Multivariate Statistical Process Control Charts: An Overview

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.quality control, process control, multivariate statistical process control, Hotelling's T-square, CUSUM, EWMA, PCA, PLS

Integrated Projection and Regression Models for Monitoring Multivariate Autocorrelated Cascade Processes

This dissertation presents a comprehensive methodology of dual monitoring for the multivariate autocorrelated cascade processes using principal component analysis and regression. Principle Components Analysis is used to alleviate the multicollinearity among input process variables and reduce the dimension of the variables. An integrated principal components selection rule is proposed to reduce the number of input variables. An autoregressive time series model is used and imposed on the time correlated output variable which depends on many multicorrelated process input variables. A generalized least squares principal component regression is used to describe the relationship between product and process variables under the autoregressive regression error model. The combined residual based EWMA control chart, applied to the product characteristics, and the MEWMA control charts applied to the multivariate autocorrelated cascade process characteristics, are proposed. The dual EWMA and MEWMA control chart has advantage and capability over the conventional residual type control chart applied to the residuals of the principal component regression by monitoring both product and the process characteristics simultaneously. The EWMA control chart is used to increase the detection performance, especially in the case of small mean shifts. The MEWMA is applied to the selected set of variables from the first principal component with the aim of increasing the sensitivity in detecting process failures. The dual implementation control chart for product and process characteristics enhances both the detection and the prediction performance of the monitoring system of the multivariate autocorrelated cascade processes. The proposed methodology is demonstrated through an example of the sugar-beet pulp drying process. A general guideline for controlling multivariate autocorrelated processes is also developed

Online network monitoring

An important problem in network analysis is the online detection of anomalous behaviour. In this paper, we introduce a network surveillance method bringing together network modelling and statistical process control. Our approach is to apply multivariate control charts based on exponential smoothing and cumulative sums in order to monitor networks generated by temporal exponential random graph models (TERGM). The latter allows us to account for temporal dependence while simultaneously reducing the number of parameters to be monitored. The performance of the considered charts is evaluated by calculating the average run length and the conditional expected delay for both simulated and real data. To justify the decision of using the TERGM to describe network data, some measures of goodness of fit are inspected. We demonstrate the effectiveness of the proposed approach by an empirical application, monitoring daily flights in the United States to detect anomalous patterns. © 2021, The Author(s)

Multivariate Statistical Process Control Charts: An Overview

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

Multivariate control charts based on Bayesian state space models

This paper develops a new multivariate control charting method for vector autocorrelated and serially correlated processes. The main idea is to propose a Bayesian multivariate local level model, which is a generalization of the Shewhart-Deming model for autocorrelated processes, in order to provide the predictive error distribution of the process and then to apply a univariate modified EWMA control chart to the logarithm of the Bayes' factors of the predictive error density versus the target error density. The resulting chart is proposed as capable to deal with both the non-normality and the autocorrelation structure of the log Bayes' factors. The new control charting scheme is general in application and it has the advantage to control simultaneously not only the process mean vector and the dispersion covariance matrix, but also the entire target distribution of the process. Two examples of London metal exchange data and of production time series data illustrate the capabilities of the new control chart.Comment: 19 pages, 6 figure

Menghilangkan Autokorelasi Pada Diagram Kontrol Shewhart Menggunakan Diagram Kontrol Residual Berdasarkan Model Extention Support Vector Regression

Kualitas merupakan faktor kunci yang mengarahkan kepada keberhasilan, pertumbuhan, dan daya saing bisnis. Kualitas juga merupakan salah satu faktor penting dalam pengambilan keputusan konsumen dalam pemilihan produk dan layanan. Guna meningkatkan kualitas produk dapat memanfaatkan beberapa cara, salah satunya adalah menerapkan statistical process control (SPC). Salah satu tool SPC yang paling banyak diterapkan adalah diagram kontrol yang berguna untuk mengetahui variansi dari proses. Diagram kontrol didasarkan pada asumsi bahwa data mengikuti distribusi normal dan tidak terdapat hubungan antara pengamatan yang berurutan (autokorelasi). Namun dalam proses industri kontinyu kebanyakan data bersifat autokorelasi. Agar bisa menggunakan diagram kontrol secara efektif, autokorelasi dalam data harus dihilangkan. Langkah yang dapat dilakukan untuk pengendalian kualitas pada data autokorelasi adalah dengan memetakan residual hasil pemodelan menggunakan metode time series pada diagram kontrol. Pada penelitian ini dikembangkan diagram kontrol residual berdasarkan model extention Support vector regression yaitu Least square support vector regression dan Genetic algorithm support vector regression untuk mengatasi kasus autokorelasi pada proses. Kriteria kebaikan model dalam penelitian ini menggunakan nilai Root Mean Square Error (RMSE). Semakin kecil nilai RMSE maka model yang digunakan semakin baik. Setelah dilakukan perhitungan menggunakan metode regresi, Support vector regression dan metode Extention support vector regression, metode yang paling baik adalah Genetic algorithm support vector regression berdasarkan nilai RMSE sebesar 1,554310 dan 0,5565. ========================================================================================================= Quality is a key factor that leads to business success, growth, and competitiveness. Quality is also an important factor in consumer decision making in the selection of products and services. In order to improve product quality can utilize several ways, one of them is apply statistical process control (SPC). One of the most widely applied SPC tools is the control chart which is useful for knowing the variance of the process. The control chart is based on the assumption that data follows a normal distribution and there is no relationship between successive observations (autocorrelation). But in the process of continuous industry most data are autocorrelation. In order to use the control chart effectively, autocorrelation in the data must be eliminated. Steps that can be done to control the quality of the autocorrelation data is to map the residual results of modeling using time series method in the control chart. In this research, the residual control charts are developed based on the extension support vector regression model that is Least square support vector regression and Genetic algorithm support vector regression to overcome the case of autocorrelation in the process. Criteria of model goodness in this research use Root Mean Square Error (RMSE). The smaller the value of RMSE then the model used the better. After calculation using regression method, Support vector regression and Extension support vector regression method, the best method is Genetic algorithm support vector regression based on RMSE value of 1.554310 and 0.5565

Distribution-free statistical process control and Bayesian feasibility determination

This thesis consists of three main parts. The first two parts focus on multivariate time-series monitoring that commonly arises in the quality control problems, and the third part considers the feasibility determination via simulation which has a broad range of applications including manufacturing process control. In Chapter 2, we consider the problem of detecting a shift in the mean of a multivariate time-series process with a general marginal distribution and a general cross- and auto-correlation structure. We propose a distribution-free monitoring procedure that does not need model fitting nor trial-and-error calibration. Control limit of the procedure can be determined analytically, which allows efficient implementation and easy generalization. The main idea is to convert each observation vector into a one-dimensional $T^2$ quantity that captures cross-correlation. The $T^2$ quantities form a univariate auto-correlated process, and CUSUM statistics are constructed on the $T^2$ quantities. Then using the fact that the CUSUM statistics on the auto-correlated process behave as a reflected Brownian motion asymptotically under some conditions, the control limits of the CUSUM procedure are analytically determined by setting the first-passage time of the Brownian motion equal to a target in-control average run length. We compare the performance of our procedure with three baseline procedures on simulated data with various cross- and auto-correlation and real data from a wafer etching process. The proposed procedure delivers actual in-control average run length close to the target and shows comparable or better performance in detecting a shift in mean compared to baseline procedures. In Chapter 3, we consider an image monitoring problem for a manufacturing process where a series of 2-dimensional images are converted into a series of random matrices and the mean of these random matrices is expected to be a matrix with rank one. Existing image-based monitoring procedures usually assume each component in a monitored image process has normally distributed observations, and the observations are independent or following a specific correlation structure. However, a real-world case such as a battery coating process often violates these assumptions. We propose a distribution-free image monitoring procedure to detect a shift in the mean matrix of monitored images. Two monitoring statistics are calculated based on the singular value decomposition technique, and the two statistics are composited into a two-variate vector. Then the two-variate vectors are monitored by the procedure introduced in Chapter 2. The effectiveness of the proposed procedure, measured by average run lengths, is demonstrated using various simulated data and a real-data example from a battery coating process. In Chapter 4, we consider the problem of finding a set of feasible inputs in the presence of constraints on multiple performance measures when the constraints are stochastic in that the performance measures can only be evaluated via noisy observations. When similar inputs are more likely to have similar performance measures and when each observation is expensive, a Gaussian process (GP) can be employed to model the performance measures. One previous work utilizes a GP for feasibility determination with a single stochastic constraint. We extend this previous work to multiple constraints. The decision on which input to test next to obtain a new observation is based on a value-of-information function but the calculation of the function can take long, hindering the efficient implementation of the Bayesian feasibility check procedure. To accelerate the computation of the proposed Bayesian procedure, we propose another version with an approximation for the value-of-information function that is quick and easy to calculate. We prove the convergence of our proposed procedures and demonstrate the effectiveness of the procedures incorporating both independent and multi-task GPs.Ph.D

Kernel methods for advanced statistical process control

This thesis investigated development and application of Kernel methods to enhance Statistical Process Control procedures. The first part of this thesis discussed the development of a control chart based on adaptive Kernel Principal Components Analysis (KPCA) to monitor non-stationary nonlinear process behaviour. Moreover, in order to have a fast adaptive KPCA model, we proposed an updating method that provides a reduced computation cost for large-scale KPCA model and a good tracking of the original matrix with a small reconstruction error. Analysis and comparison with other Principal Components Analysis control charts showed that the proposed procedure provides overall competitive detection results. The second part of this thesis investigated monitoring of nonlinear autocorrelated processes based on Support Vector Regression (SVR). The advantage of this procedure is that it allows modelling and control of nonlinear processes without the need to find analytical solutions to describe phenomena of interest. Results showed that the used control charts can effectively monitor the process behaviour while guarantying an acceptable robustness. The third part of this dissertation dealt with development of local Support Vector Domain Description (SVDD) based control chart to monitor complex and multimodal processes without specifying a probability distribution. This procedure allows simplifying and reducing the complexity of the problem which can help selecting SVDD parameters. Analysis of the proposed control chart using simulated and real case studies showed that this procedure allows better detection results while guaranteeing a reduced false alarm rate

Information and Control ICIC International c ⃝2011 ISSN

Abstract. The statistical process control (SPC) chart is effective in detecting proces