This dissertation presents novel methodologies for five problem areas in modern quality improvement and computer experiments, i.e., selective assembly, robust design with computer experiments, multivariate quality control, model selection for split plot experiments, and construction of minimax designs. Selective assembly has traditionally been used to achieve tight specifications on the clearance of two mating parts. Chapter 1 proposes generalizations of the selective assembly method to assemblies with any number of components and any assembly response function, called generalized selective assembly (GSA). Two variants of GSA are considered: direct selective assembly (DSA) and fixed bin selective assembly (FBSA). In DSA and FBSA, the problem of matching a batch of N components of each type to give N assemblies that minimize quality cost is formulated as axial multi-index assignment and transportation problems respectively. Realistic examples are given to show that GSA can significantly improve the quality of assemblies. Chapter 2 proposes methods for robust design optimization with time consuming computer simulations. Gaussian process models are widely employed for modeling responses as a function of control and noise factors in computer experiments. In these experiments, robust design optimization is often based on average quadratic loss computed as if the posterior mean were the true response function, which can give misleading results. We propose optimization criteria derived by taking expectation of the average quadratic loss with respect to the posterior predictive process, and methods based on the Lugannani-Rice saddlepoint approximation for constructing accurate credible intervals for the average loss. These quantities allow response surface uncertainty to be taken into account in the optimization process. Chapter 3 proposes a Bayesian method for identifying mean shifts in multivariate normally distributed quality characteristics. Multivariate quality characteristics are often monitored using a few summary statistics. However, to determine the causes of an out-of-control signal, information about which means shifted and the directions of the shifts is often needed. We propose a Bayesian approach that gives this information. For each mean, an indicator variable that indicates whether the mean shifted upwards, shifted downwards, or remained unchanged is introduced. Default prior distributions are proposed. Mean shift identification is based on the modes of the posterior distributions of the indicators, which are determined via Gibbs sampling. Chapter 4 proposes a Bayesian method for model selection in fractionated split plot experiments. We employ a Bayesian hierarchical model that takes into account the split plot error structure. Expressions for computing the posterior model probability and other important posterior quantities that require evaluation of at most two uni-dimensional integrals are derived. A novel algorithm called combined global and local search is proposed to find models with high posterior probabilities and to estimate posterior model probabilities. The proposed method is illustrated with the analysis of three real robust design experiments. Simulation studies demonstrate that the method has good performance. The problem of choosing a design that is representative of a finite candidate set is an important problem in computer experiments. The minimax criterion measures the degree of representativeness because it is the maximum distance of a candidate point to the design. Chapter 5 proposes algorithms for finding minimax designs for finite design regions. We establish the relationship between minimax designs and the classical set covering location problem in operations research, which is a binary linear program. We prove that the set of minimax distances is the set of discontinuities of the function that maps the covering radius to the optimal objective function value, and optimal solutions at the discontinuities are minimax designs. These results are employed to design efficient procedures for finding globally optimal minimax and near-minimax designs.

The number of technology alternatives has lately grown to satisfy the increasingly demanding goals in modern engineering. These technology alternatives are handled in the design process as either concepts or categorical design inputs. Additionally, designers desire to bring into early design more and more accurate, but also computationally burdensome, simulation tools to obtain better performing initial designs that are more valuable in subsequent design stages. It constrains the computational budget to optimize the design space. These two factors unveil the need of a conceptual design methodology to use more efficiently sophisticated tools for engineering problems with several concept solutions and categorical design choices. Enhanced initial designs and discrete alternative selection are pursued. Advances in computational speed and the development of Bayesian adaptive sampling techniques have enabled the industry to move from the use of look-up tables and simplified models to complex physics-based tools in conceptual design. These techniques focus computational resources on promising design areas. Nevertheless, the vast majority of the work has been done on problems with continuous spaces, whereas concepts and categories are treated independently. However, observations show that engineering objectives experience similar topographical trends across many engineering alternatives. In order to address these challenges, two meta-models are developed. The first one borrows the Hamming distance and function space norms from machine learning and functional analysis, respectively. These distances allow defining categorical metrics that are used to build an unique probabilistic surrogate whose domain includes, not only continuous and integer variables, but also categorical ones. The second meta-model is based on a multi-fidelity approach that enhances a concept prediction with previous concept observations. These methodologies leverage similar trends seen from observations and make a better use of sample points increasing the quality of the output in the discrete alternative selection and initial designs for a given analysis budget. An extension of stochastic mixed-integer optimization techniques to include the categorical dimension is developed by adding appropriate generation, mutation, and crossover operators. The resulted stochastic algorithm is employed to adaptively sample mixed-integer-categorical design spaces. The proposed surrogates are compared against traditional independent methods for a set of canonical problems and a physics-based rotor-craft model on a screened design space. Next, adaptive sampling algorithms on the developed surrogates are applied to the same problems. These tests provide evidence of the merit of the proposed methodologies. Finally, a multi-objective rotor-craft design application is performed in a large domain space. This thesis provides several novel academic contributions. The first contribution is the development of new efficient surrogates for systems with categorical design choices. Secondly, an adaptive sampling algorithm is proposed for systems with mixed-integer-categorical design spaces. Finally, previously sampled concepts can be brought to construct efficient surrogates of novel concepts. With engineering judgment, design community could apply these contributions to discrete alternative selection and initial design assessment when similar topographical trends are observed across different categories and/or concepts. Also, it could be crucial to overcome the current cost of carrying a set of concepts and wider design spaces in the categorical dimension forward into preliminary design.

Dans la thèse nous nous occupons de l'estimation de la moyenne d'un petit domaine sous un modèle one-fold et utilisant MINQUE pour estimer les composantes de la variance, sous un modèle two-fold avec variances aléatoires, sous des plans noninformatifs et informatifs. / Doctorat en sciences, Orientation statistique / info:eu-repo/semantics/nonPublished

Double sampling procedure is adapted from a statistical branch called acceptance sampling. The first Shewhart-type double sampling monitoring scheme was introduced in the statistical process monitoring (SPM) field in 1974. The double sampling monitoring scheme has been proven to effectively decrease the sampling effort and, at the same time, to decrease the time to detect potential out-of-control situations when monitoring the location, variability, joint location and variability using univariate or multivariate techniques. Consequently, an overview is conducted to give a full account of all 76 publications on double sampling monitoring schemes that exist in the SPM literature. Moreover, in the review conducted here, these are categorized and summarized so that any research gaps in the SPM literature can easily be identified. Next, based on the knowledge gained from the literature review about the existing designs for monitoring the process mean, a new type of double sampling design is proposed. The new charting region design lead to a class of a control charts called a side-sensitive double sampling (SSDS) monitoring schemes. In this study, the SSDS scheme is implemented to monitor the process mean when the underlying process parameters are known as well as when they are unknown. A variety of run-length properties (i.e., the 5th, 25th, 50th, 75th, 95th percentiles, the average run-length (𝐴𝑅𝐿), standard deviation of the run-length (𝑆𝐷𝑅𝐿), the average sample size (𝐴𝑆𝑆) and the average extra quadratic loss (𝐴𝐸𝑄𝐿) metrics) are used to design and implement the new SSDS scheme. Comparisons with other established monitoring schemes (when parameters are known and unknown) indicate that the proposed SSDS scheme has a better overall performance. Illustrative examples are also given to facilitate the real-life implementation of the proposed SSDS schemes. Finally, a list of possible future research ideas is given with hope that this will stimulate more future research on simple as well as complex double sampling schemes (especially using the newly proposed SSDS design) for monitoring a variety of quality characteristics in the future. / Statistics / M. Sc. (Statistics)

The field of medicine is regularly faced with the challenge of utilizing information that is complicated or difficult to characterize. Physicians often must use their best judgment in reaching decisions or recommendations for treatment in the clinical setting. The goal of this thesis is to use innovative statistical tools in tackling three specific challenges of this nature from current healthcare applications. The first aim focuses on developing a novel approach to meta-analysis when combining binary data from multiple studies of paired design, particularly in cases of high heterogeneity between studies. The challenge is in properly accounting for heterogeneity when dealing with a low or moderate number of studies, and with a rarely occurring outcome. The proposed approach uses a Rasch model for translating data from multiple paired studies into a unified structure that allows for properly handling variability associated with both pair effects and study effects. Analysis is then performed using a Bayesian hierarchical structure, which accounts for heterogeneity in a direct way within the variances of the separate generating distributions for each model parameter. This approach is applied to the debated topic within the dental community of the comparative effectiveness of materials used for pit-and-fissure sealants. The second and third aims of this research both have applications in early detection of breast cancer. The interpretation of a mammogram is often difficult since signs of early disease are often minuscule, and the appearance of even normal tissue can be highly variable and complex. Physicians often have to consider many important pieces of the whole picture when trying to assess next steps. The final two aims focus on improving the interpretation of findings in mammograms to aid in early cancer detection. When dealing with high frequency and irregular data, as is seen in most medical images, the behaviors of these complex structures are often difficult or impossible to quantify by standard modeling techniques. But a commonly occurring phenomenon in high-frequency data is that of regular scaling. The second aim in this thesis is to develop and evaluate a wavelet-based scaling estimator that reduces the information in a mammogram down to an informative and low-dimensional quantification of the innate scaling behavior, optimized for use in classifying the tissue as cancerous or non-cancerous. The specific demands for this estimator are that it be robust with respect to distributional assumptions on the data, and with respect to outlier levels in the frequency domain representation of the data. The final aim in this research focuses on enhancing the visualization of microcalcifications that are too small to capture well on screening mammograms. Using scale-mixing discrete wavelet transform methods, the existing detail information contained in a very small and course image will be used to impute scaled details at finer levels. These "informed" finer details will then be used to produce an image of much higher resolution than the original, improving the visualization of the object. The goal is to also produce a confidence area for the true location of the shape's borders, allowing for more accurate feature assessment. Through the more accurate assessment of these very small shapes, physicians may be more confident in deciding next steps.

Indiana University-Purdue University Indianapolis (IUPUI) / Long term no-till (NT) farming can improve the CH4 oxidation capacity of agricultural lands through creation of a favorable soil environment for methanotrophs and diffusive gas transport. However, limited data is available to evaluate the merit of that contention. Although the potential for biological CH4 oxidation may exist in NT soils, restricted diffusion could limit expression of that potential in fine-textured soils. A study was conducted to assess the CH4 oxidation potential and gaseous diffusivity of soils under plow till (PT) and NT for > 50 years. Intact cores and composite soils samples (0-10 and 10-20 cm) were collected from NT and PT plots located at a well-drained site (Wooster silt loam) and at a poorly-drained (Crosby silt loam) site in Ohio. Adjacent deciduous forest soils were also sampled to determine maximum rate expected in undisturbed soils in the region. Regardless of study sites and soil depth, CH4 oxidation rate (measured at near ambient CH4) and oxidation potential (Vmax, measured at elevated CH4) were 3-4 and 1.5 times higher in NT than in PT soils, respectively. Activity in the NT soils approached (66-80 %) that in the forest soils. Half saturation constants (Km) and threshold for CH4 oxidation (Th) were lower in NT (Km: 100.5 µL CH4 L-1; Th: 0.5 µL CH4 L-1) than in PT soils (Km: 134 µL CH4 L-1; Th: 2.8 µL CH4 L-1) suggesting a greater affinity of long-term NT soils for CH4, and a possible shift in methanotrophic community composition. CH4 oxidation rates were lower in intact soil cores compared to sieved soils, suggesting that CH4 oxidation was limited by diffusion, a factor that could lead to lower field-measured CH4 uptake than suggested by biological oxidation capacity measured in the laboratory. Regardless of soil drainage characteristic, long-term NT resulted in significantly higher (2-3 times) CH4 diffusivity (mean: 2.5 x 10-3 cm2 s-1) than PT (1.5 x 10-3 cm2 s-1), probably due to improved soil aggregation and greater macro-pores volume in NT soils. Overall, these results confirm the positive impact of NT on the restoration of the biological (Vmax, Km and Th) and physical (diffusivity) soil attributes essential for CH4 uptake in croplands. Long-term implementation of NT farming can therefore contribute to the mitigation of CH4 emission from agriculture.

Indiana University-Purdue University Indianapolis (IUPUI) / Medication administration error remains a leading cause of preventable death. A gap exists in understanding attentional dynamics, such as nurse situation awareness (SA) while managing interruptions during medication administration. The aim was to describe SA during medication administration and interruption handling strategies. A crosssectional, descriptive design was used. Cognitive task analysis (CTA) methods informed analysis of 230 interruptions. Themes were analyzed by SA level. The nature of the stimuli noticed emerged as a Level 1 theme, in contrast to themes of uncertainty, relevance, and expectations (Level 2 themes). Projected or anticipated interventions (Level 3 themes) reflected workload balance between team and patient foregrounds. The prevalence of cognitive time-sharing during the medication administration process was significant or may be remarkable. Findings substantiated the importance of the concept of SA within nursing as well as the contribution of CTA in understanding the cognitive work of nursing during medication administration.

Indiana University-Purdue University Indianapolis (IUPUI) / A move toward care of residents in nursing homes where they are respected and heard is finally emerging. Common strategies used in nursing homes to improve quality of care for residents are integration of person-centered care and assessing care using satisfaction surveys. Although approaches of integrating person-centered care and satisfaction surveys have been valuable in improving nursing home quality, strategies of care that include things that matter from residents’ perspectives while living in nursing homes need investigation. The purpose of this qualitative descriptive study was to describe things that residents age 65 and older state matter to them while living in the long-term care sections of nursing homes. A qualitative mode of inquiry using purposeful sampling led to a natural unfolding of data that revealed things that mattered to residents. Content analysis was used to reduce the data in a manner that kept the data close to the context yet moved the data toward new ideas about including things that mattered to residents in nursing care. The findings revealed residents’ positive and negative experiences and addressed the question: How can nurses manage residents’ positive and negative aspects of care in nursing homes? This study substantiated the importance of developing nursing care strategies derived from residents’ descriptions of care. Finding ways to promote nurses’ investment in attitudes about a person-centered care philosophy is essential for successful person-centered care implementation. Enhancing nurses’ knowledge, skills, and attitudes with an investment in person centeredness will be more likely to put nurses in a position to role-model care that is person-centered from residents’ perspectives.