Theses and Dissertations
This collection includes both ASU Theses and Dissertations, submitted by graduate students, and the Barrett, Honors College theses submitted by undergraduate students.
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- Creators: Montgomery, Douglas C.
Description
No-confounding designs (NC) in 16 runs for 6, 7, and 8 factors are non-regular fractional factorial designs that have been suggested as attractive alternatives to the regular minimum aberration resolution IV designs because they do not completely confound any two-factor interactions with each other. These designs allow for potential estimation of main effects and a few two-factor interactions without the need for follow-up experimentation. Analysis methods for non-regular designs is an area of ongoing research, because standard variable selection techniques such as stepwise regression may not always be the best approach. The current work investigates the use of the Dantzig selector for analyzing no-confounding designs. Through a series of examples it shows that this technique is very effective for identifying the set of active factors in no-confounding designs when there are three of four active main effects and up to two active two-factor interactions.
To evaluate the performance of Dantzig selector, a simulation study was conducted and the results based on the percentage of type II errors are analyzed. Also, another alternative for 6 factor NC design, called the Alternate No-confounding design in six factors is introduced in this study. The performance of this Alternate NC design in 6 factors is then evaluated by using Dantzig selector as an analysis method. Lastly, a section is dedicated to comparing the performance of NC-6 and Alternate NC-6 designs.
To evaluate the performance of Dantzig selector, a simulation study was conducted and the results based on the percentage of type II errors are analyzed. Also, another alternative for 6 factor NC design, called the Alternate No-confounding design in six factors is introduced in this study. The performance of this Alternate NC design in 6 factors is then evaluated by using Dantzig selector as an analysis method. Lastly, a section is dedicated to comparing the performance of NC-6 and Alternate NC-6 designs.
ContributorsKrishnamoorthy, Archana (Author) / Montgomery, Douglas C. (Thesis advisor) / Borror, Connie (Thesis advisor) / Pan, Rong (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
This dissertation presents methods for the evaluation of ocular surface protection during natural blink function. The evaluation of ocular surface protection is especially important in the diagnosis of dry eye and the evaluation of dry eye severity in clinical trials. Dry eye is a highly prevalent disease affecting vast numbers (between 11% and 22%) of an aging population. There is only one approved therapy with limited efficacy, which results in a huge unmet need. The reason so few drugs have reached approval is a lack of a recognized therapeutic pathway with reproducible endpoints. While the interplay between blink function and ocular surface protection has long been recognized, all currently used evaluation techniques have addressed blink function in isolation from tear film stability, the gold standard of which is Tear Film Break-Up Time (TFBUT). In the first part of this research a manual technique of calculating ocular surface protection during natural blink function through the use of video analysis is developed and evaluated for it's ability to differentiate between dry eye and normal subjects, the results are compared with that of TFBUT. In the second part of this research the technique is improved in precision and automated through the use of video analysis algorithms. This software, called the OPI 2.0 System, is evaluated for accuracy and precision, and comparisons are made between the OPI 2.0 System and other currently recognized dry eye diagnostic techniques (e.g. TFBUT). In the third part of this research the OPI 2.0 System is deployed for use in the evaluation of subjects before, immediately after and 30 minutes after exposure to a controlled adverse environment (CAE), once again the results are compared and contrasted against commonly used dry eye endpoints. The results demonstrate that the evaluation of ocular surface protection using the OPI 2.0 System offers superior accuracy to the current standard, TFBUT.
ContributorsAbelson, Richard (Author) / Montgomery, Douglas C. (Thesis advisor) / Borror, Connie (Committee member) / Shunk, Dan (Committee member) / Pan, Rong (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
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
Description
The majority of research in experimental design has, to date, been focused on designs when there is only one type of response variable under consideration. In a decision-making process, however, relying on only one objective or criterion can lead to oversimplified, sub-optimal decisions that ignore important considerations. Incorporating multiple, and likely competing, objectives is critical during the decision-making process in order to balance the tradeoffs of all potential solutions. Consequently, the problem of constructing a design for an experiment when multiple types of responses are of interest does not have a clear answer, particularly when the response variables have different distributions. Responses with different distributions have different requirements of the design.
Computer-generated optimal designs are popular design choices for less standard scenarios where classical designs are not ideal. This work presents a new approach to experimental designs for dual-response systems. The normal, binomial, and Poisson distributions are considered for the potential responses. Using the D-criterion for the linear model and the Bayesian D-criterion for the nonlinear models, a weighted criterion is implemented in a coordinate-exchange algorithm. The designs are evaluated and compared across different weights. The sensitivity of the designs to the priors supplied in the Bayesian D-criterion is explored in the third chapter of this work.
The final section of this work presents a method for a decision-making process involving multiple objectives. There are situations where a decision-maker is interested in several optimal solutions, not just one. These types of decision processes fall into one of two scenarios: 1) wanting to identify the best N solutions to accomplish a goal or specific task, or 2) evaluating a decision based on several primary quantitative objectives along with secondary qualitative priorities. Design of experiment selection often involves the second scenario where the goal is to identify several contending solutions using the primary quantitative objectives, and then use the secondary qualitative objectives to guide the final decision. Layered Pareto Fronts can help identify a richer class of contenders to examine more closely. The method is illustrated with a supersaturated screening design example.
Computer-generated optimal designs are popular design choices for less standard scenarios where classical designs are not ideal. This work presents a new approach to experimental designs for dual-response systems. The normal, binomial, and Poisson distributions are considered for the potential responses. Using the D-criterion for the linear model and the Bayesian D-criterion for the nonlinear models, a weighted criterion is implemented in a coordinate-exchange algorithm. The designs are evaluated and compared across different weights. The sensitivity of the designs to the priors supplied in the Bayesian D-criterion is explored in the third chapter of this work.
The final section of this work presents a method for a decision-making process involving multiple objectives. There are situations where a decision-maker is interested in several optimal solutions, not just one. These types of decision processes fall into one of two scenarios: 1) wanting to identify the best N solutions to accomplish a goal or specific task, or 2) evaluating a decision based on several primary quantitative objectives along with secondary qualitative priorities. Design of experiment selection often involves the second scenario where the goal is to identify several contending solutions using the primary quantitative objectives, and then use the secondary qualitative objectives to guide the final decision. Layered Pareto Fronts can help identify a richer class of contenders to examine more closely. The method is illustrated with a supersaturated screening design example.
ContributorsBurke, Sarah Ellen (Author) / Montgomery, Douglas C. (Thesis advisor) / Borror, Connie M. (Thesis advisor) / Anderson-Cook, Christine M. (Committee member) / Pan, Rong (Committee member) / Silvestrini, Rachel (Committee member) / Arizona State University (Publisher)
Created2016
Description
Yield is a key process performance characteristic in the capital-intensive semiconductor fabrication process. In an industry where machines cost millions of dollars and cycle times are a number of months, predicting and optimizing yield are critical to process improvement, customer satisfaction, and financial success. Semiconductor yield modeling is essential to identifying processing issues, improving quality, and meeting customer demand in the industry. However, the complicated fabrication process, the massive amount of data collected, and the number of models available make yield modeling a complex and challenging task. This work presents modeling strategies to forecast yield using generalized linear models (GLMs) based on defect metrology data. The research is divided into three main parts. First, the data integration and aggregation necessary for model building are described, and GLMs are constructed for yield forecasting. This technique yields results at both the die and the wafer levels, outperforms existing models found in the literature based on prediction errors, and identifies significant factors that can drive process improvement. This method also allows the nested structure of the process to be considered in the model, improving predictive capabilities and violating fewer assumptions. To account for the random sampling typically used in fabrication, the work is extended by using generalized linear mixed models (GLMMs) and a larger dataset to show the differences between batch-specific and population-averaged models in this application and how they compare to GLMs. These results show some additional improvements in forecasting abilities under certain conditions and show the differences between the significant effects identified in the GLM and GLMM models. The effects of link functions and sample size are also examined at the die and wafer levels. The third part of this research describes a methodology for integrating classification and regression trees (CART) with GLMs. This technique uses the terminal nodes identified in the classification tree to add predictors to a GLM. This method enables the model to consider important interaction terms in a simpler way than with the GLM alone, and provides valuable insight into the fabrication process through the combination of the tree structure and the statistical analysis of the GLM.
ContributorsKrueger, Dana Cheree (Author) / Montgomery, Douglas C. (Thesis advisor) / Fowler, John (Committee member) / Pan, Rong (Committee member) / Pfund, Michele (Committee member) / Arizona State University (Publisher)
Created2011
Description
Optimal design theory provides a general framework for the construction of experimental designs for categorical responses. For a binary response, where the possible result is one of two outcomes, the logistic regression model is widely used to relate a set of experimental factors with the probability of a positive (or negative) outcome. This research investigates and proposes alternative designs to alleviate the problem of separation in small-sample D-optimal designs for the logistic regression model. Separation causes the non-existence of maximum likelihood parameter estimates and presents a serious problem for model fitting purposes.
First, it is shown that exact, multi-factor D-optimal designs for the logistic regression model can be susceptible to separation. Several logistic regression models are specified, and exact D-optimal designs of fixed sizes are constructed for each model. Sets of simulated response data are generated to estimate the probability of separation in each design. This study proves through simulation that small-sample D-optimal designs are prone to separation and that separation risk is dependent on the specified model. Additionally, it is demonstrated that exact designs of equal size constructed for the same models may have significantly different chances of encountering separation.
The second portion of this research establishes an effective strategy for augmentation, where additional design runs are judiciously added to eliminate separation that has occurred in an initial design. A simulation study is used to demonstrate that augmenting runs in regions of maximum prediction variance (MPV), where the predicted probability of either response category is 50%, most reliably eliminates separation. However, it is also shown that MPV augmentation tends to yield augmented designs with lower D-efficiencies.
The final portion of this research proposes a novel compound optimality criterion, DMP, that is used to construct locally optimal and robust compromise designs. A two-phase coordinate exchange algorithm is implemented to construct exact locally DMP-optimal designs. To address design dependence issues, a maximin strategy is proposed for designating a robust DMP-optimal design. A case study demonstrates that the maximin DMP-optimal design maintains comparable D-efficiencies to a corresponding Bayesian D-optimal design while offering significantly improved separation performance.
First, it is shown that exact, multi-factor D-optimal designs for the logistic regression model can be susceptible to separation. Several logistic regression models are specified, and exact D-optimal designs of fixed sizes are constructed for each model. Sets of simulated response data are generated to estimate the probability of separation in each design. This study proves through simulation that small-sample D-optimal designs are prone to separation and that separation risk is dependent on the specified model. Additionally, it is demonstrated that exact designs of equal size constructed for the same models may have significantly different chances of encountering separation.
The second portion of this research establishes an effective strategy for augmentation, where additional design runs are judiciously added to eliminate separation that has occurred in an initial design. A simulation study is used to demonstrate that augmenting runs in regions of maximum prediction variance (MPV), where the predicted probability of either response category is 50%, most reliably eliminates separation. However, it is also shown that MPV augmentation tends to yield augmented designs with lower D-efficiencies.
The final portion of this research proposes a novel compound optimality criterion, DMP, that is used to construct locally optimal and robust compromise designs. A two-phase coordinate exchange algorithm is implemented to construct exact locally DMP-optimal designs. To address design dependence issues, a maximin strategy is proposed for designating a robust DMP-optimal design. A case study demonstrates that the maximin DMP-optimal design maintains comparable D-efficiencies to a corresponding Bayesian D-optimal design while offering significantly improved separation performance.
ContributorsPark, Anson Robert (Author) / Montgomery, Douglas C. (Thesis advisor) / Mancenido, Michelle V (Thesis advisor) / Escobedo, Adolfo R. (Committee member) / Pan, Rong (Committee member) / Arizona State University (Publisher)
Created2019
Description
Nonregular designs are a preferable alternative to regular resolution four designs because they avoid confounding two-factor interactions. As a result nonregular designs can estimate and identify a few active two-factor interactions. However, due to the sometimes complex alias structure of nonregular designs, standard screening strategies can fail to identify all active effects. In this research, two-level nonregular screening designs with orthogonal main effects will be discussed. By utilizing knowledge of the alias structure, a design based model selection process for analyzing nonregular designs is proposed.
The Aliased Informed Model Selection (AIMS) strategy is a design specific approach that is compared to three generic model selection methods; stepwise regression, least absolute shrinkage and selection operator (LASSO), and the Dantzig selector. The AIMS approach substantially increases the power to detect active main effects and two-factor interactions versus the aforementioned generic methodologies. This research identifies design specific model spaces; sets of models with strong heredity, all estimable, and exhibit no model confounding. These spaces are then used in the AIMS method along with design specific aliasing rules for model selection decisions. Model spaces and alias rules are identified for three designs; 16-run no-confounding 6, 7, and 8-factor designs. The designs are demonstrated with several examples as well as simulations to show the AIMS superiority in model selection.
A final piece of the research provides a method for augmenting no-confounding designs based on a model spaces and maximum average D-efficiency. Several augmented designs are provided for different situations. A final simulation with the augmented designs shows strong results for augmenting four additional runs if time and resources permit.
The Aliased Informed Model Selection (AIMS) strategy is a design specific approach that is compared to three generic model selection methods; stepwise regression, least absolute shrinkage and selection operator (LASSO), and the Dantzig selector. The AIMS approach substantially increases the power to detect active main effects and two-factor interactions versus the aforementioned generic methodologies. This research identifies design specific model spaces; sets of models with strong heredity, all estimable, and exhibit no model confounding. These spaces are then used in the AIMS method along with design specific aliasing rules for model selection decisions. Model spaces and alias rules are identified for three designs; 16-run no-confounding 6, 7, and 8-factor designs. The designs are demonstrated with several examples as well as simulations to show the AIMS superiority in model selection.
A final piece of the research provides a method for augmenting no-confounding designs based on a model spaces and maximum average D-efficiency. Several augmented designs are provided for different situations. A final simulation with the augmented designs shows strong results for augmenting four additional runs if time and resources permit.
ContributorsMetcalfe, Carly E (Author) / Montgomery, Douglas C. (Thesis advisor) / Jones, Bradley (Committee member) / Pan, Rong (Committee member) / Pedrielli, Giulia (Committee member) / Arizona State University (Publisher)
Created2020