Le modèle de Rasch est utilisé de nos jours dans de nombreuses applications en sciences sociales et en médecine. Parmi les applications de ce modèle, on trouve l’étude de la qualité psychométrique des items d’un test, le calibrage des items pour les tests adaptatifs, la production des mesures d’habileté en sciences de l’éducation. Il est particulièrement mis à profit dans des enquêtes internationales à grande échelle comme l’enquête PISA (Programme for International Student Assessment). L’une des hypothèses que doivent vérifier l’ensemble des items du test devant mesurer un trait donné est celle de l’unidimensionnalité, c’est-à dire que tous mis ensemble ne doivent mesurer que le trait en étude, et la réponse que donne un individu à chacun de ces items n’est fonction que du niveau de ce trait chez cet individu. Il se pose donc l’épineuse question de la détermination de la dimensionnalité de l’outil de mesure, car l’objectif étant de ne conserver ensemble que des items concourant à mesurer un seul et même trait. En pratique, les tests auxquels sont soumis les individus ne sont pas strictement unidimensionnels car nos réponses sont aussi conditionnées par nos habitudes et notre milieu. Le plus important selon Stout (1987) est d’avoir un test ayant une dimension dominante, car sinon on devra utiliser des modèles multidimensionnels qui s’avèrent souvent complexes et difficiles à interpréter pour un preneur de décision non expert en mesure. Notre travail a consisté à explorer un ensemble de conditions dans lesquelles le modèle de Rasch unidimensionnel peut produire des mesures acceptables malgré la présence de plusieurs traits déterminants dans les données. Nous avons travaillé avec des données bidimensionnelles simulées, et avons mis à profit le modèle linéaire multiple et les statistiques d’ajustement infit t du modèle de Rasch unidimensionnel. / Today, the Rasch model is most used in many applications of the social sciences and in medicine. Among the applications of this model, one can cite the study of the psychometric qualities of test items, items calibration in adaptive testing and the production of skill measures in education science. It is particularly used in international large-scale surveys such as PISA (Programme for International Student Assessment) survey. One of the assumptions test items selected to measure a given trait must satisfied is the unidimensionality assumption, that is all items put together should measure the trait under study, and the response given by an individual to each of these items is a function only of the level of the trait that the individual possesses. This raises the issue of determining the dimensionality of a measurement tool, because the goal is to keep only items that contribute to measure the single trait. In practice, not all test instruments developed to collect data from individuals are strictly unidimensional because our responses are also influenced by our habits and our environment. According to Stout (1987) the most important thing is to have a test with a dominant dimension, otherwise we will use multivariate models that are often complex and difficult to interpret for a decision maker who is not an expert in measurement theory. Our work has been to explore a set of conditions under which the Rasch model can produce acceptable measures despite the presence of several dimensions in the data. We worked with two-dimensional simulated data and have used the multiple linear regression model and infit statistics t produced by the unidimensional Rasch model. / Le logiciel de simulation des données et d'analyse est Conquest V.3

In this thesis, we study two problems in combinatorial optimization, the dominating set problem and the robustness problem. In the first half of the thesis, we focus on the dominating set problem in grid graphs and present a distributed algorithm for finding near optimal dominating sets on grids. The dominating set problem is a well-studied mathematical problem in which the goal is to find a minimum size subset of vertices of a graph such that all vertices that are not in that set have a neighbor inside that set. We first provide a simpler proof for an existing centralized algorithm that constructs dominating sets on grids so that the size of the provided dominating set is upper-bounded by the ceiling of (m+2)(n+2)/5 for m by n grids and its difference from the optimal domination number of the grid is upper-bounded by five. We then design a distributed grid domination algorithm to locate mobile agents on a grid such that they constitute a dominating set for it. The basis for this algorithm is the centralized grid domination algorithm. We also generalize the centralized and distributed algorithms for the k-distance dominating set problem, where all grid vertices are within distance k of the vertices in the dominating set. In the second half of the thesis, we study the computational complexity of checking a graph property known as robustness. This property plays a key role in diffusion of information in networks. A graph G=(V,E) is r-robust if for all pairs of nonempty and disjoint subsets of its vertices A,B, at least one of the subsets has a vertex that has at least r neighbors outside its containing set. In the robustness problem, the goal is to find the largest value of r such that a graph G is r-robust. We show that this problem is coNP-complete. En route to showing this, we define some new problems, including the decision version of the robustness problem and its relaxed version in which B=V \ A. We show these two problems are coNP-hard by showing that their complement problems are NP-hard.

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Even a modest positive autocorrelation results in a considerable increase in the number of false alarms that are produced when applying a CUSUM chart. Knowledge of the process to be controlled allows for suitable adaptation of the CUSUM procedure. If one has to suspect the normality assumption, nonparametric control procedures such as the rank-based CUSUM chart are a practical alternative. The paper reports the results of a simulation study on the robustness (in terms of sensitivity of the ARL) of the rank-based CUSUM chart against serial correlation of the control variable. The results indicate that the rank-based CUSUM chart is less affected by correlation than the observation-based chart: The rank-based CUSUM chart shows a smaller increase in the number of false alarms and a higher decrease in the ARL in the out-of-control case than the the observation-based chart. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

This thesis which consists of four papers is concerned with estimation methods in factor analysis and structural equation models. New estimation methods are proposed and investigated. In paper I an approximation of the penalized maximum likelihood (ML) is introduced to fit an exploratory factor analysis model. Approximated penalized ML continuously and efficiently shrinks the factor loadings towards zero. It naturally factorizes a covariance matrix or a correlation matrix. It is also applicable to an orthogonal or an oblique structure. Paper II, a simulation study, investigates the properties of approximated penalized ML with an orthogonal factor model. Different combinations of penalty terms and tuning parameter selection methods are examined. Differences in factorizing a covariance matrix and factorizing a correlation matrix are also explored. It is shown that the approximated penalized ML frequently improves the traditional estimation-rotation procedure. In Paper III we focus on pseudo ML for multi-group data. Data from different groups are pooled and normal theory is used to fit the model. It is shown that pseudo ML produces consistent estimators of factor loadings and that it is numerically easier than multi-group ML. In addition, normal theory is not applicable to estimate standard errors. A sandwich-type estimator of standard errors is derived. Paper IV examines properties of the recently proposed polychoric instrumental variable (PIV) estimators for ordinal data through a simulation study. PIV is compared with conventional estimation methods (unweighted least squares and diagonally weighted least squares). PIV produces accurate estimates of factor loadings and factor covariances in the correctly specified confirmatory factor analysis model and accurate estimates of loadings and coefficient matrices in the correctly specified structure equation model. If the model is misspecified, robustness of PIV depends on model complexity, underlying distribution, and instrumental variables.

Due to their frictionless operation active magnetic bearings (AMBs) are essential components in high-speed rotating machinery. Active magnetic control of a high speed rotating rotor requires precise knowledge of its position. Self-sensing endeavours to eliminate the required position sensors by deducing the rotor’s position from the voltages and currents with which it is levitated. For self-sensing AMBs to be of practical worth, they have to be robust. Robustness analysis aims to quantify a control system’s tolerance for uncertainty. In this study the stability margin of a two degree-of-freedom self-sensing AMB is estimated by means of μ-analysis. Detailed black-box models are developed for the main subsystems in the AMB by means of discrete-time system identification. Suitable excitation signals are generated for system identification in cognisance of frequency induced nonlinear behaviour of the AMB. Novel graphs that characterize an AMB’s behaviour for input signals of different amplitudes and frequency content are quite useful in this regard. In order to obtain models for dynamic uncertainty in the various subsystems (namely the power amplifier, self-sensing module and AMB plant), the identified models are combined to form a closed-loop model for the self-sensing AMB. The response of this closed-loop model is compared to the original AMB’s response and models for the dynamic uncertainty are empirically deduced. Finally, the system’s stability margin for the modelled uncertainty is estimated by means of μ-analysis. The potentially destabilizing effects of parametric uncertainty in the controller coefficients as well as dynamic uncertainty in the AMB plant and self-sensing module are examined. The resultant μ-analyses show that selfsensing AMBs are much less robust for parametric uncertainty in the controller than AMBs equipped with sensors. The μ-analyses for dynamic uncertainty confirm that self-sensing AMBs are rather sensitive for variations in the plant or the self-sensing algorithm. Validation of the stability margins estimated by μ-analysis reveal that μ-analysis is overoptimistic for parametric uncertainty on the controller and conservative for dynamic uncertainty. (Validation is performed by means of Monte Carlo simulations.) The accuracy of μ-analysis is critically dependent on the accuracy of the uncertainty model and the degree to which the system is linear or not. If either of these conditions are violated, μ-analysis is essentially worthless. / Thesis (Ph.D. (Electronical Engineering))--North-West University, Potchefstroom Campus, 2010

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Due to their frictionless operation active magnetic bearings (AMBs) are essential components in high-speed rotating machinery. Active magnetic control of a high speed rotating rotor requires precise knowledge of its position. Self-sensing endeavours to eliminate the required position sensors by deducing the rotor’s position from the voltages and currents with which it is levitated. For self-sensing AMBs to be of practical worth, they have to be robust. Robustness analysis aims to quantify a control system’s tolerance for uncertainty. In this study the stability margin of a two degree-of-freedom self-sensing AMB is estimated by means of μ-analysis. Detailed black-box models are developed for the main subsystems in the AMB by means of discrete-time system identification. Suitable excitation signals are generated for system identification in cognisance of frequency induced nonlinear behaviour of the AMB. Novel graphs that characterize an AMB’s behaviour for input signals of different amplitudes and frequency content are quite useful in this regard. In order to obtain models for dynamic uncertainty in the various subsystems (namely the power amplifier, self-sensing module and AMB plant), the identified models are combined to form a closed-loop model for the self-sensing AMB. The response of this closed-loop model is compared to the original AMB’s response and models for the dynamic uncertainty are empirically deduced. Finally, the system’s stability margin for the modelled uncertainty is estimated by means of μ-analysis. The potentially destabilizing effects of parametric uncertainty in the controller coefficients as well as dynamic uncertainty in the AMB plant and self-sensing module are examined. The resultant μ-analyses show that selfsensing AMBs are much less robust for parametric uncertainty in the controller than AMBs equipped with sensors. The μ-analyses for dynamic uncertainty confirm that self-sensing AMBs are rather sensitive for variations in the plant or the self-sensing algorithm. Validation of the stability margins estimated by μ-analysis reveal that μ-analysis is overoptimistic for parametric uncertainty on the controller and conservative for dynamic uncertainty. (Validation is performed by means of Monte Carlo simulations.) The accuracy of μ-analysis is critically dependent on the accuracy of the uncertainty model and the degree to which the system is linear or not. If either of these conditions are violated, μ-analysis is essentially worthless. / Thesis (Ph.D. (Electronical Engineering))--North-West University, Potchefstroom Campus, 2010

For the reliability design of Engine Control Unit devices in motor vehicles, the knowledge of stresses occurring in the field within the product service life is essential. In addition to the environmental influences such as temperature, moisture and humidity, vibration and shock issues are in focus. To ensure the robustness of the products and they are still easily and inexpensively made, they must be interpreted appropriately in the development process. For this, the load spectra for the mechanical influences of road conditions and operating conditions are to be determined. Work will also include temperature and humidity values examined on typical installation locations. The essential everyday situations (commuters, taxi, farmer, ...) should be considered. Existing measurement technology must be combined to this end a comprehensive logger system with communication to the vehicle.

The purpose of this thesis is to demonstrate that two-girder or two-web structural systems can be employed to design efficient bridges with an adequate level of redundancy. The issue of redundancy in two-girder bridges is a constraint for the bridge designers in North America who want to take advantage of efficiency in this type of structural system. Therefore, behavior of two-girder or two-web structural systems after failure of one main load-carrying component is evaluated to validate their safety. A procedure is developed to perform system-level reliability analysis of bridges. This procedure is applied to two bridge concepts, a twin steel girder with composite deck slab and a concrete double-T girder with unbonded external tendons. The results show that twin steel girder bridges can be designed to fulfill the requirements of a redundant structure and the double-T girder with external unbonded tendons can be employed to develop a robust structural system.