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- All Subjects: Statistics
- Creators: Montgomery, Douglas C.
- Creators: Wilson, Jeffrey
Description
Many longitudinal studies, especially in clinical trials, suffer from missing data issues. Most estimation procedures assume that the missing values are ignorable or missing at random (MAR). However, this assumption leads to unrealistic simplification and is implausible for many cases. For example, an investigator is examining the effect of treatment on depression. Subjects are scheduled with doctors on a regular basis and asked questions about recent emotional situations. Patients who are experiencing severe depression are more likely to miss an appointment and leave the data missing for that particular visit. Data that are not missing at random may produce bias in results if the missing mechanism is not taken into account. In other words, the missing mechanism is related to the unobserved responses. Data are said to be non-ignorable missing if the probabilities of missingness depend on quantities that might not be included in the model. Classical pattern-mixture models for non-ignorable missing values are widely used for longitudinal data analysis because they do not require explicit specification of the missing mechanism, with the data stratified according to a variety of missing patterns and a model specified for each stratum. However, this usually results in under-identifiability, because of the need to estimate many stratum-specific parameters even though the eventual interest is usually on the marginal parameters. Pattern mixture models have the drawback that a large sample is usually required. In this thesis, two studies are presented. The first study is motivated by an open problem from pattern mixture models. Simulation studies from this part show that information in the missing data indicators can be well summarized by a simple continuous latent structure, indicating that a large number of missing data patterns may be accounted by a simple latent factor. Simulation findings that are obtained in the first study lead to a novel model, a continuous latent factor model (CLFM). The second study develops CLFM which is utilized for modeling the joint distribution of missing values and longitudinal outcomes. The proposed CLFM model is feasible even for small sample size applications. The detailed estimation theory, including estimating techniques from both frequentist and Bayesian perspectives is presented. Model performance and evaluation are studied through designed simulations and three applications. Simulation and application settings change from correctly-specified missing data mechanism to mis-specified mechanism and include different sample sizes from longitudinal studies. Among three applications, an AIDS study includes non-ignorable missing values; the Peabody Picture Vocabulary Test data have no indication on missing data mechanism and it will be applied to a sensitivity analysis; the Growth of Language and Early Literacy Skills in Preschoolers with Developmental Speech and Language Impairment study, however, has full complete data and will be used to conduct a robust analysis. The CLFM model is shown to provide more precise estimators, specifically on intercept and slope related parameters, compared with Roy's latent class model and the classic linear mixed model. This advantage will be more obvious when a small sample size is the case, where Roy's model experiences challenges on estimation convergence. The proposed CLFM model is also robust when missing data are ignorable as demonstrated through a study on Growth of Language and Early Literacy Skills in Preschoolers.
ContributorsZhang, Jun (Author) / Reiser, Mark R. (Thesis advisor) / Barber, Jarrett (Thesis advisor) / Kao, Ming-Hung (Committee member) / Wilson, Jeffrey (Committee member) / St Louis, Robert D. (Committee member) / Arizona State University (Publisher)
Created2013
Description
Nowadays product reliability becomes the top concern of the manufacturers and customers always prefer the products with good performances under long period. In order to estimate the lifetime of the product, accelerated life testing (ALT) is introduced because most of the products can last years even decades. Much research has been done in the ALT area and optimal design for ALT is a major topic. This dissertation consists of three main studies. First, a methodology of finding optimal design for ALT with right censoring and interval censoring have been developed and it employs the proportional hazard (PH) model and generalized linear model (GLM) to simplify the computational process. A sensitivity study is also given to show the effects brought by parameters to the designs. Second, an extended version of I-optimal design for ALT is discussed and then a dual-objective design criterion is defined and showed with several examples. Also in order to evaluate different candidate designs, several graphical tools are developed. Finally, when there are more than one models available, different model checking designs are discussed.
ContributorsYang, Tao (Author) / Pan, Rong (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Borror, Connie (Committee member) / Rigdon, Steve (Committee member) / Arizona State University (Publisher)
Created2013
Description
This thesis presents a meta-analysis of lead-free solder reliability. The qualitative analyses of the failure modes of lead- free solder under different stress tests including drop test, bend test, thermal test and vibration test are discussed. The main cause of failure of lead- free solder is fatigue crack, and the speed of propagation of the initial crack could differ from different test conditions and different solder materials. A quantitative analysis about the fatigue behavior of SAC lead-free solder under thermal preconditioning process is conducted. This thesis presents a method of making prediction of failure life of solder alloy by building a Weibull regression model. The failure life of solder on circuit board is assumed Weibull distributed. Different materials and test conditions could affect the distribution by changing the shape and scale parameters of Weibull distribution. The method is to model the regression of parameters with different test conditions as predictors based on Bayesian inference concepts. In the process of building regression models, prior distributions are generated according to the previous studies, and Markov Chain Monte Carlo (MCMC) is used under WinBUGS environment.
ContributorsXu, Xinyue (Author) / Pan, Rong (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Wu, Teresa (Committee member) / Arizona State University (Publisher)
Created2014
Description
The main objective of this research is to develop an approach to PV module lifetime prediction. In doing so, the aim is to move from empirical generalizations to a formal predictive science based on data-driven case studies of the crystalline silicon PV systems. The evaluation of PV systems aged 5 to 30 years old that results in systematic predictive capability that is absent today. The warranty period provided by the manufacturers typically range from 20 to 25 years for crystalline silicon modules. The end of lifetime (for example, the time-to-degrade by 20% from rated power) of PV modules is usually calculated using a simple linear extrapolation based on the annual field degradation rate (say, 0.8% drop in power output per year). It has been 26 years since systematic studies on solar PV module lifetime prediction were undertaken as part of the 11-year flat-plate solar array (FSA) project of the Jet Propulsion Laboratory (JPL) funded by DOE. Since then, PV modules have gone through significant changes in construction materials and design; making most of the field data obsolete, though the effect field stressors on the old designs/materials is valuable to be understood. Efforts have been made to adapt some of the techniques developed to the current technologies, but they are too often limited in scope and too reliant on empirical generalizations of previous results. Some systematic approaches have been proposed based on accelerated testing, but no or little experimental studies have followed. Consequently, the industry does not exactly know today how to test modules for a 20 - 30 years lifetime.
This research study focuses on the behavior of crystalline silicon PV module technology in the dry and hot climatic condition of Tempe/Phoenix, Arizona. A three-phase approach was developed: (1) A quantitative failure modes, effects, and criticality analysis (FMECA) was developed for prioritizing failure modes or mechanisms in a given environment; (2) A time-series approach was used to model environmental stress variables involved and prioritize their effect on the power output drop; and (3) A procedure for developing a prediction model was proposed for the climatic specific condition based on accelerated degradation testing
This research study focuses on the behavior of crystalline silicon PV module technology in the dry and hot climatic condition of Tempe/Phoenix, Arizona. A three-phase approach was developed: (1) A quantitative failure modes, effects, and criticality analysis (FMECA) was developed for prioritizing failure modes or mechanisms in a given environment; (2) A time-series approach was used to model environmental stress variables involved and prioritize their effect on the power output drop; and (3) A procedure for developing a prediction model was proposed for the climatic specific condition based on accelerated degradation testing
ContributorsKuitche, Joseph Mathurin (Author) / Pan, Rong (Thesis advisor) / Tamizhmani, Govindasamy (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Wu, Teresa (Committee member) / Arizona State University (Publisher)
Created2014
Description
In this era of fast computational machines and new optimization algorithms, there have been great advances in Experimental Designs. We focus our research on design issues in generalized linear models (GLMs) and functional magnetic resonance imaging(fMRI). The first part of our research is on tackling the challenging problem of constructing
exact designs for GLMs, that are robust against parameter, link and model
uncertainties by improving an existing algorithm and providing a new one, based on using a continuous particle swarm optimization (PSO) and spectral clustering. The proposed algorithm is sufficiently versatile to accomodate most popular design selection criteria, and we concentrate on providing robust designs for GLMs, using the D and A optimality criterion. The second part of our research is on providing an algorithm
that is a faster alternative to a recently proposed genetic algorithm (GA) to construct optimal designs for fMRI studies. Our algorithm is built upon a discrete version of the PSO.
exact designs for GLMs, that are robust against parameter, link and model
uncertainties by improving an existing algorithm and providing a new one, based on using a continuous particle swarm optimization (PSO) and spectral clustering. The proposed algorithm is sufficiently versatile to accomodate most popular design selection criteria, and we concentrate on providing robust designs for GLMs, using the D and A optimality criterion. The second part of our research is on providing an algorithm
that is a faster alternative to a recently proposed genetic algorithm (GA) to construct optimal designs for fMRI studies. Our algorithm is built upon a discrete version of the PSO.
ContributorsTemkit, M'Hamed (Author) / Kao, Jason (Thesis advisor) / Reiser, Mark R. (Committee member) / Barber, Jarrett (Committee member) / Montgomery, Douglas C. (Committee member) / Pan, Rong (Committee member) / Arizona State University (Publisher)
Created2014
Description
It is common in the analysis of data to provide a goodness-of-fit test to assess the performance of a model. In the analysis of contingency tables, goodness-of-fit statistics are frequently employed when modeling social science, educational or psychological data where the interest is often directed at investigating the association among multi-categorical variables. Pearson's chi-squared statistic is well-known in goodness-of-fit testing, but it is sometimes considered to produce an omnibus test as it gives little guidance to the source of poor fit once the null hypothesis is rejected. However, its components can provide powerful directional tests. In this dissertation, orthogonal components are used to develop goodness-of-fit tests for models fit to the counts obtained from the cross-classification of multi-category dependent variables. Ordinal categories are assumed. Orthogonal components defined on marginals are obtained when analyzing multi-dimensional contingency tables through the use of the QR decomposition. A subset of these orthogonal components can be used to construct limited-information tests that allow one to identify the source of lack-of-fit and provide an increase in power compared to Pearson's test. These tests can address the adverse effects presented when data are sparse. The tests rely on the set of first- and second-order marginals jointly, the set of second-order marginals only, and the random forest method, a popular algorithm for modeling large complex data sets. The performance of these tests is compared to the likelihood ratio test as well as to tests based on orthogonal polynomial components. The derived goodness-of-fit tests are evaluated with studies for detecting two- and three-way associations that are not accounted for by a categorical variable factor model with a single latent variable. In addition the tests are used to investigate the case when the model misspecification involves parameter constraints for large and sparse contingency tables. The methodology proposed here is applied to data from the 38th round of the State Survey conducted by the Institute for Public Policy and Michigan State University Social Research (2005) . The results illustrate the use of the proposed techniques in the context of a sparse data set.
ContributorsMilovanovic, Jelena (Author) / Young, Dennis (Thesis advisor) / Reiser, Mark R. (Thesis advisor) / Wilson, Jeffrey (Committee member) / Eubank, Randall (Committee member) / Yang, Yan (Committee member) / Arizona State University (Publisher)
Created2011
Description
Value-added models (VAMs) are used by many states to assess contributions of individual teachers and schools to students' academic growth. The generalized persistence VAM, one of the most flexible in the literature, estimates the ``value added'' by individual teachers to their students' current and future test scores by employing a mixed model with a longitudinal database of test scores. There is concern, however, that missing values that are common in the longitudinal student scores can bias value-added assessments, especially when the models serve as a basis for personnel decisions -- such as promoting or dismissing teachers -- as they are being used in some states. Certain types of missing data require that the VAM be modeled jointly with the missingness process in order to obtain unbiased parameter estimates. This dissertation studies two problems. First, the flexibility and multimembership random effects structure of the generalized persistence model lead to computational challenges that have limited the model's availability. To this point, no methods have been developed for scalable maximum likelihood estimation of the model. An EM algorithm to compute maximum likelihood estimates efficiently is developed, making use of the sparse structure of the random effects and error covariance matrices. The algorithm is implemented in the package GPvam in R statistical software. Illustrations of the gains in computational efficiency achieved by the estimation procedure are given. Furthermore, to address the presence of potentially nonignorable missing data, a flexible correlated random effects model is developed that extends the generalized persistence model to jointly model the test scores and the missingness process, allowing the process to depend on both students and teachers. The joint model gives the ability to test the sensitivity of the VAM to the presence of nonignorable missing data. Estimation of the model is challenging due to the non-hierarchical dependence structure and the resulting intractable high-dimensional integrals. Maximum likelihood estimation of the model is performed using an EM algorithm with fully exponential Laplace approximations for the E step. The methods are illustrated with data from university calculus classes and with data from standardized test scores from an urban school district.
ContributorsKarl, Andrew (Author) / Lohr, Sharon L (Thesis advisor) / Yang, Yan (Thesis advisor) / Kao, Ming-Hung (Committee member) / Montgomery, Douglas C. (Committee member) / Wilson, Jeffrey R (Committee member) / Arizona State University (Publisher)
Created2012
Description
This dissertation presents methods for addressing research problems that currently can only adequately be solved using Quality Reliability Engineering (QRE) approaches especially accelerated life testing (ALT) of electronic printed wiring boards with applications to avionics circuit boards. The methods presented in this research are generally applicable to circuit boards, but the data generated and their analysis is for high performance avionics. Avionics equipment typically requires 20 years expected life by aircraft equipment manufacturers and therefore ALT is the only practical way of performing life test estimates. Both thermal and vibration ALT induced failure are performed and analyzed to resolve industry questions relating to the introduction of lead-free solder product and processes into high reliability avionics. In chapter 2, thermal ALT using an industry standard failure machine implementing Interconnect Stress Test (IST) that simulates circuit board life data is compared to real production failure data by likelihood ratio tests to arrive at a mechanical theory. This mechanical theory results in a statistically equivalent energy bound such that failure distributions below a specific energy level are considered to be from the same distribution thus allowing testers to quantify parameter setting in IST prior to life testing. In chapter 3, vibration ALT comparing tin-lead and lead-free circuit board solder designs involves the use of the likelihood ratio (LR) test to assess both complete failure data and S-N curves to present methods for analyzing data. Failure data is analyzed using Regression and two-way analysis of variance (ANOVA) and reconciled with the LR test results that indicating that a costly aging pre-process may be eliminated in certain cases. In chapter 4, vibration ALT for side-by-side tin-lead and lead-free solder black box designs are life tested. Commercial models from strain data do not exist at the low levels associated with life testing and need to be developed because testing performed and presented here indicate that both tin-lead and lead-free solders are similar. In addition, earlier failures due to vibration like connector failure modes will occur before solder interconnect failures.
ContributorsJuarez, Joseph Moses (Author) / Montgomery, Douglas C. (Thesis advisor) / Borror, Connie M. (Thesis advisor) / Gel, Esma (Committee member) / Mignolet, Marc (Committee member) / Pan, Rong (Committee member) / Arizona State University (Publisher)
Created2012
Description
Mostly, manufacturing tolerance charts are used these days for manufacturing tolerance transfer but these have the limitation of being one dimensional only. Some research has been undertaken for the three dimensional geometric tolerances but it is too theoretical and yet to be ready for operator level usage. In this research, a new three dimensional model for tolerance transfer in manufacturing process planning is presented that is user friendly in the sense that it is built upon the Coordinate Measuring Machine (CMM) readings that are readily available in any decent manufacturing facility. This model can take care of datum reference change between non orthogonal datums (squeezed datums), non-linearly oriented datums (twisted datums) etc. Graph theoretic approach based upon ACIS, C++ and MFC is laid out to facilitate its implementation for automation of the model. A totally new approach to determining dimensions and tolerances for the manufacturing process plan is also presented. Secondly, a new statistical model for the statistical tolerance analysis based upon joint probability distribution of the trivariate normal distributed variables is presented. 4-D probability Maps have been developed in which the probability value of a point in space is represented by the size of the marker and the associated color. Points inside the part map represent the pass percentage for parts manufactured. The effect of refinement with form and orientation tolerance is highlighted by calculating the change in pass percentage with the pass percentage for size tolerance only. Delaunay triangulation and ray tracing algorithms have been used to automate the process of identifying the points inside and outside the part map. Proof of concept software has been implemented to demonstrate this model and to determine pass percentages for various cases. The model is further extended to assemblies by employing convolution algorithms on two trivariate statistical distributions to arrive at the statistical distribution of the assembly. Map generated by using Minkowski Sum techniques on the individual part maps is superimposed on the probability point cloud resulting from convolution. Delaunay triangulation and ray tracing algorithms are employed to determine the assembleability percentages for the assembly.
ContributorsKhan, M Nadeem Shafi (Author) / Phelan, Patrick E (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Farin, Gerald (Committee member) / Roberts, Chell (Committee member) / Henderson, Mark (Committee member) / Arizona State University (Publisher)
Created2011
Description
Optimal experimental design for generalized linear models is often done using a pseudo-Bayesian approach that integrates the design criterion across a prior distribution on the parameter values. This approach ignores the lack of utility of certain models contained in the prior, and a case is demonstrated where the heavy focus on such hopeless models results in a design with poor performance and with wild swings in coverage probabilities for Wald-type confidence intervals. Design construction using a utility-based approach is shown to result in much more stable coverage probabilities in the area of greatest concern.
The pseudo-Bayesian approach can be applied to the problem of optimal design construction under dependent observations. Often, correlation between observations exists due to restrictions on randomization. Several techniques for optimal design construction are proposed in the case of the conditional response distribution being a natural exponential family member but with a normally distributed block effect . The reviewed pseudo-Bayesian approach is compared to an approach based on substituting the marginal likelihood with the joint likelihood and an approach based on projections of the score function (often called quasi-likelihood). These approaches are compared for several models with normal, Poisson, and binomial conditional response distributions via the true determinant of the expected Fisher information matrix where the dispersion of the random blocks is considered a nuisance parameter. A case study using the developed methods is performed.
The joint and quasi-likelihood methods are then extended to address the case when the magnitude of random block dispersion is of concern. Again, a simulation study over several models is performed, followed by a case study when the conditional response distribution is a Poisson distribution.
The pseudo-Bayesian approach can be applied to the problem of optimal design construction under dependent observations. Often, correlation between observations exists due to restrictions on randomization. Several techniques for optimal design construction are proposed in the case of the conditional response distribution being a natural exponential family member but with a normally distributed block effect . The reviewed pseudo-Bayesian approach is compared to an approach based on substituting the marginal likelihood with the joint likelihood and an approach based on projections of the score function (often called quasi-likelihood). These approaches are compared for several models with normal, Poisson, and binomial conditional response distributions via the true determinant of the expected Fisher information matrix where the dispersion of the random blocks is considered a nuisance parameter. A case study using the developed methods is performed.
The joint and quasi-likelihood methods are then extended to address the case when the magnitude of random block dispersion is of concern. Again, a simulation study over several models is performed, followed by a case study when the conditional response distribution is a Poisson distribution.
ContributorsHassler, Edgar (Author) / Montgomery, Douglas C. (Thesis advisor) / Silvestrini, Rachel T. (Thesis advisor) / Borror, Connie M. (Committee member) / Pan, Rong (Committee member) / Arizona State University (Publisher)
Created2015