This thesis consists of two parts. The first part reviews a Variable Search, a variable selection procedure for mean modeling. The second part deals with variance modeling for robust parameter design in computer experiments. In the first chapter of my thesis, Variable Search (VS) technique developed by Shainin (1988) is reviewed. VS has received quite a bit of attention from experimenters in industry. It uses the experimenters' knowledge about the process, in terms of good and bad settings and their importance. In this technique, a few experiments are conducted first at the best and worst settings of the variables to ascertain that they are indeed different from each other. Experiments are then conducted sequentially in two stages, namely swapping and capping, to determine the significance of variables, one at a time. Finally after all the significant variables have been identified, the model is fit and the best settings are determined. The VS technique has not been analyzed thoroughly. In this report, we analyze each stage of the method mathematically. Each stage is formulated as a hypothesis test, and its performance expressed in terms of the model parameters. The performance of the VS technique is expressed as a function of the performances in each stage. Based on this, it is possible to compare its performance with the traditional techniques. The second and third chapters of my thesis deal with variance modeling for robust parameter design in computer experiments. Computer experiments based on engineering models might be used to explore process behavior if physical experiments (e.g. fabrication of nanoparticles) are costly or time consuming. Robust parameter design (RPD) is a key technique to improve process repeatability. Absence of replicates in computer experiments (e.g. Space Filling Design (SFD)) is a challenge in locating RPD solution. Recently, there have been studies (e.g. Bates et al. (2005), Chen et al. (2006), Dellino et al. (2010 and 2011), Giovagnoli and Romano (2008)) of RPD issues on computer experiments. Transmitted variance model (TVM) proposed by Shoemaker and Tsui. (1993) for physical experiments can be applied in computer simulations. The approaches stated above rely heavily on the estimated mean model because they obtain expressions for variance directly from mean models or by using them for generating replicates. Variance modeling based on some kind of replicates relies on the estimated mean model to a lesser extent. To the best of our knowledge, there is no rigorous research on variance modeling needed for RPD in computer experiments. We develop procedures for identifying variance models. First, we explore procedures to decide groups of pseudo replicates for variance modeling. A formal variance change-point procedure is developed to rigorously determine the replicate groups. Next, variance model is identified and estimated through a three-step variable selection procedure. Properties of the proposed method are investigated under various conditions through analytical and empirical studies. In particular, impact of correlated response on the performance is discussed.

Thesis--University of Oklahoma. / Includes bibliographical references (leaves 64-65).

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The work for data analysis of the main methods, fullfilled in Computer mathematic systems (CMS), analysis. Also analysing and comparison of the data analysis of CMS – MAPLE, MATLAB and MATHCAD. There‘s briefly described enter and reading of data, characteristics of statistic data, analysis of variance, regression, interpolation and correlation. In the last section of data system analysis possibilities according to its sophistication, comfortable usage and variety of data function fullfillment. You will finde the examples of solved tasks with CMS after each description of data analysis method.

The current work deals with modelling longitudinal or repeated non-Gaussian measurements for a respiratory disease. The analysis of longitudinal data for non-Gaussian binary disease outcome data can broadly be modeled using three different approaches; the marginal, random effects and transition models. The marginal type model is used if one is interested in estimating population averaged effects such as whether a treatment works or not on an average individual. On the other hand random effects models are important if apart from measuring population averaged effects a researcher is also interested in subject specific effects. In this case to get marginal effects from the subject-specific model we integrate out the random effects. Transition models are also called conditional models as a general term. Thus all the three types of models are important in understanding the effects of covariates and disease progression and distribution of outcomes in a population. In the current work the three models have been researched on and fitted to data. The random effects or subject-specific model is further modified to relax the assumption that the random effects should be strictly normal. This leads to the so called hierarchical generalized linear model (HGLM) based on the h-likelihood formulation suggested by Lee and Nelder (1996). The marginal model was fitted using generalized estimating equations (GEE) using PROC GENMOD in SAS. The random effects model was fitted using PROC GLIMMIX and PROC NLMIXED in SAS (generalized linear mixed model). The latter approach was found to be more flexible except for the need of specifying initial parameter values. The transition model was used to capture the dependence between outcomes in particular the dependence of the current response or outcome on the previous response and fitted using PROC GENMOD. The HGLM was fitted using the GENSTAT software. Longitudinal disease outcome data can provide real and reliable data to model disease progression in the sense that it can be used to estimate important disease i parameters such as prevalence, incidence and others such as the force of infection. Problem associated with longitudinal data include loss of information due to loss to follow up such as dropout and missing data in general. In some cases cross-sectional data can be used to find the required estimates but longitudinal data is more efficient but may require more time, effort and cost to collect. However the successful estimation of a given parameter or function depends on the availability of the relevant data for it. It is sometimes impossible to estimate a parameter of interest if the data cannot its estimation. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2011.

The analysis of longitudinal binary data can be undertaken using any of the three families of models namely, marginal, random effects and conditional models. Each family of models has its own respective merits and demerits. The models are applied in the analysis of binary longitudinal data for childhood disease data namely the Respiratory Syncytial Virus (RSV) data collected from a study in Kilifi, coastal Kenya. The marginal model was fitted using generalized estimating equations (GEE). The random effects models were fitted using ‘Proc GLIMMIX’ and ‘NLMIXED’ in SAS and then again in Genstat. Because the data is a state transition type of data with the Markovian property the conditional model was used to capture the dependence of the current response to the previous response which is known as the history. The data set has two main complicating issues. Firstly, there is the question of developing a stochastically based probability model for the disease process. In the current work we use direct likelihood and generalized linear modelling (GLM) approaches to estimate important disease parameters. The force of infection and the recovery rate are the key parameters of interest. The findings of the current work are consistent and in agreement with those in White et al. (2003). The aspect of time dependence on the RSV disease is also highlighted in the thesis by fitting monthly piecewise models for both parameters. Secondly, there is the issue of incomplete data in the analysis of longitudinal data. Commonly used methods to analyze incomplete longitudinal data include the well known available case analysis (AC) and last observation carried forward (LOCF). However, these methods rely on strong assumptions such as missing completely at random (MCAR) for AC analysis and unchanging profile after dropout for LOCF analysis. Such assumptions are too strong to generally hold. In recent years, methods of analyzing incomplete longitudinal data have become available with weaker assumptions, such as missing at random (MAR). Thus we make use of multiple imputation via chained equations that require the MAR assumption and maximum likelihood methods that result in the missing data mechanism becoming ignorable as soon as it is MAR. Thus we are faced with the problem of incomplete repeated non–normal data suggesting the use of at least the Generalized Linear Mixed Model (GLMM) to account for natural individual heterogeneity. The comparison of the parameter estimates using the different methods to handle the dropout is strongly emphasized in order to evaluate the advantages of the different methods and approaches. The survival analysis approach was also utilized to model the data due to the presence of multiple events per subject and the time between these events. / Thesis (Ph.D.)-University of KwaZulu-Natal, Pietermarizburg, 2008.

National cultures play a critical role in effective leadership and organisational success in international businesses. Contemporary organisations are therefore challenged by cross-cultural leadership needs to address increasing diversity. In the past decades, there has been a growing interest in studies of non-Western leadership. Recent papers have focused particularly on leadership in the Asia-Pacific region. This paper compares leadership in China and New Zealand, based on the data collected by using the GLOBE (Global Leadership and Organisational Behaviour Effectiveness) project leadership questionnaire. In addition, the paper reviews the main findings of previous research in order to investigate the similarities and differences in preferred leadership behaviours/characteristics in both cultures, while attempting to examine the consistency of current findings against the previous GLOBE studies. Significant differences of leadership behaviours between China and New Zealand have been identified. This paper generally supports the findings of previous GLOBE studies that charismatic/value-based leadership is the universally contributing factor towards outstanding leadership and self-protective leadership is the universally negative factor against leadership excellence. Findings in this paper may contribute to further understanding of leadership practice in these two countries. Future research should be undertaken to examine the effects of cultural differences on organisational practice by a more comprehensive research method.