1,720,977 research outputs found
An examination of [tau] c-Pd earthquake early warning method using a strong-motion building array
No full textModeling and optimization for robust parameter design.
No full textRobust parameter design is one of the most important tools for quality improvement. Quality problems are caused by variations in the system performance. Robust parameter design is a very cost-effective approach to reduce variations and improve quality. The thesis consists of some important topics in robust parameter design. It develops new modeling and optimization methods for robust parameter design. The research on multiple target systems provides a new formulation of the problem and proposes some practical modeling and optimization methods. It identifies the underlying statistical model for the widely used dynamic signal-to-noise ratio and develops some strategies to deal with nonlinear signal-response systems. The research on control systems develops a new methodology for parameter design in the presence of a feed-forward or feed-back control. The performance measures for commonly encountered systems are derived. In the research on quality loss functions, a new set of loss functions for nonnegative variables are proposed based on Taguchi's societal loss concept. Their usefulness is demonstrated with applications to robust parameter design. The thesis also includes a study on operating window experiments, a topic that has not been systematically investigated before. New modeling, analysis, and optimization methods are proposed, which is an improvement over the existing practice. Finally, a new concept and method called failure amplification method (FAMe) is introduced for categorical response optimization. This method extends the idea of operating window and provides a more general framework for categorical response optimization. All the proposed methodologies in the thesis are illustrated with applications to some real experiments.PhDApplied SciencesIndustrial engineeringPure SciencesStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/123302/2/3068984.pd
Some problems in the theory and construction of factorial designs.
No full textAt the beginning of an investigation there may be many conceivably important factors. It is often reasonable to assume that only a few of them are important, but their identities are not known. Therefore, screening designs are needed. Screening designs can be broadly classified into two categories: orthogonal and nonorthogonal designs. Nonorthogonal designs can be popular if run size economy and flexibility with respect to level combinations are desired. One important sub-category of nonorthogonal designs are the one-factor-at-a-time (OFAT) designs. Strict and standard OFAT designs are studied in this thesis. Besides discussing the construction and statistical properties of OFAT designs of resolution III and IV, OFAT designs of resolution V are constructed for the first time. All the main effects and two-factor interactions (2fi's) are estimable in these designs. Strict OFAT designs of resolution V are saturated and standard OFAT designs have two more runs than saturated designs. The constructed designs have attractive features such as run size economy and robustness to premature termination. They are useful in computer modeling as well as in physical experiments. Comparisons with other designs show that, if the response error is small, there are no particular disadvantages in running experiments using OFAT designs. A fundamental and practically important question in the theory of fractional factorial designs is the issue of optimal factor assignment to columns of the design matrix. A new criterion called maximum estimability (maxest) is proposed as a solution to this problem for nonorthogonal designs as well as for regular and nonregular designs. The maxest criterion is a refinement of Webb's resolution and can further distinguish designs of the same resolution by using the numbers of clear or strongly clear main effects and 2fi's. It also extends the maximum resolution and the minimum aberration criteria for regular designs. For nonregular orthogonal or nonorthogonal designs, the maxest criterion focuses on low-order effects and is coding-dependent, which is different from other criteria such as the various generalized minimum aberration criteria and the minimum moment criterion. As an application, the maxest criterion is used to study the projections of nonregular two-level, three-level and mixed-level designs such as the Plackett-Burman and related designs, OA(18, 37, 2), OA(36, 312, 2), OA(18, 21 37, 2) and OA(36, 3122 11, 2). Projections of these designs are classified using the estimability vector associated with the maxest criterion and new geometric projections are discovered. Non-isomorphic designs are compared and ranked in terms of their projection properties. Their rankings under the maxest criterion are different from those under other criteria. In comparison with other classifications, the proposed classifications have fewer classes and provide more insight for statistical modeling.PhDPure SciencesStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/132766/2/3058031.pd
A theory of experimental design for multiple groups of factors.
No full textRobust parameter design is a statistical/engineering tool for performance variation reduction in industrial processes or products. Single arrays are efficient experimental plans for parameter design. In this thesis, we establish an approach for selecting optimal single arrays. Single arrays are formally defined as an extension of ordinary fractional factorial designs. The asymmetry between control factors and noise factors is discussed. The factorial effects in parameter design are classified into various types. New effect ordering principles for parameter design are proposed. Motivated by the minimum aberration criterion, an aliasing index vector is introduced. A simplified version of the aliasing index vector, defined as J, is employed to measure the aliasing severity of single arrays. The concept of clear effect is used to derive a clear estimation index vector alpha = (NC, Nn, NCC, NCn, Nnn), which reports the number of clear control main effects, clear noise main effects, clear control-by-control interactions, clear control-by-noise interactions and clear noise-by-noise interactions. Based on J and alpha, optimality criteria are developed for selecting good single arrays. Applying the optimality criteria and intensive computer search, efficient single arrays are identified and tabulated for practical use. Single arrays are typical examples of factorial designs involving more than one group of factors. Other examples include blocked designs, split-plot designs and mixed-level designs. The approach in Chapter 2 for single arrays can be adopted for factorial designs with multiple groups of factors. In order to understand the structure and properties of these designs, a theoretical framework is needed. We define a wordtype pattern matrix, and introduce a partition of the Hadamard matrix in the spirit of Wu, Zhang and Wang (1992), Tang and Wu (1996) and Mukerjee and Wu (2000). The partition induces several related designs. Structure index array and structure function are proposed to study the relation among the generated designs. A first order partial differential equation is found to be satisfied by the structure function. The solution to the equation gives an analytic expression of the structure function, which reveals the intricate relation among these designs. This theoretical result provides an effective way to construct and select optimal factorial designs with multiple groups of factors. Practical selection rules for single arrays are proposed.PhDPure SciencesStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/132723/2/9977295.pd
Optimal blocking schemes and projection properties for fractional factorial designs.
No full textThis dissertation documents the results of studies of two research topics for fractional factorial designs: (i) Blocking is commonly used in design of experiments to reduce the systematic variation and increase the precision of estimation of effects. For 2n -- k designs in 2p blocks, Sun, Wu and Chen (1997), and Sitter, Chen and Feder (1997) studied the aliasing and confounding patterns between blocking factors and treatment factors and proposed criteria to choose optimal blocking schemes. Their criteria are primarily based on the lengths of the words in the defining contrast subgroup. We point out some weakness of their criteria and suggest several modifications which allow more lower-order effects to be estimable. Extensions to 3-level fractional factorial designs are also considered. (ii) For studying quadratic response surfaces, a prevailing experimental plan in the literature is the central composite design, proposed by Box and Wilson (1951). In their paper, it was also shown that the 3n -- k designs are inappropriate for quadratic response surface study because of their uneconomical run size. We take a different approach and propose, for the 3n -- k designs, a two-stage data analysis strategy, i.e., first screening and then fitting quadratic response surfaces on the projected design of the factors identified as important in screening. Under the strategy, the run size of the 3n -- k designs can be utilized efficiently for two objectives, screening and fitting quadratic response surfaces, without adding more runs. Based on this analysis strategy, we study projection properties of the 3 n -- k designs. The projected designs are classified into different types in terms of combinatorial isomorphism and model isomorphism. Then, they are compared with some second-order designs, such as the central composite designs, in terms of D- and G-efficiencies. In addition to the 3n -- k designs, we also study the projection properties of some nonregular three-level designs, such as the OA(18, 37) and the OA (36, 312) . These three-level designs are evaluated according to an eligible projection criterion, which is based on the total of projected designs that can be used to fit quadratic response surfaces. A new method to construct designs that can significantly improve the eligible projection property of the 3n -- k designs is also presented.PhDPure SciencesStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/131618/2/9929798.pd
New techniques in clustering and microarray data analysis.
No full textIn recent years, the use of gene expression data has expanded to many areas of medical research, drug discovery and development. Technological development will enable the entire human genome to be spotted onto one microarray in the near future. It is an exciting time for statisticians to deal with the explosive growth of this type of data. This thesis tackles two of the open questions regarding analysis of large scale gene expression data. Multiplicity issues arise when attempting to discern which of the ∼10,000 genes are differentially expressed. The Multiplicity-Adjusted Order Statistics Analysis (MAOSA) technique developed in the thesis is based on the normality of the middle portion of the distribution of the test statistics. After a transformation of the test statistics to the uniform scale, known features of the uniform order statistics are used to facilitate analysis. The multiplicity problem will be dealt with by performing a Bonferroni correction on a small number of hypothesis tests. Real data are used to illustrate the technique and compare it to existing methods. There is no tool to explore the relationship between groups of clustered genes at both the cluster level and the object level (i.e., gene-to-gene). The Inter-Cluster Investigator (ICI) is developed to address this need. It identifies positive and negative associations between clusters that have previously been overlooked. These cluster-level relationships may indicate repression or regulation in gene expression data. Once a significant cluster-level association is found, the ICI procedure will move to the object (gene)-level to identity associations that are driving the between-cluster relationship. The ICI method yields an alternative way of characterizing the between-object relationship that builds upon the existing structure obtained from clustering. Effectiveness of the ICI method is demonstrated in the analysis of gene expression data.PhDBiological SciencesBiostatisticsPure SciencesStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/124394/2/3138143.pd
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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