Diagnosing the variance shifts signal in multivariate process control using ensemble classifiers

Statistical process control charts have been successfully used to monitor process stability in various industries. The need to simultaneously monitor two or more quality characteristics has led to the prevalent adoption of multivariate control charts. However, out-of-control signals in multivariate control charts may be caused by one or more variables, or a set of variables. Therefore, effective quality control requires not only the rapid detection of process fluctuations, but also the correct identification of the variable(s) responsible for those changes. This study approaches the diagnosis of out-of-control signals as a classification task and proposes a support vector machine (SVM)-based ensemble classification model focused on variance shifts in multivariate processes. We address the issues of data diversity and ensemble method in constructing an ensemble model. Simulation results demonstrate the effectiveness of the proposed ensemble classification model in identifying the source of variance change. The proposed method clearly outperforms single classifiers as well as other comparable models including bagging and boosting. The results also reveal that the use of extracted features as input vectors for SVM provides better classification performance than the use of raw data. The proposed SVM-based ensemble classification system provides a reliable tool for the interpretation of out-of-control signals in multivariate process control.     

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.     

Directionally sensitive weighted adaptive multivariate CUSUM mean charts

In many service and manufacturing industries, process monitoring involves multivariate data, instead of univariate data. In these situations, multivariate charts are employed for process monitoring. Very often when the mean vector shifts to an out-of-control situation, the exact shift size is unknown; hence, multivariate charts for monitoring a range of the mean shift sizes in the mean vector are adopted. In this paper, directionally sensitive weighted adaptive multivariate CUSUM charts are developed for monitoring a range of the mean shift sizes. Directionally sensitive charts are useful in situations where the aim lies in monitoring either an increasing or a decreasing shift in the mean vector of the quality characteristics of interest. The Monte Carlo simulation is used to compute the run length characteristics in comparing the sensitivities of the proposed and existing multivariate CUSUM charts. In general, the directionally sensitive and weighted adaptive features enhance the sensitivities of the proposed multivariate CUSUM charts in comparison with the existing multivariate CUSUM charts without the adaptive feature or those that are directionally invariant. It is also found that the variable sampling interval feature enhances the sensitivities of the proposed and existing charts as compared to their fixed sampling interval counterparts. The implementation of the proposed charts in detecting upward and downward shifts in the in-control process mean vector is demonstrated using two different datasets.     

A simulation comparison of some distance-based EWMA control charts for monitoring the covariance matrix with individual observations

It is common in modern manufacturing to simultaneously monitor more than one process quality characteristic. In such a multivariate scenario, the monitoring of the covariance matrix, along with the mean vector, plays an important role in assessing whether a process stays in control or not. However, monitoring the covariance matrix is technically more difficult, especially when there is only one observation available in each subgroup, disabling the usual sample covariance matrix as an effective estimator. To monitor the covariance matrix with individual observations in Phase II stage, several exponentially weighted moving average (EWMA) control charts have been constructed based on the distance between the estimated process covariance matrix and its target value. In this paper, two new control charts are devised using the sum of the square roots of the absolute deviations and its combination with the sum of squared deviations. These distance-based control charts are compared via the simulation experiments on different simulated out-of-control covariance matrices with respect to the number of quality characteristics being monitored, the shift pattern, and the shift magnitude. The simulation results identify the control charts that perform relatively robust and show that these various control charts may have their respective merits on different out-of-control scenarios.     

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.     

Computing the Percentage Points of the Run-Length Distributions of Multivariate CUSUM Control Charts

Multivariate CUSUM control charts are often used instead of the standard Hotelling's control charts in many practical problems when detection of small shifts in the process mean is important. However, design of multivariate CUSUM control charts are usually based on the average run length (ARL). In this work, we will compute the percentage points of the run-length distributions of two multivariate CUSUM control charts. It will be shown that interpretations based on ARL can be misleading since the in-control run-length distribution of a multivariate CUSUM is highly skewed. On the other hand, the percentage points of the run-length distribution provide additional information such as the median run length, early false out-of-control signals, and the skewness of the run-length distribution for a particular scheme. These extra information might provide quality control engineers further knowledge of a particular multivariate CUSUM control chart scheme.     

On the multivariate progressive control chart for effective monitoring of covariance matrix

With the development of modern acquisition techniques, data with several correlated quality characteristics are increasingly accessible. Thus, multivariate control charts can be employed to detect changes in the process. This study proposes two multivariate control charts for monitoring process variability (MPVC) using a progressive approach. First, when the process parameters are known, the performance of the MPVC charts is compared with some multivariate dispersion schemes. The results showed that the proposed MPVC charts outperform their counterparts irrespective of the shifts in the process dispersion. The effects of the Phase I estimated covariance matrix on the efficiency of the MPVC charts were also evaluated. The performances of the proposed methods and their counterparts are evaluated by calculating some useful run length properties. An application of the proposed chart is also considered for the monitoring of a carbon fiber tubing process.     

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.     

Monitoring Correlated Profile and Multivariate Quality Characteristics

Monitoring multivariate quality characteristics is very common in production and service environment. Therefore, many control charts have been suggested by authors for monitoring multivariate processes. In another side, profile monitoring is a new approach in the area of statistical process control. In this approach, the quality of a product or a process is characterized by a relation between one response variable and one or more independent variables. In practice, sometimes the quality of a product or a process is represented by a correlated profile and multivariate quality characteristics. To the best of our knowledge, there is no method for monitoring this type of quality characteristics. Note that monitoring correlated profile and multivariate quality characteristics separately leads to misleading results. In this article, we specifically focus on correlated simple linear profile and multivariate normal quality characteristics and propose a method using multivariate exponentially weighted moving average control chart to monitor the correlated profile and multivariate quality characteristics simultaneously. The performance of the proposed control chart is evaluated by simulation studies in terms of average run length criterion. Finally, the proposed method is applied to a real case in the electronics industry. Copyright © 2013 John Wiley & Sons, Ltd.     

Memory-type multivariate charts with fixed and variable sampling intervals for process mean when covariance matrix is unknown

Memory-type multivariate charts have been widely recognized as a potentially powerful process monitoring tool because of their excellent speed in detecting small-to-moderate shifts in the mean vector of a multivariate normally distributed process, namely, the multivariate EWMA (MEWMA), double MEWMA, Crosier multivariate CUSUM (MCUSUM), and Pignatiello and Runger MCUSUM charts. These multivariate charts are based on the assumption that the covariance matrix is known in advance; but, it may not be known in practice. It is thus not possible to use these multivariate charts unless a large Phase I dataset is available from an in-control process. In this paper, we propose multivariate charts with fixed and variable sampling intervals for the process mean vector when the covariance matrix is estimated from sample. Using the Monte Carlo simulation method, the run length characteristics of the multivariate charts are computed. It is shown that the in-control and out-of-control run length performances of the proposed multivariate charts are robust to the changes in the process covariance matrix, while the existing multivariate charts are not. A real dataset is taken to explain the implementation of the proposed multivariate charts.     

A Bayesian approach to diagnosing covariance matrix shifts

In addition to the quick detection of abnormal changes in a multivariate process, it is also critical to provide an accurate fault identification of responsible components following an out-of-control signal. In line with the work of Tan and Shi for diagnosing shifts in the mean vector, this paper develops a Bayesian approach for diagnosing shifts in the covariance matrix. The simulation comparisons favor the proposed approach. A real example is also presented to demonstrate the implementation of the proposed method.     

Misleading signals in joint schemes for the mean vector and covariance matrix

In multivariate statistical process control, it is recommendable to run two individual charts: one for the process mean vector and another one for the covariance matrix. The resulting joint scheme provides a way to satisfy Shewhart's dictum that proper process control implies monitoring both process location and spread. The multivariate quality characteristic is deemed to be out of control whenever a signal is triggered by either individual chart of the joint scheme. Consequently, a shift in the mean vector can be misinterpreted as a shift in the covariance matrix and vice versa. Compelling results are provided to give the quality control practitioner an idea of how joint schemes for the mean vector and covariance matrix are prone to trigger misleading signals that will likely lead to a incorrect diagnostic of which parameter has changed.     

Multivariate statistical process control charts: an overview

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart‐type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial least squares (PLS). Finally, we describe the most significant methods for the interpretation of an out‐of‐control signal. Copyright © 2006 John Wiley & Sons, Ltd.     

Multivariate charting techniques: a review and a line‐column approach

The primary objective of multivariate statistical process control is to monitor the related process quality characteristics over time and identify the assignable causes affecting the process using multivariate control charts. When an out‐of‐control signal is obtained from the chart, it is imperative to be able to detect the component variables that have gone out‐of‐control. In this paper we propose a new charting procedure for T², multivariate exponentially weighted moving average and multivariate cumulative sum control charts. The proposed charts will facilitate in identification of the source of out‐of‐control signal and are simple, economical and easier to implement. Copyright © 2009 John Wiley & Sons, Ltd.     

A progressive approach for the detection of the coefficient of variation

A progressive average chart usually triggers initial out-of-control (OC) signals more simply and quickly than other memory-type charts . In this paper, two progressive average control procedures are proposed for monitoring the coefficient of variation (CV) of a normally distributed process variable, namely, the progressive CV (PCV) and progressive resetting CV (PRCV) control charts , respectively. The implementation of the proposed charts is presented, and the necessary design parameters are provided. Through extensive numerical simulations, it is shown that the proposed PCV and PRCV charts outperform several existing control charts to detect the initial OC signals, especially for the small and moderate CV shifts, under each combination of the shift size, the sample size, and the in-control target value of the CV. In addition, the application of the proposed control charts is illustrated by a detection example for a spinning process.     

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.     

Economic design of the integrated multivariate EPC and multivariate SPC charts

The goal of engineering process control (EPC) is to minimize variability by adjusting some manipulative process variables. The goal of statistical process control (SPC) is to reduce variability by monitoring and eliminating assignable causes of variation. As suggested by Box and Kramer and others, it is possible to reduce both special cause and common cause variations by integrating EPC and SPC. In the integrated multivariate EPC (MEPC) and multivariate SPC (MSPC) charts, we propose some statistical and economic criteria, such as the average Euclidean distance from the target vector and the average quality cost (AQC) to evaluate the performance of the MEPC/MSPC charts. The traditional average run length (ARL), average Euclidean distance and AQC of three MSPC charts are investigated and compared. The results of the simulations show that the MEPC/MGWMA chart is more effective and more economical than both the MEPC/MEWMA chart and the MEPC/Hotelling multivariate chart in detecting small shifts of the mean vector. Copyright © 2006 John Wiley & Sons, Ltd.     

Designing a multivariate–multistage quality control system using artificial neural networks

In most real-world manufacturing systems, the production of goods comprises several autocorrelated stages and the quality characteristics of the goods at each stage are correlated random variables. This paper addresses the problem of monitoring a multivariate–multistage manufacturing process and diagnoses the possible causes of out-of-control signals. To achieve this purpose using multivariate time series models, first a model for the autocorrelated data coming from multivariate–multistage processes is developed. Then, a single neural network is designed, trained and employed to control and classify mean shifts in quality characteristics of all stages. In-control and out-of-control average run lengths and correct classification ratio indices have been chosen to investigate the performance of the designed network. The results of a simulation study show that the network is capable of detecting both in-control and out-of-control signals appropriately.     

The effects of violations of the multivariate normality assumption in multivariate Shewhart and MEWMA control charts

A multivariate Shewhart and a multivariate exponentially weighted moving average control charts are types of multivariate control charts for monitoring the mean vector. For those control charts, a multivariate normal distribution is an important assumption that is used to describe a behavior of a set of quality characteristics of interest. This research explores the sensitivity of average run lengths and standard deviation of run lengths for the multivariate Shewhart and the multivariate exponentially weighted moving average control charts when the normality assumption is incorrect.     

Monitoring multivariate process variability when sub-group size is small

The current practice of multivariate process variability monitoring, when sub-group size is small, has nothing to do with probability of false alarm (PFA). Consequently, the reliability of the existing control charts remains undetermined. In this article, we propose a control chart which is reliable, very sensitive to the change in variance for small or moderate correlation, and provides a root causes analysis of an out-of-control signal. To illustrate these advantages, an industrial example is presented and the results are compared with those issued from the existing methods.