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Title Multivariate Statistical Process Control Applications for Autocorrelated Data
Author Stefaniak, Irena
Supervisor Kulahci, Murat (Mathematical Statistics, Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
Institution Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
Thesis level Master's thesis
Year 2009
Abstract This thesis deals with applications of auto-correlated data in principal component analysis and statistical process control. The main purpose of the thesis is to search for and explore effects and patterns of not only correlation but also auto-correlation in PCA and SPC. Since nowadays we work with a different kind of data sets auto-correlation has grown to be more and more applied form of relation in time series analysis. The series used here is autoregressive model AR(1). It is a particular model of autoregressive integrated moving average (ARIMA) models. The data, which has been simulated from standard normal distribution, are a mix of correlated or not correlated variables. Some of which are also auto-correlated. The effects of auto-correlation are seen in the eigenvalues and the eigenvectors and visualized on the plots. Standardization method is used to provide data in the same scale. Thereafter, the data are used in PCA. However, non-standardization is briefly compared with standardization to show why the second way is mostly used in the analysis. Some examples of auto-correlated variables are given and presented in the figures to see the differences in variability of these variables. Afterwards, the principal components are taken to the statistical control. Shewhart control chart is used to control the scores. The crucial point is to find Average Run Length for each principal component assuming the process to be in statistical control. Three different approaches have been considered in this case. Mainly, three covariance estimators have been calculated for constructing the control limits to Shewhart control chart. Based on these estimators eigenvalues are extracted and used as standard deviations in the control limits. The way of estimating and analyzing is presented in the theoretical and practical parts. The results of the approaches is to find which covariance estimate is appropriate when working with auto-correlated data. The analysis done in the thesis is divided into two practical parts. Each of them consists of cases and scenarios of the auto-correlation and correlation of the variables. The point is to present, step by step, the influence of different kinds of correlation in the data and show how it effects PCA and SPC. In the thesis I distinguish between correlation and cross-correlation. Correlation of the variables means that the variables are correlated with each other but not correlated in time. The second term means that the variables are correlated with each other AND correlated in time, meaning they are auto-correlated and correlated.
Imprint Technical University of Denmark (DTU) : Kgs. Lyngby, Denmark
Series IMM-M.Sc.-2009-73
Fulltext
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Admin Creation date: 2009-12-15    Update date: 2010-08-25    Source: dtu    ID: 253804    Original MXD