Browsing by Subject "Analysis of covariance"
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Item Data-driven approach for control performance monitoring and fault diagnosis(2007) Yu, Jie; Qin, S. JoeDue to the industrial value, control performance and process monitoring have attracted increasing attention in recent years. However, there still exist challenges that restrict the industrial applications of monitoring technology. This dissertation presents some innovative solutions to the monitoring issues. To avoid the interactor requirement of minimum variance control (MVC) benchmark, a data-driven covariance monitoring framework is established. Relative to a user-defined benchmark, generalized eigenvalue analysis is employed to extract the directions with the worst performance. A statistical inference strategy is then developed to identify the worse or better performance directions and subspace. The covariance based indices are further derived to assess the performance degradation or improvement. To diagnose the controlled variables causing the performance change, two types of multivariate contribution methods are proposed. One is to evaluate the significance of the eigenvector loadings while the other to examine the angle between each variable and the worse/better subspace. Complementary to the data-driven performance monitoring scheme, a simplified solution to MVC benchmark is also developed. A right diagonal interactor is first factorized from process time delays and the corresponding MVC benchmark is derived with numerical simplicity. For more general MIMO processes, left and right diagonal interactors are integrated to characterize the more complex delay structure. The MVC estimation using the left/right diagonal interactors are presented. To further improve multivariable control performance, an iterative strategy of output weighting selection is proposed. Eigenvalue decomposition is implemented on the output covariance to find the directions with the largest variance inflation. A nondiagonal weighting matrix is then designed with respect to the eigendirections and more importance proportional to the corresponding eigenvalues is assigned. In addition to control performance monitoring, process monitoring is also investigated with focus on fault detection and diagnosis of multistage overlay lithography processes. In our work, a multistage state-space model for the misalignment errors is developed from the physical principles and then formulated into the general mixed linear model. Subsequently, variance component analysis is employed to estimate the mean and variance components of the potential fault sources. A hypothesis testing procedure is adopted to detect the active faults in different layers while the mean/variance estimates are used to diagnose their magnitude and orientation.Item Data-driven approach for control performance monitoring and fault diagnosis(2007-05) Yu, Jie, 1977-; Qin, S. JoeDue to the industrial value, control performance and process monitoring have attracted increasing attention in recent years. However, there still exist challenges that restrict the industrial applications of monitoring technology. This dissertation presents some innovative solutions to the monitoring issues. To avoid the interactor requirement of minimum variance control (MVC) benchmark, a data-driven covariance monitoring framework is established. Relative to a user-defined benchmark, generalized eigenvalue analysis is employed to extract the directions with the worst performance. A statistical inference strategy is then developed to identify the worse or better performance directions and subspace. The covariance based indices are further derived to assess the performance degradation or improvement. To diagnose the controlled variables causing the performance change, two types of multivariate contribution methods are proposed. One is to evaluate the significance of the eigenvector loadings while the other to examine the angle between each variable and the worse/better subspace. Complementary to the data-driven performance monitoring scheme, a simplified solution to MVC benchmark is also developed. A right diagonal interactor is first factorized from process time delays and the corresponding MVC benchmark is derived with numerical simplicity. For more general MIMO processes, left and right diagonal interactors are integrated to characterize the more complex delay structure. The MVC estimation using the left/right diagonal interactors are presented. To further improve multivariable control performance, an iterative strategy of output weighting selection is proposed. Eigenvalue decomposition is implemented on the output covariance to find the directions with the largest variance inflation. A nondiagonal weighting matrix is then designed with respect to the eigendirections and more importance proportional to the corresponding eigenvalues is assigned. In addition to control performance monitoring, process monitoring is also investigated with focus on fault detection and diagnosis of multistage overlay lithography processes. In our work, a multistage state-space model for the misalignment errors is developed from the physical principles and then formulated into the general mixed linear model. Subsequently, variance component analysis is employed to estimate the mean and variance components of the potential fault sources. A hypothesis testing procedure is adopted to detect the active faults in different layers while the mean/variance estimates are used to diagnose their magnitude and orientation.Item Discriminant analysis with proportional covariance structure(Texas Tech University, 1982-05) Li, Eldon Yu-zen,Not availableItem Nonparametric analysis of covariance in block designs(Texas Tech University, 1993-05) Chang, Guang-hwaAnalysis of Covariance (ANOCOVA) has been considered as a more effective approach in data analysis than an ordinary Analysis of Variance (ANOVA) for two reasons: (1) increasing the power and precision of the tests through the reduction in error variance, and (2) providing a means of statistically adjusting for pre-existing differences between treatment groups. The parametric analysis of covariance theory was developed with the assumption of normality. If this assumption underlying the parametric model is uncertain, then the applicability of the parametric test is doubtful. Nonparametric ANOCOVA is a robust competitor of the parametric method with less restrictive distributional assumptions. In the past two decades, several nonparametric ANOCOVA tests for one-way layouts have been suggested and shown to be robust and powerful through simulation studies. A number of nonparametric ANOCOVA procedures for higher way layouts have also been studied and the limiting results are usually based on increasing cell sizes. The model that is considered in this research is the ANOCOVA model for Randomized Block Designs (RBD) with one observation per cell, as Yij=ƒÊ+ƒÀi+„„j+0(Xij-X..)+cij, i=1,c,n;j=1,c,c, where cij's are either iid or exchangeable and have continuous cdf's. Some nonparametric aligned rank test procedures are proposed in this paper for detecting the treatment effects for the above model. The first test proposed in this paper for ANOCOVA in RBD is based on the ranks of the block-mean-aligned observations. The overall ranking is used and the proposed test statistic has asymptotically a x^ distribution. Based on the same principle in developing the above test, a test for ANOCOVA in Incomplete Block Designs is also proposed. The second test proposed in this paper for ANOCOVA in RBD also uses overall ranking on the aligned observations. A test procedure using within-block rankings on the covariate-aligned observations is also proposed. The Rank Transformation test of Conover and Iman (1981) is briefly discussed in this paper. Through a Monte Carlo simulation study, the aligned rank test based on within block rankings and the Rank Transformation test are shown to be very robust and powerful and are strongly recommended for the model we discussed. It is found that the parametric test does not present good results in most of the non-normal cases and its use is discouraged when the underlying distribution is unknown.Item Parametric inference with density-free variance in censored regression models(Texas Tech University, 2000-05) Hummer, Amanda J.Survival analysis describes the analysis of data that corresponds to the time from a well-defined time origin until the occurrence of the some particular event, the endpoint. In medical research the time origin may be the time at which the patient is recruited and the end-point may be death or recurrence of symptoms. Often patients are lost to follow-up for some reason. For example, the individual may be relocated after being recruited in a clinical trial, or may have died due to reasons unrelated to the study. For these reasons, survival times are frequently censored. Censoring occurs when the end-point of interest has not been observed for an individual participating in the trial. There are several types of censoring; right censoring, left censoring, interval censoring, etc. Right censoring, the most common type, takes place when the actual survival time is greater than the censored survival time [1]. This happens when the patient died of causes other than those under study, or when the patient withdraws from the study.Item Random perturbation of a self-adjoint operator with a multiple eigenvalue(2012-05) Gaines, George; Ruymgaart, Frits; Gilliam, David S.; Trindade, A. AlexandreWe first consider a bounded self-adjoint operator on a Hilbert space with a multiple eigenvalue as its largest eigenvalue. We perturb the operator and study the resulting cluster of eigenvalues of the perturbed operator. We study the convergence of the scattered eigenvalues to the original. We then do computer simulations. We also show an approximation for Brownian motion.