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Design and Develop of a new Multivariate Control Chart for Image based Process Control based on Principal Component Analysis for Multivariate non Normal Distribution

Farrokhnia Hamedani, Moez | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 49310 (01)
  4. University: Sharif University of Technology
  5. Department: Industrial Engineering
  6. Advisor(s): Akhavan Niaki, Taghi
  7. Abstract:
  8. Control charts have always had an undeniable role in Statistical Control of processes in many fields. The growth of quality characteristics to be monitored, has led to the vast utilization of multivariate control charts. These variables are characterized by relatively high correlation between them. The complicated structure of measured variables has lessened the reliability of conventional control charts. Projection methods have been developed to address the problem of high correlated variables by transforming the correlated variables to an uncorrelated set of variables. Among them, Principal Component Analysis based control charts have been widely used to overcome the problem of correlated variables by defining a proper transformation of variables on to a new uncorrelated dataset and finding PCs with highest contribution in addition, PCA can be used to reduce dimensionality of problems. An underlying assumption of normal distribution for observed data has limited the performance of conventional methods to construct control limits of PCA based control charts for non-normal data. However, normality assumption is widely violated in practice. As a result, it is required to develop new methods which are distribution free and no distributional assumptions restrict them. Our proposed method is to use Support Vector Machines as a substitute of conventional methods to construct control limits of PCA based control charts. Since SVM performs based on observed data, no distributional assumption is required for construction of control limits. Many simulations have been conducted using normal and non-normal datasets to compare the performance of proposed method with conventional methods and some non-parametric methods developed by other researchers. Average Run Length and Standard Deviation of Estimation that have been used as indicators of performance show the relatively excellence of proposed method compared to other methods
  9. Keywords:
  10. Support Vector Machine (SVM) ; Principal Component Analysis (PCA) ; Multivariate Control Charts ; Bootstrapping ; Non-Normal Distribution ; Nonnormal Process Control

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