMA which truncates the EWMA after a fairly short period of time so that more emphasis is placed on the most current observation. Simulated average run length (ARL) results indicate that for some situations these alternatives charts outperform the multivariate EWMA chart. Some suggestions are made for designing charts to detect a specific shift and comparing the alternative charts. Some authors have noted that past in-control data may diminish the chart's ability to detect a shift in the process mean. To examine this, the scenario will be discussed when the process is in-control initially but goes out-of-control at some random time period. This is more like a realistic manufacturing setting, where the process is in-control initially, but after some time the process mean shifts to a new mean and in this paper it will be shown which control charts detect a shift faster using this scenario.