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- All Subjects: Statistics
- All Subjects: Process control--Statistical methods.
- Creators: Montgomery, Douglas C.
- Creators: Wilson, Jeffrey
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
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
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
A P-value based method is proposed for statistical monitoring of various types of profiles in phase II. The performance of the proposed method is evaluated by the average run length criterion under various shifts in the intercept, slope and error standard deviation of the model. In our proposed approach, P-values are computed at each level within a sample. If at least one of the P-values is less than a pre-specified significance level, the chart signals out-of-control. The primary advantage of our approach is that only one control chart is required to monitor several parameters simultaneously: the intercept, slope(s), and the error standard deviation. A comprehensive comparison of the proposed method and the existing KMW-Shewhart method for monitoring linear profiles is conducted. In addition, the effect that the number of observations within a sample has on the performance of the proposed method is investigated. The proposed method was also compared to the T^2 method discussed in Kang and Albin (2000) for multivariate, polynomial, and nonlinear profiles. A simulation study shows that overall the proposed P-value method performs satisfactorily for different profile types.
ContributorsAdibi, Azadeh (Author) / Montgomery, Douglas C. (Thesis advisor) / Borror, Connie (Thesis advisor) / Li, Jing (Committee member) / Zhang, Muhong (Committee member) / Arizona State University (Publisher)
Created2013
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
A least total area of triangle method was proposed by Teissier (1948) for fitting a straight line to data from a pair of variables without treating either variable as the dependent variable while allowing each of the variables to have measurement errors. This method is commonly called Reduced Major Axis (RMA) regression and is often used instead of Ordinary Least Squares (OLS) regression. Results for confidence intervals, hypothesis testing and asymptotic distributions of coefficient estimates in the bivariate case are reviewed. A generalization of RMA to more than two variables for fitting a plane to data is obtained by minimizing the sum of a function of the volumes obtained by drawing, from each data point, lines parallel to each coordinate axis to the fitted plane (Draper and Yang 1997; Goodman and Tofallis 2003). Generalized RMA results for the multivariate case obtained by Draper and Yang (1997) are reviewed and some investigations of multivariate RMA are given. A linear model is proposed that does not specify a dependent variable and allows for errors in the measurement of each variable. Coefficients in the model are estimated by minimization of the function of the volumes previously mentioned. Methods for obtaining coefficient estimates are discussed and simulations are used to investigate the distribution of coefficient estimates. The effects of sample size, sampling error and correlation among variables on the estimates are studied. Bootstrap methods are used to obtain confidence intervals for model coefficients. Residual analysis is considered for assessing model assumptions. Outlier and influential case diagnostics are developed and a forward selection method is proposed for subset selection of model variables. A real data example is provided that uses the methods developed. Topics for further research are discussed.
ContributorsLi, Jingjin (Author) / Young, Dennis (Thesis advisor) / Eubank, Randall (Thesis advisor) / Reiser, Mark R. (Committee member) / Kao, Ming-Hung (Committee member) / Yang, Yan (Committee member) / Arizona State University (Publisher)
Created2012
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
The emergence of new technologies as well as a fresh look at analyzing existing processes have given rise to a new type of response characteristic, known as a profile. Profiles are useful when a quality variable is functionally dependent on one or more explanatory, or independent, variables. So, instead of observing a single measurement on each unit or product a set of values is obtained over a range which, when plotted, takes the shape of a curve. Traditional multivariate monitoring schemes are inadequate for monitoring profiles due to high dimensionality and poor use of the information stored in functional form leading to very large variance-covariance matrices. Profile monitoring has become an important area of study in statistical process control and is being actively addressed by researchers across the globe. This research explores the understanding of the area in three parts. A comparative analysis is conducted of two linear profile-monitoring techniques based on probability of false alarm rate and average run length (ARL) under shifts in the model parameters. The two techniques studied are control chart based on classical calibration statistic and a control chart based on the parameters of a linear model. The research demonstrates that a profile characterized by a parametric model is more efficient monitoring scheme than one based on monitoring only the individual features of the profile. A likelihood ratio based changepoint control chart is proposed for detecting a sustained step shift in low order polynomial profiles. The test statistic is plotted on a Shewhart like chart with control limits derived from asymptotic distribution theory. The statistic is factored to reflect the variation due to the parameters in to aid in interpreting an out of control signal. The research also looks at the robust parameter design study of profiles, also referred to as signal response systems. Such experiments are often necessary for understanding and reducing the common cause variation in systems. A split-plot approach is proposed to analyze the profiles. It is demonstrated that an explicit modeling of variance components using generalized linear mixed models approach has more precise point estimates and tighter confidence intervals.
ContributorsGupta, Shilpa (Author) / Montgomery, Douglas C. (Thesis advisor) / Borror, Connie M. (Thesis advisor) / Fowler, John (Committee member) / Prewitt, Kathy (Committee member) / Kulahci, Murat (Committee member) / Arizona State University (Publisher)
Created2010