Thesis (M. S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Ingram, Mary Ann; Committee Member: Blough, Douglas; Committee Member: Sivakumar, Raghupathy. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (M.Sc.). / Written for the School of Computer Science. Title from title page of PDF (viewed 2008/01/15). Includes bibliographical references.

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Includes bibliographical references (p. 299-303).

The thesis outlines the use of Orthogonal Arrays for the training of Artificial Neural Networks. Such arrays are popularly used in system optimisation and are known as Taguchi Methods. The chief advantage of the method is that the network can learn quickly. Fast training methods may be used in certain Control Systems and it has been suggested that they could find application in ‘disaster control,’ where a potentially dangerous system (for example, suffering a mechanical failure) needs to be controlled quickly. Previous work on the methods has shown that they suffer problems when used with multi-layer networks. The thesis discusses the reasons for these problems and reports on several successful techniques for overcoming them. These techniques are based on the consideration of the neuron, rather then the individual weight, as a factor to be optimised. The applications of technique and further work are also discussed.

abstract: Generalized Linear Models (GLMs) are widely used for modeling responses with non-normal error distributions. When the values of the covariates in such models are controllable, finding an optimal (or at least efficient) design could greatly facilitate the work of collecting and analyzing data. In fact, many theoretical results are obtained on a case-by-case basis, while in other situations, researchers also rely heavily on computational tools for design selection. Three topics are investigated in this dissertation with each one focusing on one type of GLMs. Topic I considers GLMs with factorial effects and one continuous covariate. Factors can have interactions among each other and there is no restriction on the possible values of the continuous covariate. The locally D-optimal design structures for such models are identified and results for obtaining smaller optimal designs using orthogonal arrays (OAs) are presented. Topic II considers GLMs with multiple covariates under the assumptions that all but one covariate are bounded within specified intervals and interaction effects among those bounded covariates may also exist. An explicit formula for D-optimal designs is derived and OA-based smaller D-optimal designs for models with one or two two-factor interactions are also constructed. Topic III considers multiple-covariate logistic models. All covariates are nonnegative and there is no interaction among them. Two types of D-optimal design structures are identified and their global D-optimality is proved using the celebrated equivalence theorem. / Dissertation/Thesis / Doctoral Dissertation Statistics 2018

In polymerase chain reaction (PCR), in order to amplify massive DNA sequences successfully, it needs to design an appropriate primer pair. The constraints derived from the traits of PCR for proceeding PCR are used in searching for primer pairs. In this paper, in order to decrease the searching space and to increase the feasible quality of primers, a double orthogonal arrays intelligent crossover genetic algorithm (DOAIGA) is used to solve the primer design problem. DOAIGA combines the traditional genetic algorithm and the Taguchi methodology to efficiently search feasible primers under required constraints. The proposed intelligent crossover subsystem mainly concentrates on the better genes more systematic. The key point of DOAIGA is to achieve the elitism goal by applying the orthogonal arrays (OAs) that is used in quality engineering with a small amount of experiment features. In this thesis, the double orthogonal arrays are used to approach a better forward and reverse primers separately. Compared to the current existing softwares, DOAIGA can obtain feasible primer pairs more effectively. Finally the correctness of primer pair is verified by PCR experiment.

abstract: Nonregular screening designs can be an economical alternative to traditional resolution IV 2^(k-p) fractional factorials. Recently 16-run nonregular designs, referred to as no-confounding designs, were introduced in the literature. These designs have the property that no pair of main effect (ME) and two-factor interaction (2FI) estimates are completely confounded. In this dissertation, orthogonal arrays were evaluated with many popular design-ranking criteria in order to identify optimal 20-run and 24-run no-confounding designs. Monte Carlo simulation was used to empirically assess the model fitting effectiveness of the recommended no-confounding designs. The results of the simulation demonstrated that these new designs, particularly the 24-run designs, are successful at detecting active effects over 95% of the time given sufficient model effect sparsity. The final chapter presents a screening design selection methodology, based on decision trees, to aid in the selection of a screening design from a list of published options. The methodology determines which of a candidate set of screening designs has the lowest expected experimental cost. / Dissertation/Thesis / Ph.D. Industrial Engineering 2013

A k × n array with entries from a q-letter alphabet is called a t-covering array if each t × n submatrix contains amongst its columns each one of the gt different words of length t that can be produced by the q letters. In the present article we use a probabilistic approach based on an appropriate Markov chain embedding technique, to study a t-covering problem where, instead of looking at all possible t ×n submatrices, we consider only submatrices of dimension t ×n with its rows being consecutive rows of the original k × n array. Moreover, an exact formula is established for the probability distribution function of the random variable, which enumerates the number of deficient submatrices (i.e., submatrices with at least one missing word, amongst their columns), in the case of a k × n binary matrix (q = 2) obtained by realizing kn Bernoulli variables.

abstract: Modern software and hardware systems are composed of a large number of components. Often different components of a system interact with each other in unforeseen and undesired ways to cause failures. Covering arrays are a useful mathematical tool for testing all possible t-way interactions among the components of a system. The two major issues concerning covering arrays are explicit construction of a covering array, and exact or approximate determination of the covering array number---the minimum size of a covering array. Although these problems have been investigated extensively for the last couple of decades, in this thesis we present significant improvements on both of these questions using tools from the probabilistic method and randomized algorithms. First, a series of improvements is developed on the previously known upper bounds on covering array numbers. An estimate for the discrete Stein-Lovász-Johnson bound is derived and the Stein- Lovász -Johnson bound is improved upon using an alteration strategy. Then group actions on the set of symbols are explored to establish two asymptotic upper bounds on covering array numbers that are tighter than any of the presently known bounds. Second, an algorithmic paradigm, called the two-stage framework, is introduced for covering array construction. A number of concrete algorithms from this framework are analyzed, and it is shown that they outperform current methods in the range of parameter values that are of practical relevance. In some cases, a reduction in the number of tests by more than 50% is achieved. Third, the Lovász local lemma is applied on covering perfect hash families to obtain an upper bound on covering array numbers that is tightest of all known bounds. This bound leads to a Moser-Tardos type algorithm that employs linear algebraic computation over finite fields to construct covering arrays. In some cases, this algorithm outperforms currently used methods by more than an 80% margin. Finally, partial covering arrays are introduced to investigate a few practically relevant relaxations of the covering requirement. Using probabilistic methods, bounds are obtained on partial covering arrays that are significantly smaller than for covering arrays. Also, randomized algorithms are provided that construct such arrays in expected polynomial time. / Dissertation/Thesis / Doctoral Dissertation Computer Science 2016

This research work is focused on the balanced and partially balanced incomplete block designs when observations within blocks are correlated. The topic for this dissertation was motivated by a problem in pharmaceutical research, when several treatments are allocated to individuals, and repeated measurements are taken on each individual. In that case, there is correlation among the observations taken on the same individual. Typically, it is reasonable to assume that the observations within individual close to each other are highly correlated than observations that are far away from each other. It is also reasonable to assume that the correlation between any two observations within each individual is same. We have characterized balanced and partially balanced incomplete block designs when observations within blocks are autocorrelated. In Chapter 3, we have provided an explicit expression for the average variance of estimated elementary treatment contrasts for designs obtained by Type I and II series of orthogonal arrays, under autocorrelated errors, and compared them with the corresponding balanced incomplete block designs with uncorrelated errors. The relative efficiency of balanced incomplete block design compared to the corresponding balanced incomplete block design obtained by Types I and II series of orthogonal array under autocorrelated errors does not depend on the number of treatments (v) and is an increasing function of the block size (k). When orthogonal arrays of Type I or Type II do not exist for a given number of treatments, we provided alternative partially balanced designs with autocorrelated errors. In Chapter 4, we rearranged the treatments in each block of symmetric balanced incomplete block designs and used them with autocorrelated error structure of the plots in a block. The C-matrix of estimated treatment effects under autocorrelation was given and the relative efficiency of symmetric balanced incomplete block designs with independent errors compared to the autocorrelated designs is given. In Chapter 5, we discussed the compound symmetry correlation structure within blocks. An explicit expression of the average variance of designs obtained by Type I and II series of orthogonal arrays and symmetric balanced incomplete block designs under compound symmetric errors has been provided and compared them with the corresponding balanced incomplete block designs with uncorrelated errors. Finally, the relative efficiencies of these designs with autocorrelated errors vs. compound symmetric error structure are given / Statistics