Graduate students in the Brigham Young University Chemistry Department are working to develop a filtering device that can be used to separate substances into their constituent parts. The device consists of a monomer and water mixture that is polymerized into a monolith inside of a capillary. The ideal monolith is completely solid with interconnected pores that are small enough to cause the constituent parts to pass through the capillary at different rates, effectively separating the substance. Although the end objective is to minimize pore sizes, it is necessary to first identify an experimental region where any combination of input variables will consistently yield homogeneous monoliths capable of flow. To accomplish this task, an experimental mixture design is used to model the relationship between the variables related to the creation of the monolith and the probability of creating an acceptable polymer. The results of the mixture design suggest that, inside of the constrained experimental region, mixtures with higher proportions of monomer and surfactant, low amounts of initiator and salt, and DEGDA as the monomer have the highest probability of producing a workable monolith. Confirmatory experiments are needed before future experimentation to minimize pore sizes is performed using the refined constrained experimental region determined by the results of this analysis.

In response surface methodology, the central composite design is the most popular choice for fitting a second order model. The choice of the distance for the axial runs, alpha, in a central composite design is very crucial to the performance of the design. In the literature, there are plenty of discussions and recommendations for the choice of alpha, among which a rotatable alpha and an orthogonal blocking alpha receive the greatest attention. Box and Hunter (1957) discuss and calculate the values for alpha that achieve rotatability, which is a way to stabilize prediction variance of the design. They also give the values for alpha that make the design orthogonally blocked, where the estimates of the model coefficients remain the same even when the block effects are added to the model. In the last ten years, people have begun to realize the importance of a split-plot structure in industrial experiments. Constructing response surface designs with a split-plot structure is a hot research area now. In this dissertation, Box and Hunters' choice of alpha for rotatablity and orthogonal blocking is extended to central composite designs with a split-plot structure. By assigning different values to the axial run distances of the whole plot factors and the subplot factors, we propose two-strata rotatable splitplot central composite designs and orthogonally blocked split-plot central composite designs. Since the construction of the two-strata rotatable split-plot central composite design involves an unknown variance components ratio d, we further study the robustness of the two-strata rotatability on d through simulation. Our goal is to provide practical recommendations for the value of the design parameter alpha based on the philosophy of traditional response surface methodology. / Ph. D.

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Practical restrictions on randomization are commonplace in industrial experiments due to the presence of hard-to-change or costly-to-change factors. Employing a split-plot design structure minimizes the number of required experimental settings for the hard-to-change factors. In this research, we propose classes of equivalent estimation second-order response surface split-plot designs for which the ordinary least squares estimates of the model are equivalent to the generalized least squares estimates. Designs that possess the equivalence property enjoy the advantages of best linear unbiased estimates and design selection that is robust to model misspecification and independent of the variance components. We present a generalized proof of the equivalence conditions that enables the development of several systematic design construction strategies and provides the ability to verify numerically that a design provides equivalent estimates, resulting in a broad catalog of designs. We explore the construction of balanced and unbalanced split-plot versions of the central composite and Box-Behnken designs. In addition, we illustrate the utility of numerical verification in generating D-optimal and minimal point designs, including split-plot versions of the Notz, Hoke, Box and Draper, and hybrid designs. Finally, we consider the practical implications of analyzing a near-equivalent design when a suitable equivalent design is not available. By simulation, we compare methods of estimation to provide a practitioner with guidance on analysis alternatives when a best linear unbiased estimator is not available. Our goal throughout this research is to develop practical experimentation strategies for restricted randomization that are consistent with the philosophy of traditional response surface methodology. / Ph. D.

When a reliability experiment is used, practitioners can understand better what lifetimes to expect of a product under different operating conditions and what factors are important to designing reliability into a product. Reliability experiments, however, can be very challenging to analyze because often the reliability or lifetime data tend to follow distinctly non-normal distributions and the experiments typically involve censoring. Time and cost constraints may also lead to reliability experiments with experimental protocols that are not completely randomized. In many industrial experiments, for example, the split-plot structure arises when the randomization of the experimental runs is restricted. Additionally, for many reliability experiments, it is often cost effective to apply a treatment combination to a stand with multiple units on it as opposed to each unit individually, which introduces subsampling. The analysis of lifetime data assuming a completely randomized design has been well studied, but until recently analysis methodologies for more complex experimental designs with multiple error terms have not been a focus of the reliability field. This dissertation provides two analysis methods for analyzing right-censored Weibull distributed lifetime data from a split-plot experiment with subsampling. We evaluate the proposed methods through a simulation study. Companies also routinely perform life tests on their products to ensure that products meet requirements. Each of these life tests typically involves testing several units simultaneously with interest in the times to failure. Again, the fact that lifetime data tend to be nonnormally distributed and censored make the development of a control charting procedure more demanding. In this dissertation, one-sided lower and upper likelihood ratio based cumulative sum (CUSUM) control charting procedures are developed for right-censored Weibull lifetime data to monitor changes in the scale parameter, also known as the characteristic life, for a fixed value of the Weibull shape parameter. Because a decrease in the characteristic life indicates a decrease in the mean lifetime of a product, a one-sided lower CUSUM chart is the main focus. We illustrate the development and implementation of the chart and evaluate the properties through a simulation study. / Ph. D.

Fractional factorial designs are a popular choice in designing experiments for studying the effects of multiple factors simultaneously. The first step in planning an experiment is the selection of an appropriate fractional factorial design. An appro- priate design is one that has the statistical properties of interest of the experimenter and has a small number of runs. This requires that a catalog of candidate designs be available (or be possible to generate) for searching for the "good" design. In the attempt to generate the catalog of candidate designs, the problem of design isomor- phism must be addressed. Two designs are isomorphic to each other if one can be obtained from the other by some relabeling of factor labels, level labels of each factor and reordering of runs. Clearly, two isomorphic designs are statistically equivalent. Design catalogs should therefore contain only designs unique up to isomorphism. There are two computational challenges in generating such catalogs. Firstly, testing two designs for isomorphism is computationally hard due to the large number of possible relabelings, and, secondly, the number of designs increases very rapidly with the number of factors and run-size, making it impractical to compare all designs for isomorphism. In this dissertation we present a new approach for tackling both these challenging problems. We propose graph models for representing designs and use this relationship to develop efficient algorithms. We provide a new efficient iso- morphism check by modeling the fractional factorial design isomorphism problem as graph isomorphism problem. For generating the design catalogs efficiently we extend a result in graph isomorphism literature to improve the existing sequential design catalog generation algorithm. The potential of the proposed methods is reflected in the results. For 2-level regular fractional factorial designs, we could generate complete design catalogs of run sizes up to 4096 runs, while the largest designs generated in literature are 512 run designs. Moreover, compared to the next best algorithms, the computation times for our algorithm are 98% lesser in most cases. Further, the generic nature of the algorithms makes them widely applicable to a large class of designs. We give details of graph models and prove the results for two classes of designs, namely, 2-level regular fractional factorial designs and 2-level regular fractional factorial split-plot designs, and provide discussions for extensions, with graph models, for more general classes of designs.

abstract: In mixture-process variable experiments, it is common that the number of runs is greater than in mixture-only or process-variable experiments. These experiments have to estimate the parameters from the mixture components, process variables, and interactions of both variables. In some of these experiments there are variables that are hard to change or cannot be controlled under normal operating conditions. These situations often prohibit a complete randomization for the experimental runs due to practical and economical considerations. Furthermore, the process variables can be categorized into two types: variables that are controllable and directly affect the response, and variables that are uncontrollable and primarily affect the variability of the response. These uncontrollable variables are called noise factors and assumed controllable in a laboratory environment for the purpose of conducting experiments. The model containing both noise variables and control factors can be used to determine factor settings for the control factor that makes the response "robust" to the variability transmitted from the noise factors. These types of experiments can be analyzed in a model for the mean response and a model for the slope of the response within a split-plot structure. When considering the experimental designs, low prediction variances for the mean and slope model are desirable. The methods for the mixture-process variable designs with noise variables considering a restricted randomization are demonstrated and some mixture-process variable designs that are robust to the coefficients of interaction with noise variables are evaluated using fraction design space plots with the respect to the prediction variance properties. Finally, the G-optimal design that minimizes the maximum prediction variance over the entire design region is created using a genetic algorithm. / Dissertation/Thesis / Ph.D. Industrial Engineering 2010

Made available in DSpace on 2014-12-17T15:26:40Z (GMT). No. of bitstreams: 1 AlexWP_DISSERT.pdf: 4684149 bytes, checksum: 9c1ad1c83e674604f7a176282c182ff1 (MD5) Previous issue date: 2014-03-13 / Em experimentos com v?rios fatores em que alguns s?o mais dif?ceis de mudar que outros, pode ser inconveniente executar as provas do experimento em uma forma completamente aleat?ria, levando o pesquisador a criar naturalmente uma restri??o na ordem de execu??o para poupar tempo ou reduzir os custos. Este tipo de restri??o pode resultar em uma generaliza??o do planejamento fatorial, conhecida como experimentos em parcelas subdivididas. Na pr?tica, ? comum executar um experimento em parcelas subdivididas e analis?-lo como se fosse completamente aleatorizado. O objetivo principal do trabalho ? avaliar o impacto de analisar um experimento com restri??o na aleatoriza??o como completamente aleatorizado

Freshwater mussels (Unionidae) in the United States have experienced dramatic declines, and 25% species are listed as federally endangered. Hence, recovery plans for endangered species proposed a strategy of propagation of young mussels for release to natal rivers to augment declining populations. In this study, I conducted laboratory experiments, assessed site suitability for mussel restoration, and evaluated survival and growth rates of released mussels to meet the requirements of recovery plan. I conducted multiple experiments to develop an improved protocol for juvenile mussel propagation and culture. Significantly greater survival and growth rates were found in newly metamorphosed juveniles of the rainbow mussel (Villosa iris) reared in a substrate of fine sediment and one-month-old juveniles of wavy-rayed lampmussel (Lampsilis fasciola) fed on natural food in pond water. Bio-filter media greatly increased water quality by reducing the concentration of ammonia and nitrite. The negative impacts of flatworm predation and filamentous algae in juvenile culture were controlled, and juvenile escapement was prevented. Juvenile mussels were successfully produced and cultured to stockable size (>15 mm) for release. I released laboratory-propagated mussels at three historically important sites in Clinch and Powell rivers for the assessment of site suitability. Use of cages was the most effective method to determine site suitability because the free-released mussels (untagged, tagged) had low catchability. Mussels released at Horton Ford, Clinch River, exhibited significantly faster growth. Horton Ford is the most suitable site, while environmental conditions at Fugate Ford, Powell River, are deemed unsuitable for mussel restoration and recovery. To facilitate the detection of released mussels, I applied Passive Integrated Transponder tags to laboratory-produced juveniles of the endangered Cumberlandian combshell (Epioblasma brevidens) and released them near Brooks Bridge, Powell River. The detection probability increased above 98%. I developed a set of hierarchical Bayesian models incorporating individual variations, seasonal variations, periodic growth stages and growth cessation to estimate survival, detection probability and growth of released mussels in a changing environment. Mussels of E. brevidens exhibited great survival (> 99% per month) and growth, indicating suitable conditions for recovery of this endangered species at this site. / Ph. D.