Adaptive Charting Techniques: Literature Review and Extensions
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paper_title: Applying manufacturing batch techniques to fraud detection with incomplete customer information

paper_content:

Fraud detection is an important issue in service industries. Its technical challenges include the existence of complex patterns, its multivariate nature, and the incompleteness of records. As similar problems are observed in batch manufacturing process analysis, existing batch manufacturing techniques can be adapted and mapped to the fraud detection problem in the service sector. In particular, the batch library method can be modified to incorporate new information into incomplete customer records for analysis, while controlling the overall type I error rate. A real case is used to demonstrate the effectiveness of this approach, and simulation results are presented to show that the proposed approach consistently outperforms existing approaches.
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paper_title: The Use of Control Charts in Health-Care and Public-Health Surveillance

paper_content:

There are many applications of control charts in health-care monitoring and in public-health surveillance. We introduce these applications to industrial practitioners and discuss some of the ideas that arise that may be applicable in industrial monitoring. The advantages and disadvantages of the charting methods proposed in the health-care and public-health areas are considered. Some additional contributions in the industrial statistical process control literature relevant to this area are given. There are many application and research opportunities available in the use of control charts for health-related monitoring.
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paper_title: An adaptive exponentially weighted moving average: control chart

paper_content:

Lucas and Saccucci showed that exponentially weighted moving average (EWMA) control charts can be designed to quickly detect either small or large shifts in the mean of a sequence of independent observations. But a single EWMA chart cannot perform well for small and large shifts simultaneously. Furthermore, in the worst-case situation, this scheme requires a few observations to overcome its initial inertia. The main goal of this article is to suggest an adaptive EWMA (AEWMA) chart that weights the past observations of the monitored process using a suitable function of the current “error.” The resulting scheme can be viewed as a smooth combination of a Shewhart chart and an EWMA chart. A design procedure for the new control schemes is suggested. Comparisons of the standard and worst-case average run length profiles of the new scheme with those of different control charts show that AEWMA schemes offer a more balanced protection against shifts of different sizes.
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paper_title: Combined Shewhart-CUSUM Quality Control Schemes

paper_content:

The Shewhart-CUSUM quality control scheme which combines the key features of the Shewhart and CUSUM control procedures is described and evaluated. In this scheme the CUSUM feature will quickly detect small shifts from the goal while the addition of Shew..
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paper_title: SHEWMA: an end-of-line SPC scheme using wafer acceptance test data

paper_content:

In this paper, an end-of-line quality control scheme based on wafer acceptance test (WAT) data is presented. Due to the multiple-stream and sequence-disorder effects typically present in the WAT data, an abnormal process shift caused by one machine at an in-line step may become vague for detection using end-of-line WAT data. A methodology for generating robust design parameters for the simultaneous application of Shewhart and EWMA control charts to WAT data is proposed. This SHEWMA scheme is implemented in a foundry environment and its detection and diagnosis-enhancing capabilities are validated using both numerical derivations and fab data. Results show that the SHEWMA scheme is superior to the current practices in detection speed. Its use is complementary to the existing in-line SPC for process integration.
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paper_title: An X and EWMA Chart for Individual Observations

paper_content:

While there is much experience in monitoring processes with individual observations it is not clear which procedure is best. We compare individual observation control procedures that are combinations of the moving range (MR), exponentially weighted movi..
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paper_title: Should Exponentially Weighted Moving Average and Cumulative Sum Charts Be Used With Shewhart Limits

paper_content:

Traditional Shewhart control charts are usually considered effective for detecting large shifts in process parameters, but ineffective for detecting small shifts. For detecting small parameter shifts, it is much better to use exponentially weighted moving average (EWMA) control charts or cumulative sum (CUSUM) control charts, but these charts are not considered as effective as Shewhart charts for large parameter shifts. It is frequently recommended that EWMA or CUSUM charts be used in combination with a Shewhart chart to gain the benefits of both types of charts, so that both small and large shifts can be detected quickly. Here we consider the problem of process monitoring when a continuous process variable is being observed and the objective is to detect small or large shifts in either the process mean μ or the process standard deviation σ. In this situation it is customary to use a combination of two control charts, one chart designed to monitor μ, and the other designed to monitor σ. For this situation...
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paper_title: A Markov Chain Model for the Adaptive CUSUM Control Chart

paper_content:

When the magnitude of a future shift is unknown, a control chart designed to perform over a range of shifts is a better option than optimizing the performance at detecting a certain level of shifts. In this sense, the adaptive cumulative sum (ACUSUM) ch..
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paper_title: Adaptive multivariate statistical process control for monitoring time-varying processes

paper_content:

An adaptive multivariate statistical process monitoring (MSPC) approach is described for the monitoring of a process with incurs operating condition changes. Samplewise and blockwise recursive formulas for updating a weighted mean and covariance matrix are derived. By utilizing these updated mean and covariance structures and the current model, a new model is derived recursively. On the basis of the updated principal component analysis (PCA) representation, two monitoring metrics, Hotelling's T2 and the Q-statistic, are calculated and their control limits are updated. For more efficient model updating, forgetting factors, which change with time, for the updating of the mean and covariance are considered. Furthermore, the updating scheme proposed is robust in that it not only reduces the false alarm rate in the monitoring charts but also makes the model insensitive to outliers. The adaptive MSPC approach developed is applied to a multivariate static system and a continuous stirred tank reactor process, and...
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paper_title: Wavelet-based multiscale statistical process monitoring: A literature review

paper_content:

Data that represent complex and multivariate processes are well known to be multiscale due to the variety of changes that could occur in a process with different localizations in time and frequency. Examples of changes may include mean shift, spikes, drifts and variance shifts all of which could occur in a process at different times and at different frequencies. Acoustic emission signals arising from machining, images representing MRI scans and musical audio signals are some examples that contain these changes and are not suited for single scale analysis. The recent literature contains several wavelet-decomposition-based multiscale process monitoring approaches including many real life process monitoring applications. These approaches are shown to be effective in handling different data types and, in concept, are likely to perform better than existing single scale approaches. There also exists a vast literature on the theory of wavelet decomposition and other statistical elements of multiscale monitoring methods, such as principal components analysis, denoising and charting. To our knowledge, no comprehensive review of the work relevant to multiscale monitoring of both univariate and multivariate processes has been presented to the literature. In this paper, over 150 both published and unpublished papers are cited for this important subject, and some extensions of the current research are also discussed.
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paper_title: Statistical Process Control Charts for Batch Operations Based on Independent Component Analysis

paper_content:

A significant step forward in recent years, in regard to multivariate statistical process control (MSPC) for operational condition monitoring and fault diagnosis, has been the introduction of principal component analysis (PCA) for the compression of process data. An alternative technique that has been studied more recently for data compression is independent component analysis (ICA). Published work has shown that, in some applications of statistical process monitoring, ICA-based methods have exhibited advantages over those based on other data compression techniques. However, it is inappropriate to use ICA in the same way as PCA to derive Hotelling's T2 and SPE (squared prediction error) charts, because the independent components are separated by maximizing their non-Gaussianity, whereas the satisfying Gaussian distribution is the basis of T2 and SPE monitoring charts, as well as univariate statistical process control (SPC) charts. In this paper, we propose a new method for deriving SPC charts based on ICA...
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paper_title: Principal Component Analysis

paper_content:

When large multivariate datasets are analyzed, it is often desirable to reduce their dimensionality. Principal component analysis is one technique for doing this. It replaces the p original variables by a smaller number, q, of derived variables, the principal components, which are linear combinations of the original variables. Often, it is possible to retain most of the variability in the original variables with q very much smaller than p. Despite its apparent simplicity, principal component analysis has a number of subtleties, and it has many uses and extensions. A number of choices associated with the technique are briefly discussed, namely, covariance or correlation, how many components, and different normalization constraints, as well as confusion with factor analysis. Various uses and extensions are outlined. ::: ::: ::: Keywords: ::: ::: dimension reduction; ::: factor analysis; ::: multivariate analysis; ::: variance maximization
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paper_title: Statistical Monitoring of Nonlinear Product and Process Quality Profiles

paper_content:

In many quality control applications, use of a single (or several distinct) quality characteristic(s) is insufficient to characterize the quality of a produced item. In an increasing number of cases, a response curve (profile) is required. Such profiles can frequently be modeled using linear or nonlinear regression models. In recent research others have developed multivariate T2 control charts and other methods for monitoring the coefficients in a simple linear regression model of a profile. However, little work has been done to address the monitoring of profiles that can be represented by a parametric nonlinear regression model. Here we extend the use of the T2 control chart to monitor the coefficients resulting from a parametric nonlinear regression model fit to profile data. We give three general approaches to the formulation of the T2 statistics and determination of the associated upper control limits for Phase I applications. We also consider the use of non-parametric regression methods and the use of metrics to measure deviations from a baseline profile. These approaches are illustrated using the vertical board density profile data presented in Walker and Wright (Comparing curves using additive models. Journal of Quality Technology 2002; 34:118–129). Copyright © 2007 John Wiley & Sons, Ltd.
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paper_title: Process monitoring and diagnosis by multiblock PLS methods

paper_content:

Schemes for monitoring the operating performance of large continuous processes using multivariate statistical projection methods such as principal component analysis (PCA ) and projection to latent structures (PLS) are extended to situations where the processes can be naturally blocked into subsections. The multiblock projection methods allow one to establish monitoring charts for the individual process subsections as well as for the entire process. When a special event or fault occurs in a subsection of the process, these multiblock methods can generally detect the event earlier and reveal the subsection within which the event has occurred. More detailed diagnostic methods based on interrogating the underlying PCA /PLS models are also developed. These methods show those process variables which are the main contributors to any deviations that have occurred, thereby allowing one to diagnose the cause of the event more easily. These ideas are demonstrated using detailed simulation studies on a multisection tubular reactor for the production of lowdensity polyethylene.
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paper_title: Statistical Process Monitoring with Multivariate Exponentially Weighted Moving Average and Independent Component Analysis

paper_content:

The ever increasing number of variables measured in chemical and biological plants has led to increased emphasis on monitoring performance and fault detection in process system engineering. However, conventional T2 and squared prediction error (SPE) charts based on principal component analysis (PCA) and partial least squares (PLS) are ill-suited to detecting small disturbances resulting from process faults because these monitoring techniques only use information from the most recent samples. In this paper, a new statistical process monitoring algorithm is proposed for detecting process changes resulting from small shifts in process variables. This new algorithm is based on the multivariate exponentially weighted moving average (MEWMA) monitoring concept combined with independent component analysis (ICA) and kernel density estimation. ICA is a recently developed statistical technique for revealing hidden, statistically independent factors that underlie sets of measurements. In this research, three monitoring charts (I2, Ie2 and SPE) obtained using a combination of ICA and MEWMA are developed to better monitor processes undergoing small mean shifts with autocorrelation, where the control limits for these statistics are obtained by kernel density estimation. The proposed monitoring method is applied to fault detection in both a simple multivariate process and the simulation benchmark of the biological wastewater treatment process (WWTP). For a small shift in these processes, the simulation results illustrated the monitoring power of MEWMA-ICA and ICA-MEWMA versus various existing methods (conventional PCA, ICA, MEWMA-PCA and PCA-MEWMA monitoring).
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paper_title: Statistical monitoring and diagnosis of automatic controlled processes using dynamic PCA

paper_content:

As manufacturing quality has become a decisive factor in competing in a global market, statistical quality techniques such as statistical process control (SPC) are becoming very popular in industries. With advances in sensing and data capture technology, large volumes of data are being routinely collected in automatic controlled processes. There is a growing need for SPC monitoring and diagnosis in these environments, but an effective implementing scheme is still lacking. This research provides an integrated approach to simultaneously monitor and diagnose an automatic controlled process by using dynamic principal component analysis (DPCA) and minimax distance classifier. Through a step-by-step implementation procedure, the proposed scheme is expected to have an impact on many manufacturing industries with automatic process control (APC) or engineering process control (EPC).
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paper_title: Choosing principal components for multivariate statistical process control

paper_content:

Principal components are useful for multivariate process control. Typically, the principal component variables are often selected to summarize the variation in the process data. We provide an analysis to select the principal component variables to be included in a multivariate control chart that incorporates the unique aspects of the process control problem (rather than using traditional principal component guidelines).
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paper_title: Model selection for partial least squares regression

paper_content:

Partial least squares (PLS) regression is a powerful and frequently applied technique in multivariate statistical process control when the process variables are highly correlated. Selection of the number of latent variables to build a representative model is an important issue. A metric frequently used by chemometricians for the determination of the number of latent variables is that of Wold's R criterion, whilst more recently a number of statisticians have advocated the use of Akaike Information Criterion (AIC). In this paper, a comparison between Wold's R criterion and AIC for the selection of the number of latent variables to include in a PLS model that will form the basis of a multivariate statistical process control representation is undertaken based on a simulation study. It is shown that neither Wold's R criterion nor AIC exhibit satisfactory performance. This is in contrast to the adjusted Wold's R criteria which is shown to demonstrate satisfactory performance in terms of the number of times the known true model is selected. Two industrial applications are then used to demonstrate the methodology. The first relates to the modelling of a product quality using data from an industrial fluidised bed reactor and the second focuses on an industrial NIR data set. The results are consistent with those of the simulation studies.
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paper_title: Dynamic monitoring method for multiscale fault detection and diagnosis in MSPC

paper_content:

A dynamic monitoring method for multiscale fault detection and diagnosis (MFDD) in the wastewater treatment process (WWTP) is proposed. This method is based on dynamic principal component analysis (DPCA) and the D statistic and the monitoring of individual eigenvalues of generic dissimilarity measure (GDM). DPCA method, where the original measurements are lagged, describes a cause and effect of the process. Then the GDM of the DPCA score value, called the D statistic, is used to detect faults and events of the current operating condition. Additionally, monitoring of individual eigenvalues enables the diagnosis of diverse kinds of fault and disturbance sources. The DPCA and the dynamic GDM of the MFDD can be used as a remedy to the problem of analyzing nonstationary processes. The proposed method was applied to fault monitoring and isolation in simulation benchmark data and real plant data. The simulation results clearly show that the method effectively detects faults in a dynamic, multivariate, and multis...
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paper_title: Statistical process monitoring with principal components

paper_content:

Most industrial processes are characterized by a system of several variables, all of which are subject to drifts, disturbances, and assignable causes of variation. In the chemical and process industries, there are often inertial forces arising from raw material streams, reactors and tanks that introduce serial correlation over time into these variables. This autocorrelation can have a profound impact on the effectiveness of the statistical monitoring methods used for such processes. This paper reviews some of the available methodology for multivariate process monitoring and shows the effectiveness of principal components in this context. An application of the principal components approach with correlated observation vectors is presented. The effectiveness of this procedure to indicate process upsets is discussed.
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paper_title: Multivariate SPC Charts for Monitoring Batch Processes

paper_content:

The problem of using time-varying trajectory data measured on many process variables over the finite duration of a batch process is considered. Multiway principal-component analysis is used to compress the information contained in the data trajectories into low-dimensional spaces that describe the operation of past batches. This approach facilitates the analysis of operational and quality-control problems in past batches and allows for the development of multivariate statistical process control charts for on-line monitoring of the progress of new batches. Control limits for the proposed charts are developed using information from the historical reference distribution of past successful batches. The method is applied to data collected from an industrial batch polymerization reactor.
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paper_title: Wavelet-based Data Reduction Techniques for Process Fault Detection

paper_content:

This article presents new data reduction methods based on the discrete wavelet transform to handle potentially large and complicated nonstationary data curves. The methods minimize objective functions to balance the trade-off between data reduction and modeling accuracy. Theoretic investigations provide the optimality of the methods and the large-sample distribution of a closed-form estimate of the thresholding parameter. An upper bound of errors in signal approximation (or estimation) is derived. Based on evaluation studies with popular testing curves and real-life datasets, the proposed methods demonstrate their competitiveness with the existing engineering data compression and statistical data denoising methods for achieving the data reduction goals. Further experimentation with a tree-based classification procedure for identifying process fault classes illustrates the potential of the data reduction tools. Extension of the engineering scalogram to the reduced-size semiconductor fabrication data leads ...
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paper_title: Multiscale PCA with Application to Multivariate Statistical Process Monitoring

paper_content:

Multiscale principal-component analysis (MSPCA) combines the ability of PCA to decorrelate the variables by extracting a linear relationship with that of wavelet analysis to extract deterministic features and approximately decorrelate autocorrelated measurements. MSPCA computes the PCA of wavelet coefficients at each scale and then combines the results at relevant scales. Due to its multiscale nature, MSPCA is appropriate for the modeling of data containing contributions from events whose behavior changes over time and frequency. Process monitoring by MSPCA involves combining only those scales where significant events are detected, and is equivalent to adaptively filtering the scores and residuals, and adjusting the detection limits for easiest detection of deterministic changes in the measurements. Approximate decorrelation of wavelet coefficients also makes MSPCA effective for monitoring autocorrelated measurements without matrix augmentation or time-series modeling. In addition to improving the ability to detect deterministic changes, monitoring by MSPCA also simultaneously extracts those features that represent abnormal operation. The superior performance of MSPCA for process monitoring is illustrated by several examples.
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paper_title: Phase I Analysis for Monitoring Nonlinear Profiles in Manufacturing Processes

paper_content:

Phase I analysis of nonlinear profiles aims at identifying the data from an in-control process as accurately as possible so that quality engineers can have a good reference to establish the control charts for a future process. Unlike linear profiles, which can be represented by a linear regression model with its model parameters used for monitoring and detection, nonlinear profiles are often sampled into high-dimensional data vectors and analyzed by nonparametric methods. Meanwhile, automatic in-process data-collection devices generate huge historical data sets, which must be analyzed for the presence of observations from out-of-control process conditions. The high dimensionality and data contamination present a challenge to the Phase I analysis of nonlinear profiles. This paper presents a strategy that consists of two major components: a data-reduction component that projects the original data into a lower dimension subspace while preserving the data-clustering structure and a data-separation technique that can detect single and multiple shifts as well as outliers in the data. Simulated data sets as well as nonlinear profile signals from a forging process are used to illustrate the effectiveness of the proposed strategy.
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paper_title: Using Profile Monitoring Techniques for a Data-rich Environment with Huge Sample Size

paper_content:

In-process sensors with huge sample size are becoming popular in the modern manufacturing industry, due to the increasing complexity of processes and products and the availability of advanced sensing technology. Under such a data-rich environment, a sample with huge size usually violates the assumption of homogeneity and degrades the detection performance of a conventional control chart. Instead of charting summary statistics such as the mean and standard deviation of observations that assume homogeneity within a sample, this paper proposes charting schemes based on the quantile‐quantile (Q‐Q) plot and profile monitoring techniques to improve the performance. Different monitoring schemes are studied based on various shift patterns in a huge sample and compared via simulation. Guidelines are provided for applying the proposed schemes to similar industrial applications in a data-rich environment. Copyright c � 2005 John Wiley & Sons, Ltd.
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paper_title: Fault detection for a via etch process using adaptive multivariate methods

paper_content:

Multivariate process control charts like Hotelling T/sup 2/ and squared prediction error are gaining acceptance in the semiconductor industry to monitor the increasing amount of data available by modern process tools. These methods require models built based on the covariance matrix of a trainings data set. Slowly drifting manufacturing processes degrade this estimation for the covariance matrix creating false alarms. To overcome the problem, adaptive modeling schemes are considered. The tradeoff between sensitivity and false alarms for static and adaptive models applied to a via etching process is demonstrated. Possible improvements by incorporating domain knowledge are shown.
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paper_title: The dynamic T 2 chart for monitoring feedback-controlled processes

paper_content:

As manufacturing quality has become a decisive factor in global market competition, statistical quality techniques such as Statistical Process Control (SPC) are widely used in industry. With advances in information, sensing, and data collection technology, large volumes of data are routinely available in processes employing Automatic Process Control (APC) and Engineering Process Control (EPC). Although there is a growing need for SPC monitoring in these feedback-controlled environments, an effective implementation scheme is still lacking. This research provides a monitoring method, termed the dynamic T1 chart that improves the detection of assignable causes in feedback-controlled processes.
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paper_title: Algorithmic Statistical Process Control: An Elaboration

paper_content:

Statistical process control (SPC) has traditionally been applied to processes in which successive observations would ideally be independent and identically distributed as a basis for achieving fundamental process improvement. Stochastic control, on the other hand, addresses situations in which observations are dynamically related over time; its intent is to run the existing process well, as opposed to improving it as such. A schema is presented for uniting traditional SPC and feedforward/feedback control into a system that exploits the strengths of both, Building on past work by MacGregor, Box, Astrom, and others, we discuss the theory and practice of such an approach, along with a consideration of research and technical issues that arise.
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paper_title: Statistical Monitoring of Nonlinear Product and Process Quality Profiles

paper_content:

In many quality control applications, use of a single (or several distinct) quality characteristic(s) is insufficient to characterize the quality of a produced item. In an increasing number of cases, a response curve (profile) is required. Such profiles can frequently be modeled using linear or nonlinear regression models. In recent research others have developed multivariate T2 control charts and other methods for monitoring the coefficients in a simple linear regression model of a profile. However, little work has been done to address the monitoring of profiles that can be represented by a parametric nonlinear regression model. Here we extend the use of the T2 control chart to monitor the coefficients resulting from a parametric nonlinear regression model fit to profile data. We give three general approaches to the formulation of the T2 statistics and determination of the associated upper control limits for Phase I applications. We also consider the use of non-parametric regression methods and the use of metrics to measure deviations from a baseline profile. These approaches are illustrated using the vertical board density profile data presented in Walker and Wright (Comparing curves using additive models. Journal of Quality Technology 2002; 34:118–129). Copyright © 2007 John Wiley & Sons, Ltd.
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paper_title: Time series and system analysis with applications

paper_content:

A comprehensive, applications-oriented treatment of time series analysis. Integrates time series theory with methods of systems analysis. Clearly explains the use of ARMA forecasts and includes a complete treatment of the Box/Jenkins approach to modelling. Provides worked examples.
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paper_title: The Autoregressive T2 Chart for Monitoring Univariate Autocorrelated Processes

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The use of the autoregressive T2 control chart for statistical process control of autocorrelated processes is examined. The T2 statistic can be broken down into the sum of the squares of the residual errors for various order autoregressive time series m..
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paper_title: Some Statistical Process Control Methods for Autocorrelated Data

paper_content:

Traditionally, control charts are developed assuming that the sequence of process observations to which they are applied are uncorrelated. Unfortunately, this assumption is frequently violated in practice. The presence of autocorrelation has a serious i..
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paper_title: On the Monitoring of Linear Profiles

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Control chart methods are proposed for process monitoring when the quality of a process or product is characterized by a liner function. Among the methods recommended for Phase I are the use of a bivariate T(2) chart to check for stability of the reg..
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paper_title: EWMA CONTROL CHARTS FOR MONITORING THE MEAN OF AUTOCORRELATED PROCESSES

paper_content:

A standard assumption when using a control chart to monitor a process is that the observations of output are independent. However, for many processes the observations are autocorrelated. This can have a significant effect on the performance of the con..
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paper_title: A CUSUM Scheme for Autocorrelated Observations

paper_content:

The cumulative sum (CUSUM) chart is known to be effective at detecting sustained shifts in the process mean. Unfortunately, its performance deteriorates when the process observations are autocorrelated. To eliminate the effect of autocorrelation in monitoring changes in the mean, the CUSUM chart is typically applied on the residuals of the chosen time-series model for the process observations. As an alternative, we develop a CUSUM scheme for detecting a step change in the process mean that directly utilizes the autocorrelated process observations. Analysis shows that the performance of the proposed scheme is very competitive when compared with the Shewhart and CUSUM charts based on residuals.
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paper_title: Using Profile Monitoring Techniques for a Data-rich Environment with Huge Sample Size

paper_content:

In-process sensors with huge sample size are becoming popular in the modern manufacturing industry, due to the increasing complexity of processes and products and the availability of advanced sensing technology. Under such a data-rich environment, a sample with huge size usually violates the assumption of homogeneity and degrades the detection performance of a conventional control chart. Instead of charting summary statistics such as the mean and standard deviation of observations that assume homogeneity within a sample, this paper proposes charting schemes based on the quantile‐quantile (Q‐Q) plot and profile monitoring techniques to improve the performance. Different monitoring schemes are studied based on various shift patterns in a huge sample and compared via simulation. Guidelines are provided for applying the proposed schemes to similar industrial applications in a data-rich environment. Copyright c � 2005 John Wiley & Sons, Ltd.
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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: Guidelines for the application of adaptive control charting schemes

paper_content:

A comprehensive performance study and comparison of several adaptive statistical process control procedures is presented. These adaptive control chart procedures are modifications to standard Shewhart control charts that include changing the sampling interval, the sample size or both according to rules based on the value of the sample statistic. Adaptive control techniques are known to improve the performance of the standard Shewhart control charts. In this paper we develop a four-state adaptive sample size control chart and several variations of a three-state combined adaptive sample size and sampling interval control chart. We then compare these new schemes with the previously developed schemes, the two-state adaptive sampling interval, the two-state adaptive sample size and two-state combined adaptive sample size and sampling interval control chart, three-state adaptive sample size control chart and non-adaptive Shewhart control charts. These results show that the addition of the third and fourth state...
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paper_title: A Survey of Recent Developments in the Design of Adaptive Control Charts

paper_content:

This survey presents, in a comprehensive way, the substantial recent developments in the statistical and economic design of adaptive or dynamic charts that allow some of their parameters to change during production. After discussing several different me..
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paper_title: Fault detection for a via etch process using adaptive multivariate methods

paper_content:

Multivariate process control charts like Hotelling T/sup 2/ and squared prediction error are gaining acceptance in the semiconductor industry to monitor the increasing amount of data available by modern process tools. These methods require models built based on the covariance matrix of a trainings data set. Slowly drifting manufacturing processes degrade this estimation for the covariance matrix creating false alarms. To overcome the problem, adaptive modeling schemes are considered. The tradeoff between sensitivity and false alarms for static and adaptive models applied to a via etching process is demonstrated. Possible improvements by incorporating domain knowledge are shown.
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paper_title: The Statistical Design of EWMA Control Charts With Estimated Parameters

paper_content:

[This abstract is based on the author's abstract.] In designing exponentially weighted moving average (EWMA) control charts it is generally assumed that the parameters are known. In most industrial and service applications, however, the parameters are u..
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paper_title: Effects of parameter estimation on control chart properties : A literature review

paper_content:

Control charts are powerful tools used to monitor the quality of processes. In practice, control chart limits are often calculated using parameter estimates from an in-control Phase I reference sample. In Phase II of the monitoring scheme, statistics based on new samples are compared with the estimated control limits to monitor for departures from the in-control state. Many studies that evaluate control chart performance in Phase II rely on the assumption that the in-control parameters are known. Although the additional variability introduced into the monitoring scheme through parameter estimation is known to affect the chart performance, many studies do not consider the effect of estimation on the performance of the chart. This paper contains a review of the literature that explicitly considers the effect of parameter estimation on control chart properties. Some recommendations are made and future research ideas in this area are provided.
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paper_title: Controversies and Contradictions in Statistical Process Control

paper_content:

Statistical process control (SPC) methods are widely used to monitor and improve manufacturing processes and service operations. Disputes over the theory and application of these methods are frequent and often very intense. Some of the controversies and issues discussed are the relationship between hypothesis testing and control charting,the role of theory and the modeling of control chart performance,the relative merits of competing methods,the relevance of research on SPC and even the relevance of SPC itself. One purpose of the paper is to offer a resolution of some of these disagreements in order to improve the communication between practitioners and researchers.
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paper_title: The Run Length Distribution of the CUSUM with Estimated Parameters

paper_content:

The performance of the CUSUM control chart used to monitor the performance of production processes is usually evaluated with the assumption that the process parameters are know. In practice, however, the parameters are seldom known and are often replace..
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paper_title: Using Profile Monitoring Techniques for a Data-rich Environment with Huge Sample Size

paper_content:

In-process sensors with huge sample size are becoming popular in the modern manufacturing industry, due to the increasing complexity of processes and products and the availability of advanced sensing technology. Under such a data-rich environment, a sample with huge size usually violates the assumption of homogeneity and degrades the detection performance of a conventional control chart. Instead of charting summary statistics such as the mean and standard deviation of observations that assume homogeneity within a sample, this paper proposes charting schemes based on the quantile‐quantile (Q‐Q) plot and profile monitoring techniques to improve the performance. Different monitoring schemes are studied based on various shift patterns in a huge sample and compared via simulation. Guidelines are provided for applying the proposed schemes to similar industrial applications in a data-rich environment. Copyright c � 2005 John Wiley & Sons, Ltd.
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paper_title: An adaptive exponentially weighted moving average: control chart

paper_content:

Lucas and Saccucci showed that exponentially weighted moving average (EWMA) control charts can be designed to quickly detect either small or large shifts in the mean of a sequence of independent observations. But a single EWMA chart cannot perform well for small and large shifts simultaneously. Furthermore, in the worst-case situation, this scheme requires a few observations to overcome its initial inertia. The main goal of this article is to suggest an adaptive EWMA (AEWMA) chart that weights the past observations of the monitored process using a suitable function of the current “error.” The resulting scheme can be viewed as a smooth combination of a Shewhart chart and an EWMA chart. A design procedure for the new control schemes is suggested. Comparisons of the standard and worst-case average run length profiles of the new scheme with those of different control charts show that AEWMA schemes offer a more balanced protection against shifts of different sizes.
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paper_title: A Markov Chain Model for the Adaptive CUSUM Control Chart

paper_content:

When the magnitude of a future shift is unknown, a control chart designed to perform over a range of shifts is a better option than optimizing the performance at detecting a certain level of shifts. In this sense, the adaptive cumulative sum (ACUSUM) ch..
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paper_title: Multivariate control charts for monitoring autocorrelated processes

paper_content:

Hotelling's T 2 chart is one of the most popular control charts for monitoring identically and independently distributed random vectors. Recently, Alwan and Alwan (1994) and Apley and Tsung (2002) studied the use of the T 2 chart for detecting mean shifts of a univariate autocorrelated process by transforming the univariate variables into multivariate vectors. This paper examines the global properties of the T 2 test when shift information is unavailable. When shift directions are known a priori, the efficiency of the T 2 test can be improved by a generalized likelihood ratio test (GLRT) taking into consideration the special shift patterns. The proposed control chart has an intrinsic relationship with the residuals-based GLRT procedure studied in Vander Wiel (1996) and Apley and Shi (1999). Retaining the T 2 chart's advantages of a wide range sensitivity for mean shift detection, the proposed control chart is shown to outperform the T 2 chart and the residual-based GLRT procedure when monitoring the mean of a univariate autocorrelated process. Performance enhancement and deterioration in the face of gradual shifts are also discussed.
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paper_title: A review of multivariate control charts

paper_content:

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: Cycle-based signal monitoring using a directionally variant multivariate control chart system

paper_content:

Cycle-based signals are generally obtained through the automatic sensing of critical process variables during each repetitive operation cycle of a manufacturing process, and they thus contain a significant amount of information about the process condition. Increasing attention has been paid recently to the problem of effectively monitoring these signals as an aid to the detection of process changes. In general, either based on process engineering knowledge or on historical data analysis, it is possible to obtain process faults and the corresponding signal patterns (the direction and magnitude of a mean shift). In order to fully utilize such fault pattern information in process monitoring, this paper proposes a directionally variant control chart obtained through the effective combination of a multivariate χ2 chart and a univariate projection chart. It is shown that the addition of the univariate projection chart can improve the detection power for pre-known process faults, however, this may be at the cost of a deterioration in the detection power for unknown faults. A detailed quantitative analysis is provided to justify the application conditions of the proposed chart. A case study of cycle-based tonnage monitoring of a forging process is presented to illustrate the design procedures and the effectiveness of the proposed control chart system.
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paper_title: Regression Adjustment for Variables in Multivariate Quality Control

paper_content:

Multivariate process control problems are inherently more difficult than univariate problems. It is not always clear what type of multivariate statistic should be used, and the most statistically powerful techniques do not indicate the cause(s) of a sig..
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paper_title: An adaptive exponentially weighted moving average: control chart

paper_content:

Lucas and Saccucci showed that exponentially weighted moving average (EWMA) control charts can be designed to quickly detect either small or large shifts in the mean of a sequence of independent observations. But a single EWMA chart cannot perform well for small and large shifts simultaneously. Furthermore, in the worst-case situation, this scheme requires a few observations to overcome its initial inertia. The main goal of this article is to suggest an adaptive EWMA (AEWMA) chart that weights the past observations of the monitored process using a suitable function of the current “error.” The resulting scheme can be viewed as a smooth combination of a Shewhart chart and an EWMA chart. A design procedure for the new control schemes is suggested. Comparisons of the standard and worst-case average run length profiles of the new scheme with those of different control charts show that AEWMA schemes offer a more balanced protection against shifts of different sizes.
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paper_title: The GLRT for statistical process control of autocorrelated processes

paper_content:

This paper presents an on-line Statistical Process Control (SPC) technique, based on a Generalized Likelihood Ratio Test (GLRT), for detecting and estimating mean shifts in autocorrelated processes that follow a normally distributed Autoregressive Integrated Moving Average (ARIMA) model. The GLRT is applied to the uncorrelated residuals of the appropriate time-series model. The performance of the GLRT is compared to two other commonly applied residual-based tests ‐ a Shewhart individuals chart and a CUSUM test. A wide range of ARIMA models are considered, with the conclusion that the best residual-based test to use depends on the particular ARIMA model used to describe the autocorrelation. For many models, the GLRT performance is far superior to either a CUSUM or Shewhart test, while for others the diAerence is negligible or the CUSUM test performs slightly better. Simple, intuitive guidelines are provided for determining which residual-based test to use. Additional advantages of the GLRT are that it directly provides estimates of the magnitude and time of occurrence of the mean shift, and can be used to distinguish diAerent types of faults, e.g., a sustained mean shift versus a temporary spike.
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paper_title: Cycle-based signal monitoring using a directionally variant multivariate control chart system

paper_content:

Cycle-based signals are generally obtained through the automatic sensing of critical process variables during each repetitive operation cycle of a manufacturing process, and they thus contain a significant amount of information about the process condition. Increasing attention has been paid recently to the problem of effectively monitoring these signals as an aid to the detection of process changes. In general, either based on process engineering knowledge or on historical data analysis, it is possible to obtain process faults and the corresponding signal patterns (the direction and magnitude of a mean shift). In order to fully utilize such fault pattern information in process monitoring, this paper proposes a directionally variant control chart obtained through the effective combination of a multivariate χ2 chart and a univariate projection chart. It is shown that the addition of the univariate projection chart can improve the detection power for pre-known process faults, however, this may be at the cost of a deterioration in the detection power for unknown faults. A detailed quantitative analysis is provided to justify the application conditions of the proposed chart. A case study of cycle-based tonnage monitoring of a forging process is presented to illustrate the design procedures and the effectiveness of the proposed control chart system.
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Title: Adaptive Charting Techniques: Literature Review and Extensions

Section 1: Introduction
Description 1: Provide an overview of Statistical Process Control (SPC), its applications, and the evolving challenges it faces. Introduce the concept of adaptive control charts and outline the structure of the paper.

Section 2: The Challenges facing SPC
Description 2: Summarize the main challenges facing SPC, including detecting unknown or mixed-range shifts, dealing with high dimensionalities, and monitoring processes with dynamic means. 

Section 3: Detecting unknown or mixed-range shifts
Description 3: Discuss the criteria for evaluating SPC schemes, the difficulty in detecting shifts of unknown magnitude, and introduce adaptive charts as a promising solution. 

Section 4: Dealing with high dimensionalities
Description 4: Explain the complexity introduced by monitoring multiple correlated variables, techniques for dimension reduction, and recent research on adaptive multivariate charts.

Section 5: Monitoring processes with dynamic means
Description 5: Address situations where the normal process status changes over time and describe adaptive control charts applied in such scenarios.

Section 6: Detecting dynamic shifts
Description 6: Discuss the challenge of capturing time-varying shifts caused by factors like process autocorrelation and feedback control, and review methods for detecting such shifts.

Section 7: Adaptive Control Charts for Process Monitoring
Description 7: Introduce and review various adaptive control charts, categorized into those with adaptive sampling parameters and those with adaptive design parameters.

Section 8: Recursive estimation of in-control mean/variance/covariance parameters
Description 8: Review the use of recursive estimation techniques for parameters critical to SPC performance and their impact on control chart accuracy.

Section 9: Recursive estimation of out-of-control mean shifts
Description 9: Discuss methods for online estimation of mean shifts and introduce adaptive CUSUM and EWMA procedures designed to handle these shifts.

Section 10: Recursive estimation of shift directions of multivariate processes
Description 10: Explore the importance of estimating shift directions in multivariate processes and review adaptive charts that aim to optimize performance based on these estimates.

Section 11: A double-sided directionally variant chart for multivariate processes
Description 11: Propose and validate a new double-sided directionally variant chart designed to improve the detection of both positive and negative shifts in multivariate processes.

Section 12: Conclusions
Description 12: Summarize the key points of the review, highlight the strengths of adaptive control charts in meeting modern SPC challenges, and suggest directions for future research.