Multivariate Statistical Process Control Charts and the Problem of Interpretation : A Short Overview and Some Applications in Industry
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paper_title: RESEARCH ISSUES AND IDEAS IN STATISTICAL PROCESS CONTROL

paper_content:

An overview is given of current research on control charting methods for process monitoring and improvement. A historical perspective and ideas for future research also are given. Research topics include: variable sample size and sampling interval met..
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paper_title: Multivariate SPC Methods for Process and Product Monitoring

paper_content:

Statistical process control methods for monitoring processes with multivariate measurements in both the product quality variable space and the process variable space are considered. Traditional multivariate control charts based on X2 and T2 statistics ..
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paper_title: Generalized contribution plots in multivariate statistical process monitoring

paper_content:

Abstract This paper discusses contribution plots for both the D -statistic and the Q -statistic in multivariate statistical process control of batch processes. Contributions of process variables to the D -statistic are generalized to any type of latent variable model with or without orthogonality constraints. The calculation of contributions to the Q -statistic is discussed. Control limits for both types of contributions are introduced to show the relative importance of a contribution compared to the contributions of the corresponding process variables in the batches obtained under normal operating conditions. The contributions are introduced for off-line monitoring of batch processes, but can easily be extended to on-line monitoring and to continuous processes, as is shown in this paper.
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paper_title: Comparisons of Multivariate CUSUM Charts

paper_content:

We consider several distinct approaches for controlling the mean of a multivariate normal process including two new and distinct multivariate CUSUM charts, several multiple univariate CUSUM charts, and a Shewhart x2 control chart. The performances of th..
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paper_title: A review of multivariate control charts

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A review of the literature on control charts for multivariate quality control (MQC) is given, with a concentration on developments occurring since the mid-1980s. Multivariate cumulative sum (CUSUM) control procedures and a multivariate exponentially weighted moving average (EWMA) control chart are reviewed and recommendations are made regarding their use. Several recent articles that give methods for interpreting an out-of-control signal on a multivariate control chart are analyzed and discussed. Other topics such as the use of principal components and regression adjustment of variables in MQC, as well as frequently used approximations in MQC, are discussed.
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paper_title: Multivariate generalizations of cumulative sum quality-control schemes

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This article presents the design procedures and average run lengths for two mulativariater cumulative sum (CUSUM) quality-control procedures. The first CUSUM procedure reduces each multivariate observation to a scalar and then forms a CUSUM of the scalars. The second CUSUM procedure forms a CUSUM vector directly from the observations. These two procedures are compared with each other and with the multivariate Shewhart chart. Other multivariate quality-control procedures are mentioned. Robustness, the fast initial response feature for CUSUM schemes, and combined Shewhart-CUSUM schemes are discussed.
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paper_title: Multivariate statistical process control—recent results and directions for future research

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The performance of a product often depends on several quality characteristics. These characteristics may have interactions. In answering the question “Is the process in control?”, multivariate statistical process control methods take these interactions into account. In this paper, we review several of these multivariate methods and point out where to fill up gaps in the theory. The review includes multivariate control charts, multivariate CUSUM charts, a multivariate MMA chart, and multivariate process capability indices. The most important open question from a practical point of view is how to detect the variables that caused an out-of-control signal. Theoretically, the statistical properties of the methods should be investigated more profoundly.
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paper_title: Multivariate CUSUM Quality- Control Procedures

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It is a common practice to use, simultaneously, several one-sided or two-sided CUSUM procedures of the type proposed by Page (1954). In this article, this method of control is considered to be a single multivariate CUSUM (MCUSUM) procedure. Methods are given for approximating parameters of the distribution of the minimum of the run lengths of the univariate CUSUM charts. Using a new method of comparing multivariate control charts, it is shown that an MCUSUM procedure is often preferable to Hotelling's TZ procedure for the case in which the quality characteristics are bivariate normal random variables.
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paper_title: Multivariate Statistical Process Control with Industrial Applications

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This applied, self-contained text provides detailed coverage of the practical aspects of multivariate statistical process control (MVSPC) based on the application of Hotelling's T2 statistic. MVSPC is the application of multivariate statistical techniques to improve the quality and productivity of an industrial process. The authors, leading researchers in this area who have developed major software for this type of charting procedure, provide valuable insight into the T2 statistic. Intentionally including only a minimal amount of theory, they lead readers through the construction and monitoring phases of the T2 control statistic using numerous industrial examples taken primarily from the chemical and power industries. These examples are applied to the construction of historical data sets to serve as a point of reference for the control procedure and are also applied to the monitoring phase, where emphasis is placed on signal location and interpretation in terms of the process variables. Specifically devoted to the T2 methodology, Multivariate Statistical Process Control with Industrial Applications is the only book available that concisely and thoroughly presents such topics as how to construct a historical data set; how to check the necessary assumptions used with this procedure; how to chart the T2 statistic; how to interpret its signals; how to use the chart in the presence of autocorrelated data; and how to apply the procedure to batch processes. The book comes with a CD-ROM containing a 90-day demonstration version of the QualStat multivariate SPC software specifically designed for the application of T2 control procedures. The CD-ROM is compatible with Windows 95, Windows 98, Windows Me Millennium Edition, and Windows NT operating systems.
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paper_title: Improving the Performance of the Chi-square Control Chart via Runs Rules

paper_content:

The most popular multivariate process monitoring and control procedure used in the industry is the chi-square control chart. As with most Shewhart-type control charts, the major disadvantage of the chi-square control chart, is that it only uses the information contained in the most recently inspected sample; as a consequence, it is not very efficient in detecting gradual or small shifts in the process mean vector. During the last decades, the performance improvement of the chi-square control chart has attracted continuous research interest. In this paper we introduce a simple modification of the chi-square control chart which makes use of the notion of runs to improve the sensitivity of the chart in the case of small and moderate process mean vector shifts.
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paper_title: Multivariate Profile Charts for Statistical Process Control

paper_content:

The multivariate profile (MP) chart is a new control chart for simultaneous display of univariate and multivariate statistics. It is designed to analyze and display extended structures of statistical process control data for various cases of grouping, reference distribution, and use of nominal specifications. For each group of observations, the scaled deviations from reference values are portrayed together as a modified profile plot symbol. The vertical location of the symbol is determined by the multivariate distance of the vector of means from the reference values. The graphical display in the MP chart enjoys improved visual characteristics as compared with previously suggested methods. Moreover, the perceptual tasks required by the use of the MP chart provide higher accuracy in retrieving the quantitative information. This graphical display is used to display other combined univariate and multivariate statistics, such as measures of dispersion, principal components, and cumulative sums
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paper_title: Multivariate SPC Methods for Process and Product Monitoring

paper_content:

Statistical process control methods for monitoring processes with multivariate measurements in both the product quality variable space and the process variable space are considered. Traditional multivariate control charts based on X2 and T2 statistics ..
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paper_title: Multivariate Quality Control Using Finite Intersection Tests

paper_content:

Multivariate quality control problems involve the evaluation of a process based on the simultaneous behavior of p variables. Most multivariate quality control procedures evaluate the in-control or out-of-control condition based upon an overall statistic..
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paper_title: Decomposition of T2 for Multivariate Control Chart Interpretation

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Cumulative sum (CUSUM) control charts have been widely used for monitoring the process mean. Relatively little attention has been given to the use of CUSUM charts for monitoring the process variance. The properties of CUSUM charts based on the logarithm..
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paper_title: A Practical Approach for Interpreting Multivariate T2 Control Chart Signals

paper_content:

A persistent problem in multivariate control chart procedures is the interpretation of a signal. Determining which variable or group of variables is contributing to the signal can be a difficult task fo rthe practitioner. However, a procedure for decomp..
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paper_title: Generalized contribution plots in multivariate statistical process monitoring

paper_content:

Abstract This paper discusses contribution plots for both the D -statistic and the Q -statistic in multivariate statistical process control of batch processes. Contributions of process variables to the D -statistic are generalized to any type of latent variable model with or without orthogonality constraints. The calculation of contributions to the Q -statistic is discussed. Control limits for both types of contributions are introduced to show the relative importance of a contribution compared to the contributions of the corresponding process variables in the batches obtained under normal operating conditions. The contributions are introduced for off-line monitoring of batch processes, but can easily be extended to on-line monitoring and to continuous processes, as is shown in this paper.
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paper_title: Investigation and characterization of a control scheme for multivariate quality control

paper_content:

A new scheme for multivariate statistical quality control is investigated and characterized. The control scheme consists of three steps and it will identify any out-of-control samples, select the subset of variables that are out of control, and diagnose the out-of-control variables. A new control variable selection algorithm, the backward selection algorithm, and a new control variable diagnosis method, the hyperplane methods, are proposed. It is shown by simulation that the control scheme is useful in cases where the process variables are correlated and where they are uncorrelated.
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paper_title: Identification and Quantification in Multivariate Quality Control Problems

paper_content:

Many quality control problems are multivariate in character since the quality of a given product or object consists simultaneously of more than one variable. A good multivariate quality control procedure should possess three important properties, namely, the control of the overall error rate, the easy identification of errant variables, and the easy quantification of any changes in the variable means. In this paper a procedure is suggested based on the construction of exact simultaneous confidence intervals for each of the variable means that meets each of these three goals. Both parametric and nonparametric procedures are considered, and critical point evaluation through tables, numerical integration, and simulation is discussed. Various examples of the implementation of the procedure are given.
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paper_title: IDENTIFYING THE OUT OF CONTROL VARIABLE IN A MULTIVARIATE CONTROL CHART

paper_content:

The identification of the out of control variable, or variables, after a multivariate control chart signals, is an appealing subject for many researchers in the last years. In this paper we propose a new method for approaching this problem based on principal components analysis. Theoretical control limits are derived and a detailed investigation of the properties and the limitations of the new method is given. A graphical technique which can be applied in some of these limiting situations is also provided.
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paper_title: Improving the Sensitivity of the T2 Statistic in Multivariate Process Control

paper_content:

The T2 statistic in multivariate process control is a function of the residuals taken from a set of linear regressions of the process variables. These residuals are contained in the conditional T2 terms of the orthogonal decomposition of the statistic...
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paper_title: Monitoring a Multivariate Step Process

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The productivity of an industrial processing unit often depends on equipment that changes over time. These changes may not be consistent, and , in many cases, may appear to occur in stages. Although changes in the process levels within each stage may ap..
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paper_title: Multivariate Control Charts for Individual Observations

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When p correlated process characteristics are being measured simultaneously, often individual observations are initially collected. The process data are monitored and special causes of variation are identified in order to establish control and to obtain..
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paper_title: Visualization of multivariate data with radial plots using SAS

paper_content:

Data visualization tools can provide very powerful information and insight when performing data analysis. In many situations, a set of data can be adequately analyzed through data visualization methods alone. In other situations, data visualization can be used for preliminary data analysis. In this paper, radial plots are developed as a SAS-based data visualization tool that can improve one's ability to monitor, analyze and control a process. Using the program developed in this research, we present two examples of data analysis using radial plots; the first example is based on data from a particle board manufacturing process and the second example is a business process for monitoring the time-varying level of stock return data.
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paper_title: Multivariate Process Monitoring Using the Dynamic Biplot

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Summary ::: ::: In this article, we present a method for monitoring multivariate process data based on the Gabriel biplot. In contrast to existing methods that are based on some form of dimension reduction, we use reduction to two dimensions for displaying the state of the process but all the data for determining whether it is in a state of statistical control. This approach allows us to detect changes in location, variation, and correlational structure accurately yet display a large amount of information concisely. We illustrate the use of the biplot on an example of industrial data and also discuss some of the issues related to a practical implementation of the method.
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paper_title: IDENTIFYING THE OUT OF CONTROL VARIABLE IN A MULTIVARIATE CONTROL CHART

paper_content:

The identification of the out of control variable, or variables, after a multivariate control chart signals, is an appealing subject for many researchers in the last years. In this paper we propose a new method for approaching this problem based on principal components analysis. Theoretical control limits are derived and a detailed investigation of the properties and the limitations of the new method is given. A graphical technique which can be applied in some of these limiting situations is also provided.
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Title: Multivariate Statistical Process Control Charts and the Problem of Interpretation: A Short Overview and Some Applications in Industry

Section 1: INTRODUCTION
Description 1: Introduce the basic concept of Statistical Process Control (SPC), highlight the limitations of univariate SPC in process industries, and provide an overview of multivariate SPC techniques and their historical development.

Section 2: CONTROLLING AND MONITORING MULTIVARIATE PROCESSES USING CONTROL CHARTS
Description 2: Describe the implementation of multivariate statistical process control using control charts, including detailed explanations of Phase I and Phase II control charting, and discuss different types of multivariate control charts such as Shewhart, CUSUM, and EWMA.

Section 3: IDENTIFYING THE OUT-OF-CONTROL VARIABLE
Description 3: Present various methods for detecting which specific variables are out of control when an out-of-control signal is identified in a multivariate control chart, including Bonferroni limits, principal component analysis, and contribution plots.

Section 4: APPLICATIONS OF MULTIVARIATE SPC TECHNIQUES IN THE INDUSTRIAL ENVIRONMENT
Description 4: Discuss real-world applications of multivariate SPC techniques in industry, focusing on a three-variable case study in a chemical process, and describe Phase I and Phase II analysis procedures along with identification methods for out-of-control variables.

Section 5: COMMENTS
Description 5: Offer concluding remarks and discuss potential areas for further research in the domain of multivariate SPC, such as robust design, nonparametric control charts, and improved methods for interpreting out-of-control signals.