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The demand for increased diversity, reduced cycle time, and reduced work-in-process has caused increased popularity of mixed-model assembly lines. These lines combine the productivity of an assembly line and the flexibility of a job shop. The mixed-model assembly line allows setup time between models to be zero. Large lines mixed-model assembly lines require a timely, near-optimal method. A well balanced line reduces worker idle time and simplifies the mixed-model assembly line sequencing problem. Prior attempts to solve the balancing problem have been in-adequate. Heuristic techniques are too simple to find near-optimal solutions and yield only one solution. An exhaustive search requires too much processing time. Simulated Annealing works well, but yields only one solution per run and the solutions may vary because of the random nature of the Simulated Annealing process. Multiple runs are required to get more than one solution, each run requiring some amount of time which depends on problem size. If only one run is performed, the solution achieved may be far from optimal. In addition, Simulated Annealing requires different parameters depending on the size of the problem. The Genetic Algorithm (GA) is a probabilistic heuristic search strategy. In most cases, it begins with a population of random solutions. Then the population is reproduced using crossover and mutation with the fittest solutions having a higher probability of being parents. The idea is survival of the fittest, poor or unfit solutions do not reproduce and are replaced by better or fitter solutions. The final generation should yield multiple near optimal solutions. The objective of this study is to investigate the Genetic Algorithm and its performance compared to Simulated Annealing for large mixed-model assembly lines. The results will show that the Genetic Algorithm will perform comparably to the Simulated Annealing. The Genetic Algorithm will be used to solve various mixed-model assembly line problems to discover the correct parameters to solve any mixed-model assembly line balancing problem. / Master of Science

We have seen an increased interest and extensive research in the monitoring of a process over time whose characteristics are represented mathematically in functional forms such as profiles. Most of the current techniques require all of the data for each profile to determine the state of the process. Thus, quality engineers from industrial processes such as agricultural, aquacultural, and chemical cannot make process corrections to the current profile that are essential for correcting their processes at an early stage. In addition, the focus of most of the current techniques is on the statistical significance of the parameters or features of the model instead of the practical significance, which often relates to the actual quality characteristic. The goal of this research is to provide alternatives to address these two main concerns. First, we study the use of a Shewhart type control chart to monitor within profiles, where the central line is the predictive mean profile and the control limits are formed based on the prediction band. Second, we study a statistic based on a non-linear mixed model recognizing that the model leads to correlations among the estimated parameters. / Doctor of Philosophy / Checking the stability over time of the quality of a process which is best expressed by a relationship between a quality characteristic and other variables involved in the process has received increasing attention. The goal of this research is to provide alternative methods to determine the state of such a process. Both methods presented here are compared to the current methodologies. The first method will allow us to monitor a process while the data is still being collected. The second one is based on the quality characteristic of the process and takes full advantage of the model structure. Both methods seem to be more robust than the current most well-known method.

Harvesting practices in the southern Appalachians have moved away from clearcutting in favor of variable retention harvesting systems. A study was initiated in 1995-8 to investigate the effects of retaining varying numbers of residual trees on regeneration in seven silvicultural treatments. A second study specifically focused on stump sprouting in only three of those treatments. The treatments for first study included: a clearcut, commercial harvest, leave-tree, shelterwood, group selection, midstory treatment, and an uncut control. The second only focused on the clearcut, leave-tree, and shelterwood. These treatments were implemented in seven stands in Virginia and West Virginia over two physiographic provinces, the Appalachian plateau and Ridge and Valley. The stands were even-aged oak dominated Appalachian hardwood stands on fair quality sites with average ages ranging from 63 to 100 yrs. Permanent plots were randomly located in each stand and all overstory trees (>5m tall) were inventoried and tagged prior to harvest. Regeneration was also quantified. Harvest occurred between 1995-8. For the current studies the plots were re-inventoried 9-11 years post-harvest and all regeneration in all treatments as well as stump sprouts in the selected treatments were quantified. The first study utilized a mixed model ANOVA to analyze five species groups: oak, maple, black cherry-yellow-poplar, miscellaneous, and midstory. Response variables included importance value, average height, and density compared within species group and among treatments. Differences between sprout and seedling origin regeneration were also investigated within species group among treatment. Results indicated that oak densities were similar in all of the treatments, and stump sprouts were larger and more frequent than seedlings. Maple exhibited an increase from pre-harvest overstory importance and exhibited competitive sprouting. The black cherry-yellow-poplar group had few but highly competitive sprouts and a considerable increase in seedling origin regeneration in all treatments. The miscellaneous species densities increased as well with more competitive sprouting in some treatments. The midstory species were excluded from the analysis as it was assumed these species would not occupy canopy positions in a mature stand. The second study investigated differences in the percent of stumps that sprouted and the number of sprouts per stump. The percent data were analyzed using a non-parametric one-way ANOVA and regression analysis, while the sprouts per stump data were compared in a mixed model ANOVA and regression. Species were combined into six groups: the red oak group, chestnut oak, red maple, white oak/hickory group, mixed mesic group, and midstory group. The plateau tended to have reduced sprouting compared to the Ridge and Valley for most species groups and treatments. The red oak group, chestnut oak, and red maple exhibited reduced sprouting with increased residual basal area. The mixed mesic group did not show any effect in sprouting related to residual basal area. Only chestnut oak showed fewer sprouts per stump as residual basal area increased. / Master of Science

With the rapid development of modern high-throughput technologies, scientists can now collect high-dimensional complex data in different forms, such as medical images, genomics measurements. However, acquisition of more data does not automatically lead to better knowledge discovery. One needs efficient and reliable analytical tools to extract useful information from complex datasets. The main objective of this dissertation is to develop innovative Bayesian methodologies to enable effective and efficient knowledge discovery from complex high-dimensional data. It contains two parts—the development of computationally efficient functional mixed models and the modeling of data heterogeneity via Dirichlet Diffusion Tree. The first part focuses on tackling the computational bottleneck in Bayesian functional mixed models. We propose a computational framework called variational functional mixed model (VFMM). This new method facilitates efficient data compression and high-performance computing in basis space. We also propose a new multiple testing procedure in basis space, which can be used to detect significant local regions. The effectiveness of the proposed model is demonstrated through two datasets, a mass spectrometry dataset in a cancer study and a neuroimaging dataset in an Alzheimer's disease study. The second part is about modeling data heterogeneity by using Dirichlet Diffusion Trees. We propose a Bayesian latent tree model that incorporates covariates of subjects to characterize the heterogeneity and uncover the latent tree structure underlying data. This innovative model may reveal the hierarchical evolution process through branch structures and estimate systematic differences between groups of samples. We demonstrate the effectiveness of the model through the simulation study and a brain tumor real data. / Doctor of Philosophy / With the rapid development of modern high-throughput technologies, scientists can now collect high-dimensional data in different forms, such as engineering signals, medical images, and genomics measurements. However, acquisition of such data does not automatically lead to efficient knowledge discovery. The main objective of this dissertation is to develop novel Bayesian methods to extract useful knowledge from complex high-dimensional data. It has two parts—the development of an ultra-fast functional mixed model and the modeling of data heterogeneity via Dirichlet Diffusion Trees. The first part focuses on developing approximate Bayesian methods in functional mixed models to estimate parameters and detect significant regions. Two datasets demonstrate the effectiveness of proposed method—a mass spectrometry dataset in a cancer study and a neuroimaging dataset in an Alzheimer's disease study. The second part focuses on modeling data heterogeneity via Dirichlet Diffusion Trees. The method helps uncover the underlying hierarchical tree structures and estimate systematic differences between the group of samples. We demonstrate the effectiveness of the method through the brain tumor imaging data.