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Profile monitoring is a well-known approach used in statistical process control where the quality of the product or process is characterized by a profile or a relationship between a response variable and one or more explanatory variables. Profile monitoring is conducted over two phases, labeled as Phase I and Phase II. In Phase I profile monitoring, regression methods are used to model each profile and to detect the possible presence of out-of-control profiles in the historical data set (HDS). The out-of-control profiles can be detected by using the statis-tic. However, previous methods of calculating the statistic are based on using all the data in the HDS including the data from the out-of-control process. Consequently, the ability of using this method can be distorted if the HDS contains data from the out-of-control process. This work provides a new profile monitoring methodology for Phase I analysis. The proposed method, referred to as the cluster-based profile monitoring method, incorporates a cluster analysis phase before calculating the statistic. Before introducing our proposed cluster-based method in profile monitoring, this cluster-based method is demonstrated to work efficiently in robust regression, referred to as cluster-based bounded influence regression or CBI. It will be demonstrated that the CBI method provides a robust, efficient and high breakdown regression parameter estimator. The CBI method first represents the data space via a special set of points, referred to as anchor points. Then a collection of single-point-added ordinary least squares regression estimators forms the basis of a metric used in defining the similarity between any two observations. Cluster analysis then yields a main cluster containing at least half the observations, with the remaining observations comprising one or more minor clusters. An initial regression estimator arises from the main cluster, with a group-additive DFFITS argument used to carefully activate the minor clusters through a bounded influence regression frame work. CBI achieves a 50% breakdown point, is regression equivariant, scale and affine equivariant and distributionally is asymptotically normal. Case studies and Monte Carlo results demonstrate the performance advantage of CBI over other popular robust regression procedures regarding coefficient stabil-ity, scale estimation and standard errors. The cluster-based method in Phase I profile monitoring first replaces the data from each sampled unit with an estimated profile, using some appropriate regression method. The estimated parameters for the parametric profiles are obtained from parametric models while the estimated parameters for the nonparametric profiles are obtained from the p-spline model. The cluster phase clusters the profiles based on their estimated parameters and this yields an initial main cluster which contains at least half the profiles. The initial estimated parameters for the population average (PA) profile are obtained by fitting a mixed model (parametric or nonparametric) to those profiles in the main cluster. Profiles that are not contained in the initial main cluster are iteratively added to the main cluster provided their statistics are "small" and the mixed model (parametric or nonparametric) is used to update the estimated parameters for the PA profile. Those profiles contained in the final main cluster are considered as resulting from the in-control process while those not included are considered as resulting from an out-of-control process. This cluster-based method has been applied to monitor both parametric and nonparametric profiles. A simulated example, a Monte Carlo study and an application to a real data set demonstrates the detail of the algorithm and the performance advantage of this proposed method over a non-cluster-based method is demonstrated with respect to more accurate estimates of the PA parameters and improved classification performance criteria. When the profiles can be represented by vectors, the profile monitoring process is equivalent to the detection of multivariate outliers. For this reason, we also compared our proposed method to a popular method used to identify outliers when dealing with a multivariate response. Our study demonstrated that when the out-of-control process corresponds to a sustained shift, the cluster-based method using the successive difference estimator is clearly the superior method, among those methods we considered, based on all performance criteria. In addition, the influence of accurate Phase I estimates on the performance of Phase II control charts is presented to show the further advantage of the proposed method. A simple example and Monte Carlo results show that more accurate estimates from Phase I would provide more efficient Phase II control charts. / Ph. D.

The first part of my thesis is concerned with estimation for longitudinal data using generalized semi-parametric mixed models and multilevel generalized linear mixed models for a binary response. Likelihood based inferences are hindered by the lack of a closed form representation. Consequently, various integration approaches have been proposed. We propose a spherical radial integration based approach that takes advantage of the hierarchical structure of the data, which we call the 2 SR method. Compared to Pinheiro and Chao's multilevel Adaptive Gaussian quadrature, our proposed method has an improved time complexity with the number of functional evaluations scaling linearly in the number of subjects and in the dimension of random effects per level. Simulation studies show that our approach has similar to better accuracy compared to Gauss Hermite Quadrature (GHQ) and has better accuracy compared to PQL especially in the variance components. The second part of my thesis is concerned with identifying differentially expressed gene pathways/gene sets. We propose a logistic kernel machine to model the gene pathway effect with a binary response. Kernel machines were chosen since they account for gene interactions and clinical covariates. Furthermore, we established a connection between our logistic kernel machine with GLMMs allowing us to use ideas from the GLMM literature. For estimation and testing, we adopted Clarkson's spherical radial approach to perform the high dimensional integrations. For estimation, our performance in simulation studies is comparable to better than Bayesian approaches at a much lower computational cost. As for testing of the genetic pathway effect, our REML likelihood ratio test has increased power compared to a score test for simulated non-linear pathways. Additionally, our approach has three main advantages over previous methodologies: 1) our testing approach is self-contained rather than competitive, 2) our kernel machine approach can model complex pathway effects and gene-gene interactions, and 3) we test for the pathway effect adjusting for clinical covariates. Motivation for our work is the analysis of an Acute Lymphocytic Leukemia data set where we test for the genetic pathway effect and provide confidence intervals for the fixed effects.

This is a bachelor thesis which handles a balancing problem in a manual assembly line for mixed models. Many product variations that are assembled in an assembly line have different cycle times in each operation in the process. The products that are assembled in the line have also large variations in their lead times. This leads to large balancing losses leading to reduced productivity and efficiency. Many balancing losses occur due to the inefficient time that one of the products causes. Other balancing losses occur due to bottlenecks that occur in some operations. The purpose of this study is to investigate the balancing losses in a manual assembly line with mixed models. The goal is to develop a proposal for a balanced layout, as well as to minimize balancing losses and waste and maximize productivity as much as possible. Two research questions have been developed as guidelines for the study: RQ1: What factors can lead to balancing losses in a mixed-model assembly line? RQ2: How can a mixed-model assembly line be balanced without leading to other types of losses? The study is a case study that looks for problems in one case company. It is based on a literature study and the collection of real-world data, which has been collected at the case company by observations, interviews and documents that include data about production times and balancing reports.  A proposal on how balancing losses can be reduced in the best possible way has been developed. The inefficient time has been reduced and the assembly line has become more efficient and productive. With help of this improvement proposal, other types of losses could be avoided, such as losses of human resources and financial resources. This study aimed to reduce the balancing losses that one product causes in the assembly line. No rebalancing of the other products was done, but other products were considered so that the balancing of the product does not lead to extra imbalance on the other products in the line. It was important for the fall company to be able to implement a solution that does not lead to a lot of other losses. Based on the three solutions proposed, this solution was the most suitable for what the company wants. A new layout for the product’s stations has been proposed. With this layout, efficiency will increase, and downtime will decrease, thus increasing productivity. Proposal three shows that it is possible to balance a mixed-model assembly line, by terminating a product and removing it earlier from the assembly line.   Keywords: Line balancing, manual assembly, balancing loss, mixed products, mixed-model assembly / Det här är ett examensarbete på grundnivå, som behandlar ett balanseringsproblem i en manuell monteringslinje för mixade modeller. Det monteras många produktkonfigurationer som har olika cykeltider i varje station i processen. Produkterna som monteras i linan har även stora variationer i deras ledtider. Detta medför stora balanseringsförluster som leder till minskad produktivitet och effektivitet. Många balanseringsförluster uppstår på grund av den ineffektiva tiden som en av produkterna orsakar. Andra balanseringsförluster uppstår på grund av flaskhalsar som förekommer i vissa stationer.  Syftet med denna studie är att undersöka balansringsförlusterna i en manuell monteringslinje med mixade modeller. Målet är att ta fram ett förslag på en balanserad layout, samt att minimera balanseringsförlusterna och slöseri och maximera produktiviteten så mycket som möjligt.   Två forskningsfrågor har tagits fram som riktlinjer för studien: F1: Vilka faktorer kan leda till balanseringsförluster i en mixad-modellmonteringslinje?  F2: Hur kan en mixad-modellmonteringslina balanseras utan att leda till andra typer av förluster? Studien är en fallstudie som undersöker problem hos ett fallföretag. Studien är baserad på en initial litteraturstudie och insamlad data, som har samlats in från fallföretaget via observationer, intervjuer samt dokument med data om produktionstider och balansrapporter.  Ett förslag på hur balanseringsförlusterna kan minskas på bästa möjliga sätt har tagits fram. Den ineffektiva tiden har minskats och monteringslinan har blivit effektivare och produktivare. Med hjälp av det här förbättringsförslaget, kunde andra typer av förluster undvikas, som exempelvis förluster av mänskliga resurser och ekonomiska resurser.   Denna studie är gjord för att minska balanseringsförlusterna som en av produkterna orsakar i monteringslinjen. Ingen ombalansering på de andra produkterna gjordes, men det togs hänsyn till andra produkter så att balanseringen av den produkten inte leder till extra obalans på de andra produkter i linan. Det var viktigt för fallföretaget att kunna implementera en lösning som inte leder till massa andra förluster. Utifrån de tre lösningarna som föreslagits var denna lösning den mest lämplig för vad företaget önskar sig. En ny layout på produktens stationer har tagits fram. Med denna layout kommer effektiviteten att öka och dötiden minska, och därmed ökas produktiviteten. Förslag tre visar sig att det är möjligt att kunna balansera en mixad-modellmonteringslina, genom att avsluta en produkt och ta ut den tidigare ur monteringslinan.   Nyckelord: Line balancing, manuell montering, balanseringsförluster, mixed products, mixed-model assembly line.

Just-In-Time (JIT) production systems is a popular area for researchers but real-world issues such as sequence dependent setups are often overlooked. This research investigates an approach for determining stability and an approach for mixed product sequencing in production systems with sequence dependent setups and buffer thresholds which signal replenishment of a given buffer. Production systems in this research operate under JIT pull production principles by producing only when demand exists and idle when no demand exists. In the first approach, an iterative method is presented to determine stability for a multi-product production system that operates with replenishment signals and may have sequence dependent setups. In this method, a network of nodes representing machine states and arcs representing the buffer inventory levels is used to find a stable trajectory for the production system via an iterative procedure. The method determines suitable buffer levels for the production system that ensure that a trajectory originating from any point within a buffer region will always map to a point contained on another buffer region for all future mappings. This iterative method for determining the stability of a production system was implemented using an algorithm to calculate the buffer inventory regions for all arcs in a given arc-node network. The algorithm showed favorable results for two and three product systems in which sequence dependent setups may exist. In the second approach, a product sequencing algorithm determines a product sequence for a production system based on system parameters – setup times, buffer levels, usage rates, production rates, etc. The algorithm selects a product by evaluating the goodness of each product that has reached the replenishment threshold at the current time. The algorithm also incorporates a lookahead function that calculates the goodness for some time interval into the future. The lookahead function considers all branches of the tree of potential sequences to prevent the sequence from travelling down a dead-end branch in which the system will be unable to avoid a depleted buffer. The sequencing algorithm allows the user to weight the five terms of the goodness equations (current and lookahead) to control the behavior of the sequence.

In this study, I investigated how proficiently seventh-grade students enrolled in two Southwestern schools solve algebra word problems. I analyzed various factors that could affect this proficiency and explored the differences between English Learners (ELs) and native English Primary students (EPs). I collected the data as part of the Animal Watch project, a computer-based initiative designed to improve the mathematical skills of children from grades 5-8 in the Southwest. A sample of 86 students (26 ELs and 60 EPs), clustered in four different classes, was used for this project. A Generalized Linear Mixed Model (GLMM) approach with the GLIMMIX procedure in SAS 9.3 showed that students from the classes that had a higher percentage of EL students performed better than those in the classes where the EL concentration was lower. Classes with more EL males were better at learning mathematics than classes with more EP females. The results also indicated: (a) a positive correlation between the students' ability to solve algebra word problems on their first attempt and their success ratio in solving all problems, and (b) a negative correlation between the percentage of problems solved correctly and those considered too hard from the very beginning. I conclude my dissertation by making specific recommendations for further research.

Master of Science / Department of Statistics / Christopher Vahl / In animal health research, it is quite common for a clinical trial to be designed to demonstrate the efficacy of a new drug where a binary response variable is measured on an individual experimental animal (i.e., the observational unit). However, the investigational treatments are applied to groups of animals instead of an individual animal. This means the experimental unit is the group of animals and the response variable could be modeled with the binomial distribution. Also, the responses of animals within the same experimental unit may then be statistically dependent on each other. The usual logit model for a binary response assumes that all observations are independent. In this report, a logit model with a random error term representing the group of animals is considered. This is model belongs to a class of models referred to as generalized linear mixed models and is commonly fit using the SAS System procedure PROC GLIMMIX. Furthermore, practitioners often adjust the denominator degrees of freedom of the test statistic produced by PROC GLIMMIX using one of several different methods. In this report, a simulation study was performed over a variety of different parameter settings to compare the effects on the type I error rate and power of two methods for adjusting the denominator degrees of freedom, namely “DDFM = KENWARDROGER” and “DDFM = NONE”. Despite its reputation for fine performance in linear mixed models with normally distributed errors, the “DDFM = KENWARDROGER” option tended to perform poorly more often than the “DDFM = NONE” option in the logistic regression model with one random effect.

Auditory Steady-State Response (ASSR) is a promising tool for detecting hearing loss. In this project, we analyzed hearing threshold data obtained from two ASSR methods and a gold standard, pure tone audiometry, applied to both normal and hearing-impaired subjects. We constructed a repeated measures linear model to identify factors that show significant differences in the mean response. The analysis shows that there are significant differences due to hearing status (normal or impaired) and ASSR method, and that there is a significant interaction between hearing status and test signal frequency. The second task of this project was to predict the PTA threshold (gold standard) from the ASSR-A and ASSR-B thresholds separately at each frequency, in order to measure how accurate the ASSR measurements are and to obtain a ¡°correction function¡± to correct the bias in the ASSR measurements. We used two approaches. In the first, we modeled the relation of the PTA responses to the ASSR values for the two hearing status groups as a mixture model and tried two prediction methods. The mixture modeling was successful, but the predictions gave disappointing results. A second approach, using logistic regression to predict group membership based on ASSR value and then using those predictions to obtain a predictor of the PTA value, gave successful results.

O objetivo do presente trabalho é analisar a presença da restrição financeira nas decisões de investimentos em condições de incerteza de um conjunto de 1223 empresas brasileiras no período de 1986 a 2006. A incerteza é incorporada no modelo de investimento considerando o comportamento das variáveis vendas e fluxo de caixa como um movimento browniano com drift. Além disso, a variável fluxo de caixa é analisada em baixa e alta incerteza, considerando três diferentes medidas para a incerteza: a variação anual do índice Ibovespa, o desvio-padrão de vendas e de fluxo de caixa. Já para considerar o efeito da restrição financeira sobre as decisões de investimento as firmas são agrupadas de acordo com o grau de intensidade de capital, tamanho da firma e grau tecnológico. A estimação dos parâmetros da equação do investimento é realizada considerando-se o modelo misto. O modelo misto, ainda não utilizado em estudos brasileiros na análise do comportamento das decisões de investimento, permite considerar a heterogeneidade nos coeficientes das variáveis independentes, o que evita o viés introduzido pela suposição de homogeneidade. Os resultados obtidos neste estudo mostraram uma maior sensibilidade do investimento ao fluxo de caixa para as firmas mais intensivas em capital, firmas de médio porte e firmas com alto grau tecnológico. Esses resultados se mantêm quando a variável fluxo de caixa é analisada em alta incerteza, ou seja, o investimento das firmas com alta intensidade de capital, médio porte e com alto grau tecnológico é mais sensível ao fluxo de caixa em condições de alta incerteza. / The aim of this research is to analyze the presence of financial constraints on investments decisions under uncertainty using data from 1223 Brazilian firms over the 1986 to 2006 period. Uncertainty is incorporated in the model of investment decisions considering the sales and cash flow variables, which are estimated by a stochastic equation of Brownian motion. In addition, the variable cash flow is grouped by high and low uncertainty according to annual rate of the Ibovespa index, the standard deviation of sales and cash flow. To consider the effects of financial constraints on firms investment decisions, this study used the degree of capital intensity, size, and the technological degree to classify firms. The investment equation parameters are estimated considering the mixed model. The mixed model, it has not yet been used in analysis of Brazilian firms, allows considering the heterogeneity on explanatory variables, which avoids the bias introduced by assumption of homogeneity. The results show greater sensitivity of investment to cash flow for more capital-intensive firms, medium and high-tech ones. These results keep when cash-flow variable is analyzed by high uncertainty, i.e, for these firms the investment is more sensitive to cash flow under higher uncertainty.

O milho é uma espécie alógama cujo produto comercial são os híbridos, os quais originam-se do cruzamento de duas linhagens endogâmicas. Uma forma para obtenção de tais linhagens é por meio das técnicas de indução de haploidia e posterior obtenção dos duplo-haploides, permitindo até 100% de homozigose. Essas técnicas retornam resultados importantes no melhoramento de milho. Uma variável de interesse importante, obtida a partir dessas técnicas é a taxa de indução de haploidia, a qual trata-se de uma proporção entre o número de sementes haploides e o número total de sementes. O conjunto de dados foi obtido pelo cruzamento da linhagem indutora LI- ESALQ, com cinco genótipos comerciais de milho (2B587PW, 30F53H, BM820, DKB390 e STATUS VIPTERA), em duas gerações F1 e F2, por meio de um delineamento em blocos ao acaso, na área experimental do Departamento de Genética da ESALQ/USP. A teoria dos modelos lineares generalizados (MLGs) possibilita mais opções para a distribuição da variável resposta, exigindo somente que a mesma pertença à família exponencial sob a forma canônica. Tal classe de distribuições pode ser ainda expandida para modelos que permitem efeitos aleatórios no preditor linear, caracterizando a classe dos modelos lineares generalizados mistos (MLGMs). O objetivo deste trabalho foi analisar a taxa de indução de haploidia em milho tropical, utilizando um modelo binomial misto, com efeito aleatório em nível de indivíduo. O método de estimação foi o de máxima verossimilhança. Com base em tal modelagem, verificou-se que o genótipo 30F53H, destacou-se em relação aos demais quanto à eficiência da taxa de indução de haploidia. Todas as análises foram implementadas no software R. / The maize is an allogeneic species whose commercial product are the hybrids, which are gerated by the crossing of two endogenous lines. An alternative to obtain these lines is using the haploid induction techniques and subsequent doubled haploid production, that allows up to 100% homozygous. Artificial production of doubled haploids is important in plant breeding. An important variable, that results from these techniques, is the haploid induction rate, which is a proportion between the number of haploid seeds and the total number of seeds. The data set was obtained by crossing the inductive line LI-ESALQ, with five commercial genotypes of corn (2B587PW, 30F53H, BM820, DKB390 and STATUS VIPTERA), in two generations F1 e F2, in a randomized block design, in the experimental area of Department of Genetics, ESALQ/USP. The generalized linear models (GLMs) allow more options for the variable response distribution, requiring only that it belongs to the exponential family in canonical form. The GLM class can be expanded to models that allow random effects in the linear predictor, the mixed generalized linear models (MGLM) class. This work aimed to analyze the haploid induction rate in the tropical maize. The binomial mixed model, that included random effects in individual level, was proposed. The maximum likelihood method was used to estimate the parameters. The result revealed that the genotype 30F53H stands out in relation to the others regarding the efficiency in the haploid induction rate. All the analyzes were implemented in the software R.