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.

The aim of this study is to quantify the extent to which political correctness, understood as an implicit social convention of restraint on public expression, operates within a community. Due to a scarcity of prior experimental research in the area, a new method was developed for the purpose of the study. Using random selection, the treatment consists of exposing groups averaging 10 individuals to a survey on diversity and immigration matters. The effect is measured as the discrepancy in attitudes that is revealed between anonymous and non-anonymous responses to the treatment survey. Control groups are similarly exposed to a survey on traditional left-right matters. The discrepancies are then compared. The results are controlled for possible influence by factors including group size, sex ratio, and length of study. The general effect of the treatment is not statistically significant, possibly as a result of small sample size. Further analysis shows a significant positive correlation between the proportion of women and the extent of attitude discrepancy. On one interpretation, this means that women in the population are on average more responsive to political correctness than men. Due to the population’s skewed characteristics, the results are not generalised. Future researchers in the area are advised to draw their sample from a more representative population, to investigate additional subject matters and to collect more sophisticated data, in particular on the level of the individual.

We examine three topics related to experimental design in this dissertation. Two are related to the analysis of experimental data and the other focuses on the design of paired comparison experiments, in this case knockout tournaments. The two analysis topics are motivated by how to estimate and test causal effects when the assignment mechanism fails to create balanced treatment groups. In Chapter 2, we apply conditional randomization tests to experiments where, through random chance, the treatment groups differ in their covariate distributions. In Chapter 4, we apply principal stratification to factorial experiments where the subjects fail to comply with their assigned treatment. The sources of imbalance differ, but, in both cases, ignoring the imbalance can lead to incorrect conclusions. In Chapter 3, we consider designing knockout tournaments to maximize different objectives given a prior distribution on the strengths of the players. These objectives include maximizing the probability the best player wins the tournament. Our emphasis on balance in the other two chapters comes from a desire to create a fair comparison between treatments. However, in this case, the design uses the prior information to intentionally bias the tournament in favor of the better players. / Statistics

Because of the needs for producing highly reliable products and reducing product development time, Accelerated Life Testing (ALT) has been widely used in new product development as an alternative to traditional testing methods. The basic idea of ALT is to expose a limited number of test units of a product to harsher-than-normal operating conditions to expedite failures. Based on the failure time data collected in a short time period, an ALT model incorporating the underlying failure time distribution and life-stress relationship can be developed to predict the product reliability under the normal operating condition. However, ALT experiments often consume significant amount of energy due to the harsher-than-normal operating conditions created and controlled by the test equipment used in the experiments. This challenge may obstruct successful implementations of ALT in practice. In this dissertation, a new ALT design methodology is developed to improve the reliability estimation precision and the efficiency of energy utilization in ALT. This methodology involves two types of ALT design procedures - the sequential optimization approach and the simultaneous optimization alternative with a fully integrated double-loop design architecture. Using the sequential optimum ALT design procedure, the statistical estimation precision of the ALT experiment will be improved first followed by energy minimization through the optimum design of controller for the test equipment. On the other hand, we can optimize the statistical estimation precision and energy consumption of an ALT plan simultaneously by solving a multi-objective optimization problem using a controlled elitist genetic algorithm. When implementing either of the methods, the resulting statistically and energy efficient ALT plan depends not only on the reliability of the product to be evaluated but also on the physical characteristics of the test equipment and its controller. Particularly, the statistical efficiency of each candidate ALT plan needs to be evaluated and the corresponding controller capable of providing the required stress loadings must be designed and simulated in order to evaluate the total energy consumption of the ALT plan. Moreover, the realistic physical constraints and tracking performance of the test equipment are also addressed in the proposed methods for improving the accuracy of test environment. In this dissertation, mathematical formulations, computational algorithms and simulation tools are provided to handle such complex experimental design problems. To the best of our knowledge, this is the first methodological investigation on experimental design of statistically precise and energy efficient ALT. The new experimental design methodology is different from most of the previous work on planning ALT in that (1) the energy consumption of an ALT experiment, depending on both the designed stress loadings and controllers, cannot be expressed as a simple function of the related decision variables; (2) the associated optimum experimental design procedure involves tuning the parameters of the controller and evaluating the objective function via computer experiment (simulation). Our numerical examples demonstrate the effectiveness of the proposed methodology in improving the reliability estimation precision while minimizing the total energy consumption in ALT. The robustness of the sequential optimization method is also verified through sensitivity analysis.

A computational and experimental study of the Richtmyer-Meshkov instability is presented here for an inclined interface perturbation. The computational work is composed of simulation studies of the inclined interface RMI performed using the Arbitrary Lagrange Eulerian (ALE) code called ARES. These simulations covered a wide range of Mach numbers (1.2 to 3.5), gas pairs (Atwood numbers 0.23to 0.95), inclination angles (30° to 85°), and explored various perturbation types (both inclined interface and sinusoidal). The computational work included the first parametric study of the inclined interface RMI. This study yielded the first scaling method for the inclined interface RMI mixing width growth rates. It was extended to explore the effect of perturbation linearity and identified that a sharp transition in growth regimes occurs for an initial perturbation inclination angle of 75° with angles below (above) this growing faster (slower). Finally a study of the effects of incident shock strength on the refracted shock wave perturbation decay rate is presented. This study examined how the perturbations induced on the transmitted shock front by the RMI decay with time and found that the decay rates follow a power law model, Alpha=Beta∗S^(Epsilon). When the coefficients from the power law decay model were plotted versus Mach number, a distinct transition region was found which is likely a result of the post-shock heavy gas velocity transitioning from the subsonic to supersonic range. The experimental portion of this work was conducted using the TAMUFMSTF, completed in May of 2012. This facility uses a variable inclination shock tube, with a modular construction design for incident shock strengths of up to Mach 3.0. It employs optical systems for measuring density and velocity fields simultaneously using the planar laser induced fluorescence and particle imaging velocimetry techniques. The design and construction of this facility is reviewed in detail in chapter 4 of this work. The initial experiments performed in the TAMUFMSTF provided the first known extensive experimental data for an inclined interface RMI. Planar laser Mie scattering images and velocity vectors were obtained for a N_(2)/CO_(2) interface at a 60° inclination angle and an incident shock strength of Mach 1.55. These images have been compared with simulations made using the ARES codes and have been shown to have some distinct differences. Some of these differences indicate that the initial conditions in the experiments deviate from the ideal planar interface. Other differences have revealed features which have not been resolved by the simulations due to resolution limitations.

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Resilient modulus is an important property for asphalt concrete design and for mechanistic analysis of pavement response under traffic loading. This study investigates the different factors affecting the resilient modulus of hot mix asphalt. A fractional factorial design of experiment was carried out to investigate six factors each factor was studied at two levels. These factors are: the maximum nominal aggregate size, specimen diameter and thickness, the load pulse form and duration, and the compaction method. Two types of hot mix asphalts with different maximum aggregate sizes (10 mm and 14 mm) were studied. Gyratory and Marshall compaction methods were used to prepare the specimens. Sinusoidal and triangular load pulse forms were used in the measurement of the resilient modulus. This study attempts to examine how the different factors interrelate to affect the resilient modulus. In addition to this, two other investigations will be carried out. The first is the comparison of the strain backcalculated using the resilient modulus test results with the strain measured using strain gages and strain values obtained from finite element modelling (FEM), and determine whether the FEM or the closed form equation is the more accurate method for determining strain. The second is the investigation of the relationship between the flexural, complex and resilient modulus. Analysis of the factorial experimental design showed that the maximum nominal aggregate size is the most important factor affecting the resilient modulus, followed by the load duration, the specimen geometry represented by the thickness and diameter then the interactions between the different factors. The strain comparison suggested that the closed form equations were indeed a suitable approach to determine maximum horizontal strain during a resilient modulus test. The modulus comparison suggested that it is possible to predict either resilient, complex and flexural modulus given that only one of them is known, but only for AC10 specimens.

One-way and two-way classification models in experimental design for both balanced and unbalanced cases are considered when the errors have Generalized Secant Hyperbolic distribution. Efficient and robust estimators for main and interaction effects are obtained by using the modified maximum likelihood estimation (MML) technique. The test statistics analogous to the normal-theory F statistics are defined to test main and interaction effects and a test statistic for testing linear contrasts is defined. It is shown that test statistics based on MML estimators are efficient and robust. The methodogy obtained is also generalized to situations where the error distributions from block to block are non-identical.

Good process control is often critical for the economic viability of large-scale production of several commercial products. In this work, the production of biodiesel from microalgae is investigated. Successful implementation of a model-based control strategy requires the identification of a model that properly captures the biochemical dynamics of microalgae, yet is simple enough to allow its implementation for controller design. For this purpose, two model reparameterization algorithms are proposed that partition the parameter space into estimable and inestimable subspaces. Both algorithms are applied using a first principles ODE model of a microalgal bioreactor, containing 6 states and 12 unknown parameters. Based on initial simulations, the non-linear algorithm achieved better degree of output prediction when compared to the linear one at a greatly decreased computational cost. Using the parameter estimates obtained through implementation of the non-linear algorithm on experimental data from a fed-batch bioreactor, the possible improvement in volumetric productivity was recognized. / Process Control

A new experimental setup for studies on wake flow instability and its control that successfully has been designed and manufactured, is introduced and de- scribed. The main body is a dual-sided flat plate with an elliptic leading edge and a blunt trailing edge. Permeable surfaces enable boundary layer suction and/or blowing that introduce the unique feature of adjusting the inlet condition of the wake created behind the plate. This, in combination with a trailing edge that is easily modified, makes it an ideal experiment for studies of different control methods for the wake flow instability as well as extensive parameter studies. Experimental validation of the setup has been performed by means of measurements of the wake symmetry and boundary layer velocity profiles at the trailing edge. Some preliminary results on the Strouhal number versus different inlet conditions are reported. Additionally, an in-house vortex detection (VD) program has been developed in order to detect, analyse and compare small-scale vortical structures in instantaneous velocity fields from flow measurements. This will be a powerful tool for comparison of wake characteristics for varying inlet conditions and control methods in the new experimental setup. Measurements from three completely separate experimental setups with different geometries and flow cases, have been analysed by the VD-program.          i.     In order to obtain improved ventilation we have studied the effect of pulsating inflow into a closed volume compared to having the inflow at a constant flow rate. We show that the number of small-scale eddies is significantly increased and that the stagnation zones are reduced in size, which enhances the mixing.         ii.     Instantaneous velocity fields in the wake behind a porous cylinder subjected to suction or blowing through the entire cylinder surface have also been analysed using the VD-program. The results show that the major change for different levels of blowing or suction is the location of vortices while the most common vortex size and strength are essentially unchanged.        iii.     Another study on how the geometry of a V-shaped mixer in a pipe flow affects the mixing have also been examined, where no general differences were found between different thicknesses, why a thickness that is favourable from an acoustic point of view can be chosen.   We also propose a new method, using global mode analysis on experimental data, showing that randomly ordered snapshots of the velocity field behind the porous cylinder can be re-ordered and phase-averaged. / QC 20111108 / Active control of vortex shedding behind bluff bodies