Multivariate Quality Control Charts Research Articles

Robust multivariate quality control charts for enhanced variability monitoring

AbstractIn this research, it was proposed to create three new robust multivariate charts corresponding to the |S|‐ chart, which are robust to outliers, using three methods, an algorithm, namely the Rousseuw and Leroy algorithm, Maronna and Zamar, and the family of ‘concentration algorithms’ by Olive and Hawkins. Then the comparison between the proposed and classical method of the researcher Shewhart depends on the total variance (trace variance matrix), the general variance (determinant of the variance matrix), and the difference between the upper and lower control limits to obtain the most efficient charts against outliers through simulation and real data and using a program in the MATLAB language designed for this purpose. The study concluded that the proposed charts dealt with the problem of the influence of outliers and were more efficient than the classical method, in addition, the proposed robust chart (Orthogonalized Gnanadesikan‐Kettenring) was more efficient than the rest of the proposed charts.

Using of Multivariate Hotelling T2 Quality Control Charts in Bazyan Cement Factory

Cement is representing the major element of concrete ingredient and most of Kurdish houses and buildings depending on concrete structure. Cement has physical and chemical characteristics that rely on them to attain good quality. Using quality control charts to know that the process is under control or not could be apply on cement factories in Kurdistan Regional Government (KRG). The objective of this paper is to use univariate and multivariate Quality Control Charts (QCC) to monitor the cement production in Bazyan factory. The data analyses were done through Statgraphics v.16 mainly for 4 cement characteristics (1 physical and 3 chemical) with 100 observations for each characteristic. The data was divided into 25 subgroups and then X-bar charts founded for the variables and compared them with the results of multivariate QCC using Hotelling T2. It was discovered that the process is not under control due to 2 chemical characteristics (Al2O3 and SO3). It is recommended to use the suggested multivariate chart by responsible authority especially the directorates concerned with monitoring of cement factories

On the results of non-normality of process characteristics on x̄ and Hotelling’s χ2 -control charts

The development and application of the traditional univariate and multivariate quality control charts are distribution-based following the assumption that the process outputs come from some specified distribution(normal for continuous measurements and binomial or poison for attribute data).However, in many quality/process control applications, these distributional assumptions are either not satisfied or there is simply lack of enough information to verify the assumptions and this condition drops the performance of the charts. Yet, many researchers and quality practitioners always resort to their use probably because of unfamiliarity of the nonparametric alternatives. This paper aims to show the nature and extent of non-normality on these traditional X-bar charts and Hotelling’s χ2 control chart.

Robust multivariate control charts based on Birnbaum–Saunders distributions

ABSTRACTMultivariate control charts are powerful and simple visual tools for monitoring the quality of a process. This multivariate monitoring is carried out by considering simultaneously several correlated quality characteristics and by determining whether these characteristics are in control or out of control. In this paper, we propose a robust methodology using multivariate quality control charts for subgroups based on generalized Birnbaum–Saunders distributions and an adapted Hotelling statistic. This methodology is constructed for Phases I and II of control charts. We estimate the corresponding parameters with the maximum likelihood method and use parametric bootstrapping to obtain the distribution of the adapted Hotelling statistic. In addition, we consider the Mahalanobis distance to detect multivariate outliers and use it to assess the adequacy of the distributional assumption. A Monte Carlo simulation study is conducted to evaluate the proposed methodology and to compare it with a standard methodology. This study reports the good performance of our methodology. An illustration with real-world air quality data of Santiago, Chile, is provided. This illustration shows that the methodology is useful for alerting early episodes of extreme air pollution, thus preventing adverse effects on human health.

Integrating Auto-Associative Neural Networks with Hotelling T2 Control Charts for Wind Turbine Fault Detection

This paper presents a novel methodology to detect a set of more suitable attributes that may potentially contribute to emerging faults of a wind turbine. The set of attributes were selected from one-year historical data for analysis. The methodology uses the k-means clustering method to process outlier data and verifies the clustering results by comparing quartiles of boxplots, and applies the auto-associative neural networks to implement the residual approach that transforms the data to be approximately normally distributed. Hotelling T2 multivariate quality control charts are constructed for monitoring the turbine’s performance and relative contribution of each attribute is calculated for the data points out of upper limits to determine the set of potential attributes. A case using the historical data and the alarm log is given and illustrates that our methodology has the advantage of detecting a set of susceptible attributes at the same time compared with only one independent attribute is monitored.

A hybrid root transformation and decision on belief approach to monitor multiattribute Poisson processes

Most of industrial applications of statistical process control involve more than one quality characteristics to be monitored. These characteristics are usually correlated, causing challenges for the monitoring methods. These challenges are resolved using multivariate quality control charts that have been widely developed in recent years. Nonetheless, multivariate process monitoring methods encounter a problem when the quality characteristics are of the attribute type and follow nonnormal distributions such as multivariate binomial or multivariate Poisson. Since the data analysis in the latter case is not as easy as the normal case, more complexities are involved to monitor multiattribute processes. In this paper, a hybrid procedure is developed to monitor multiattribute correlated processes, in which number of defects in each characteristic is important. Two phases are proposed to design the monitoring scheme. In the first phase, the inherent skewness of multiattribute Poisson data is almost removed using a root transformation technique. In the second phase, a method based on the decision on belief concept is employed. The transformed data obtained from the first phase are implemented on the decision on belief (DOB) method. Finally, some simulation experiments are performed to compare the performances of the proposed methodology with the ones obtained using the Hotelling T2 and the MEWMA charts in terms of in-control and out-of-control average run length criteria. The simulation results show that the proposed methodology outperforms the other two methods.

A comparison of multivariate control charts for skewed distributions using weighted standard deviations

The quality of a manufacturing process usually depends on more than one quality characteristic. Thus, most process monitoring data are multivariate in nature. The assumption that the underlying process follows a multivariate normal distribution is usually required by most multivariate quality control charts. However, in most process monitoring situations, the multivariate normality assumption is often violated. Multivariate control charts for skewed distributions have been suggested to enable process monitoring to be made when the underlying process distribution is skewed. Among the recent heuristic multivariate charts for skewed distributions suggested in the literature are those based on the weighted standard deviation (WSD) approach. This paper compares the performances of three multivariate charts for skewed distributions incorporating the WSD method, namely, the WSD T 2 , WSD multivariate cumulative sum (WSD MCUSUM) and WSD multivariate exponentially weighted moving average (WSD MEWMA) charts. These heuristic charts are compared based on the multivariate lognormal, gamma and Weibull distributions. The charts’ performances are evaluated using the false alarm rates, computed via a Monte-carlo simulation. The chart with the lowest false alarm rate for most of the skewness levels and sample sizes will be identified as the chart having the best performance.

A Framework for Diagnosing the Out-of-Control Signals in Multivariate Process Using Optimized Support Vector Machines

Multivariate statistical process control is the continuation and development of unitary statistical process control. Most multivariate statistical quality control charts are usually used (in manufacturing and service industries) to determine whether a process is performing as intended or if there are some unnatural causes of variation upon an overall statistics. Once the control chart detects out-of-control signals, one difficulty encountered with multivariate control charts is the interpretation of an out-of-control signal. That is, we have to determine whether one or more or a combination of variables is responsible for the abnormal signal. A novel approach for diagnosing the out-of-control signals in the multivariate process is described in this paper. The proposed methodology uses the optimized support vector machines (support vector machine classification based on genetic algorithm) to recognize set of subclasses of multivariate abnormal patters, identify the responsible variable(s) on the occurrence of abnormal pattern. Multiple sets of experiments are used to verify this model. The performance of the proposed approach demonstrates that this model can accurately classify the source(s) of out-of-control signal and even outperforms the conventional multivariate control scheme.

On line detection of mean and variance shift using neural networks and support vector machine in multivariate processes

The effective recognition of unnatural control chart patterns (CCPs) is one of the most important tools to identify process problems. In multivariate process control, the main problem of multivariate quality control charts is that they can detect an out of control event but do not directly determine which variable or group of variables has caused the out of control signal and how much is the magnitude of out of control. Recently machine learning techniques, such as artificial neural networks (ANNs), have been widely used in the research field of CCP recognition. This study presents a modular model for on-line analysis of out of control signals in multivariate processes. This model consists of two modules. In the first module using a support vector machine (SVM)-classifier, mean shift and variance shift can be recognized. Then in the second module, using two special neural networks for mean and variance, it can be recognized magnitude of shift for each variable simultaneously. Through evaluation and comparison, our research results show that the proposed modular performs substantially better than the traditional corresponding control charts. The main contributions of this work are recognizing the type of unnatural pattern and classifying the magnitude of shift for mean and variance in each variable simultaneously.

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

AbstractTraditional 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.

On-line analysis of out-of-control signals in multivariate manufacturing processes using a hybrid learning-based model

Advanced automatic data acquisition is now widely adopted in manufacturing industries and it is common to monitor several correlated quality variables simultaneously. Most of multivariate quality control charts are effective in detecting out-of-control signals based upon an overall statistics in multivariate manufacturing processes. The main problem of such charts is that they can detect an out-of-control event but do not directly determine which variable or group of variables has caused the out-of-control signal and what is the magnitude of out of control. This study presents a hybrid learning-based model for on-line analysis of out-of-control signals in multivariate manufacturing processes. This model consists of two modules. In the first module using a support vector machine-classifier, type of unnatural pattern can be recognized. Then by using three neural networks for shift mean, trend and cycle it can be recognized magnitude of mean shift, slope of trend and cycle amplitude for each variable simultaneously in the second module. The performance of the proposed approach has been evaluated using two examples. The output generated by trained hybrid model is strongly correlated with the corresponding actual target value for each quality characteristic. The main contributions of this work are recognizing the type of unnatural pattern and classification major parameters for shift, trend and cycle and for each variable simultaneously by proposed hybrid model.

Interpreting the Out-of-Control Signals of Multivariate Control Charts Employing Neural Networks

Multivariate quality control charts show some advantages to monitor several variables in comparison with the simultaneous use of univariate charts, nevertheless, there are some disadvantages. The main problem is how to interpret the out-ofcontrol signal of a multivariate chart. For example, in the case of control charts designed to monitor the mean vector, the chart signals showing that it must be accepted that there is a shift in the vector, but no indication is given about the variables that have produced this shift. The MEWMA quality control chart is a very powerful scheme to detect small shifts in the mean vector. There are no previous specific works about the interpretation of the out-of-control signal of this chart. In this paper neural networks are designed to interpret the out-of-control signal of the MEWMA chart, and the percentage of correct classifications is studied for different cases. Keywords—Multivariate quality control. Artificial Intelligence. Neural Networks. Computer Applications

A hybrid learning-based model for on-line monitoring and diagnosis of out-of-control signals in multivariate manufacturing processes

In multivariate statistical process control, most multivariate quality control charts are shown to be effective in detecting out-of-control signals based upon overall statistics. But these charts do not relieve the need for pinpointing the source(s) of the out-of-control signals. In addition, these charts cannot provide more detailed process information, such as quantitative abnormal assessment values and visualisation of process changes, which would be very useful for quality practitioners to locate the assignable causes that give rise to the out-of-control situation. In this study, a hybrid learning-based model has been investigated for monitoring and diagnosing out-of-control signals in a bivariate process. In this model, a minimum quantisation error (MQE) chart based on the self-organization map (SOM) neural network (NN) was developed for monitoring process changes (i.e., mean shifts), and a selective NN ensemble approach (DPSOEN) was developed for diagnosing signals that are judged as out-of-control signals by MQE charts. The simulation results demonstrate that the proposed model outperforms the conventional multivariate control scheme in terms of average run length (ARL), and can accurately classify the source(s) of out-of-control signals. An extensive experiment is also carried out to examine the effects of six statistical features on the performance of DPSOEN.

Identifying source(s) of out-of-control signals in multivariate manufacturing processes using selective neural network ensemble

In multivariate statistical process control (MSPC), most multivariate quality control charts 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 pinpointing source(s) of the out-of-control signals. Neural networks (NNs) have excellent noise tolerance and high pattern identification capability in real time, which have been applied successfully in MSPC. This study proposed a selective NN ensemble approach DPSOEN, where several selected NNs are jointly used to classify source(s) of out-of-control signals in multivariate processes. The immediate location of the abnormal source(s) can greatly narrow down the set of possible assignable causes, facilitating rapid analysis and corrective action by quality operators. The performance of DPSOEN is analyzed in multivariate processes. It shows improved generalization performance that outperforms those of single NNs and Ensemble All approach. The investigation proposed a heuristic approach for applying the DPSOEN-based model as an effective and useful tool to identify abnormal source(s) in bivariate statistical process control (SPC) with potential application for MSPC in general.

A neural network ensemble-based model for on-line monitoring and diagnosis of out-of-control signals in multivariate manufacturing processes

In multivariate statistical process control, most multivariate quality control charts are shown to be effective in detecting out-of-control signals based upon an overall statistics. But these charts do not relieve the need for pinpointing source(s) of the out-of-control signals, which would be very useful for quality practitioners to locate the assignable causes that give rise to the out-of-control situation. In this study, a learning-based model has been investigated for monitoring and diagnosing out-of-control signals in a bivariate process. In this model, a selective neural network (NN) ensemble approach (DPSOEN, Discrete Particle Swarm Optimization) was developed for performing these tasks. The simulation results demonstrate that the proposed model outperforms the conventional multivariate control scheme in terms of average run length (ARL), and can accurately classify source(s) of out-of-control signals. Extensive experiment is also carried out to examine the effects of six statistical features on the performance of DPSOEN. Analysis from this study provides guidelines in developing NN ensemble-based Statistical process control recognition systems in multivariate processes.

Monitoring Variability and Analyzing Multivariate Autocorrelated Processes

Traditional multivariate quality control charts are based on independent observations. In this paper, we explain how to extend univariate residual charts to multivariate cases and how to combine the traditional statistical process control (SPC) approaches to monitor changes in process variability in a dynamic environment. We propose using Alt's (1984) W chart on vector autoregressive (VAR) residuals to monitor the variability for multivariate processes in the presence of autocorrelation. We study examples jointly using the Hotelling T2 chart on VAR residuals, the W chart, and the Portmanteau test to diagnose the types of shift in process parameters.

A model‐based approach to quality control of paper production

AbstractThis paper uses estimated model parameters as inputs into multivariate quality control charts. The thickness of paper leaving a paper mill is measured at a high sampling rate, and these data are grouped into successive data segments. A stochastic model for paper is fitted to each data segment, leading to parameter estimates and information‐based standard errors for these estimates. The estimated model parameters vary by more than one can be explained by the information‐based standard errors, suggesting that the ‘true’ underlying parameters are not constant over time. A model is formulated for the true parameters in which the information matrix dictates the distribution for the observed parameters given the true parameters. Copyright © 2004 John Wiley & Sons, Ltd.

Ternary and Multivariate Quality Control Charts of Aggregate Gradation for Hot Mix Asphalt

Several statistical methods for controlling the quality of aggregate gradation are proposed, based on a multivariate model that describes compositional data. First, ternary quality control charts are developed to control a three-part gradation such as that given by the restricted zone method, with both hexagonal and elliptical acceptance regions. Second, multivariate quality control charts are developed with multiple category and \iT² acceptance regions. Hexagonal and multiple category regions use fixed lower and upper control limits for each category and are easier to interpret by a visual plot, whereas elliptical and \iT² regions account for the correlations among the categories and are more accurate and efficient. The control charts may be used to show the dynamic status of consecutive average values and can easily be applied with spreadsheet software such as Microsoft Excel.

Applied Multivariate Statistical Analysis.

(NOTE: Each chapter begins with an Introduction, and concludes with Exercises and References.) I. GETTING STARTED. 1. Aspects of Multivariate Analysis. Applications of Multivariate Techniques. The Organization of Data. Data Displays and Pictorial Representations. Distance. Final Comments. 2. Matrix Algebra and Random Vectors. Some Basics of Matrix and Vector Algebra. Positive Definite Matrices. A Square-Root Matrix. Random Vectors and Matrices. Mean Vectors and Covariance Matrices. Matrix Inequalities and Maximization. Supplement 2A Vectors and Matrices: Basic Concepts. 3. Sample Geometry and Random Sampling. The Geometry of the Sample. Random Samples and the Expected Values of the Sample Mean and Covariance Matrix. Generalized Variance. Sample Mean, Covariance, and Correlation as Matrix Operations. Sample Values of Linear Combinations of Variables. 4. The Multivariate Normal Distribution. The Multivariate Normal Density and Its Properties. Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation. The Sampling Distribution of 'X and S. Large-Sample Behavior of 'X and S. Assessing the Assumption of Normality. Detecting Outliners and Data Cleaning. Transformations to Near Normality. II. INFERENCES ABOUT MULTIVARIATE MEANS AND LINEAR MODELS. 5. Inferences About a Mean Vector. The Plausibility of ...m0 as a Value for a Normal Population Mean. Hotelling's T 2 and Likelihood Ratio Tests. Confidence Regions and Simultaneous Comparisons of Component Means. Large Sample Inferences about a Population Mean Vector. Multivariate Quality Control Charts. Inferences about Mean Vectors When Some Observations Are Missing. Difficulties Due To Time Dependence in Multivariate Observations. Supplement 5A Simultaneous Confidence Intervals and Ellipses as Shadows of the p-Dimensional Ellipsoids. 6. Comparisons of Several Multivariate Means. Paired Comparisons and a Repeated Measures Design. Comparing Mean Vectors from Two Populations. Comparison of Several Multivariate Population Means (One-Way MANOVA). Simultaneous Confidence Intervals for Treatment Effects. Two-Way Multivariate Analysis of Variance. Profile Analysis. Repealed Measures, Designs, and Growth Curves. Perspectives and a Strategy for Analyzing Multivariate Models. 7. Multivariate Linear Regression Models. The Classical Linear Regression Model. Least Squares Estimation. Inferences About the Regression Model. Inferences from the Estimated Regression Function. Model Checking and Other Aspects of Regression. Multivariate Multiple Regression. The Concept of Linear Regression. Comparing the Two Formulations of the Regression Model. Multiple Regression Models with Time Dependant Errors. Supplement 7A The Distribution of the Likelihood Ratio for the Multivariate Regression Model. III. ANALYSIS OF A COVARIANCE STRUCTURE. 8. Principal Components. Population Principal Components. Summarizing Sample Variation by Principal Components. Graphing the Principal Components. Large-Sample Inferences. Monitoring Quality with Principal Components. Supplement 8A The Geometry of the Sample Principal Component Approximation. 9. Factor Analysis and Inference for Structured Covariance Matrices. The Orthogonal Factor Model. Methods of Estimation. Factor Rotation. Factor Scores. Perspectives and a Strategy for Factor Analysis. Structural Equation Models. Supplement 9A Some Computational Details for Maximum Likelihood Estimation. 10. Canonical Correlation Analysis Canonical Variates and Canonical Correlations. Interpreting the Population Canonical Variables. The Sample Canonical Variates and Sample Canonical Correlations. Additional Sample Descriptive Measures. Large Sample Inferences. IV. CLASSIFICATION AND GROUPING TECHNIQUES. 11. Discrimination and Classification. Separation and Classification for Two Populations. Classifications with Two Multivariate Normal Populations. Evaluating Classification Functions. Fisher's Discriminant Function...nSeparation of Populations. Classification with Several Populations. Fisher's Method for Discriminating among Several Populations. Final Comments. 12. Clustering, Distance Methods and Ordination. Similarity Measures. Hierarchical Clustering Methods. Nonhierarchical Clustering Methods. Multidimensional Scaling. Correspondence Analysis. Biplots for Viewing Sample Units and Variables. Procustes Analysis: A Method for Comparing Configurations. Appendix. Standard Normal Probabilities. Student's t-Distribution Percentage Points. ...c2 Distribution Percentage Points. F-Distribution Percentage Points. F-Distribution Percentage Points (...a = .10). F-Distribution Percentage Points (...a = .05). F-Distribution Percentage Points (...a = .01). Data Index. Subject Index.