In this thesis, the design of experiment is studied. Firstly, a theoretic background in mathematical statistics necessary for understanding is built (chapter 2). The design of experiment is then presented in chapters 3 and 4. Chapter 3 is divided into several subchapters in which its brief history is provided as well as its complex theoretic description (basic principles, steps for planning, etc.). Chapter 4 deals with particular types of the design of experiment (Factorial experiments or Response surface design). Simple examples are provided to illustrate the theory in chapters 3 and 4. Last part of the thesis is strictly practical and focuses on an application of the theory for particular data sets and its evaluation (chapter 5).

Within the realms of biological and medical research, toxicity studies which measure impaired reproduction are becoming more and more common, yet methods for efficiently designing experiments for these studies have received little attention. In this research, response surface design criteria are applied to four models for impaired reproduction data. The important role of control observations in impairment studies is discussed, and for one model, a normal error linear model, a design criterion is introduced for allocating a portion of the sample to the control. Special attention is focused on issues surrounding optimal design of experiments for two of the models, a Poisson exponential model and a Poisson linear model. As most of the optimal designs for these models are obtained via numerical methods rather than directly from criteria, equivalence theory is used to prove analytically that the numerically obtained designs are truly optimal. A further complication associated with designing experiments for Poisson regression is the need to know parameter values in order to implement the optimal designs. Thus, two stage design of experiments is investigated as one solution to this problem. Finally, since researchers frequently do not know the appropriate model for their data a priori, the optimal designs for these two different models are compared, and designs which are robust to model misspecification are highlighted. / Ph. D.

Neural networks are being used increasingly often as alternatives to traditional statistical models. As a result, their performance needs to be examined in a statistical framework. Following a brief overview of many types of neural networks, details concerning the implementation of the single hidden layer feedforward neural network (SHLFNN) are presented. The focus of the presentation is on the application of this network in a regression setting. One area where the SHLFNN is being used more frequently is in response surface modeling based on designed experiments. Due to the small sample sizes typically employed by response surface designs, the ability of the SHLFNN to accurately approximate the underlying model is questionable. The results of a simulation which compares the performance of the SHLFNN with that of a second order polynomial model are presented. Finally, methods are explored for combining the SHLFNN model with a linear model. Such a combined model has advantages over each of its components. The combined model will be able to approximate any underlying nonlinear function better than a linear model, and it will allow for easy assessment of the impact of any effects of interest to the researcher, an ability that is lost when only the SHLFNN model is used. / Ph. D.

This thesis deals with the possibility of applying the method of Design of Experiments (DoE) on specific data. In the first chapter of theoretical part, this method is described in detail. The basic principles and guidelines for the design of the experiment are written there. In the next two chapters, factorial design of the experiment and response surface design are described. The latter one includes a central composite design and Box-Behnken design. The following chapter contains practical part, which focuses on modelling firing range of ball from a catapult using the above three types of experimental design. In this work, the models are analysed together with their different characteristics. Their comparison is made by using prediction and confidence intervals and by response optimizing. The last part of the thesis comprises overall evaluation.

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The overall objective of this study was to develop an optimised Ultra-High-Performance Concrete (UHPC) matrix based on the modified Andreasen and Andersen optimum particle packing model by using available South African materials. The focus of this study was to determine the optimum combined fibre and superplasticiser content for UHPC by using a response surface design. The UHPC was appropriately designed, produced and tested. Various changes in mechanical properties resulting from different combinations of steel fibre and superplasticiser contents was investigated. The flowability, density and mechanical properties of the designed UHPC were measured and analysed. Both the fibre and superplasticiser content play a significant role in the flowability of the fresh concrete. The addition of fibres significantly improved the strength of the concrete. The results show that the superplasticiser content can be increased if a more workable mix is required without decreasing the strength significantly. The statistical analysis of the response surface methodology confirms that the designed models can be used to navigate the design space defined by the Central Composite Design. The optimum combined fibre and superplasticiser content depend on the required mechanical properties and cost. Using the modified Andreasen and Andersen particle packing model and surface response design methodology, it is possible to efficiently produce a dense Ultra-High-Performance Fibre Reinforced Concrete (UHPFRC) with a relatively low binder amount, low fibre content and good workability. The effect of heat curing on the mechanical properties was investigated. It was concluded that heat curing is not recommended when considering the long-term strength development. The estimated strength development of concrete obtained by using the fib Model Code 2010 (2013) does not incorporate the detrimental effect of high curing temperatures on long-term strength and therefore overestimate the long-term strengths. The strength estimates for both early and long-term ages can be improved by considering this effect in the strength development functions obtained from fib Model Code 2010 (2013). The effect of specimen size on the compressive and flexural tensile strength of UHPFRC members were established. It was found that the specimen size has a significant effect on the measured cube compressive strength. Smaller beam specimens showed higher ductility compared to those of the larger beam specimens. The crack width decreased as the beam’s depth decreased. A lower variability was experienced in the beams with limited depth (< 45 mm). Further testing is required to determine whether a span-to-depth ratio of 10 would yield optimum results. The utilisation of by-products, such as undensified silica fume and fly ash, as cement replacement materials makes UHPFRC sustainable, leading to a reduced life-cycle cost. The calculated Embodied Energy per unit strength (EE/unit strength) and Embodied Carbon per unit strength (EC/unit strength) values for the UHPFRC mixture yield lower values compared to that of the 30 MPa concrete mixture, indicating that UHPFRC can be used to reduce the environmental footprint of the concrete industry. The inverse analysis method used was successful in providing an improved simplified stress-strain response for the UHPFRC. The analysis provided valuable information into the stress-strain, load-deflection and moment-curvature responses of the UHPFRC. Standard material test results were used to theoretically calculate moment-curvature responses and were then compared to the experimental results obtained. The study demonstrated that it is possible to efficiently produce a dense and workable UHPFRC with relatively low binder amount and low fibre content. This can result in more cost-effective UHPFRC, thus improving the practical application thereof. / Dissertation (MEng)--University of Pretoria, 2020. / Civil Engineering / MEng (Structural engineering) / Unrestricted

This thesis is aimed to Design of Experiments methodology. Main purpose of this thesis is to create detailed materials for lessons of Design of Experiments in Quality Control courses. Thesis contains case studies which are applicable for education purposes. Design of Experiments has been applied for solder joints quality evaluation. Solder joints have been modeled in software ANSYS and finite element method has been applied for thermomechanical stress evaluation.