A parameter design introduced by Taguchi provides a new quality control method which can reduce cost-effectively the product variation due to various uncontrollable noise factors such as product deterioration, manufacturing imperfections, and environmental factors under which a product is actually used. This experimental design technique identifies the optimal setting of the control factors which is least sensitive to the noise factors. Taguchi’s method utilizes orthogonal arrays which allow the investigation of main effects only, under the assumption that interaction effects are negligible. In this paper new techniques are developed to investigate two-factor interactions for 2^t and 3^t factorial parameter designs. The major objective is to be able to identify influential two-factor interactions and take those into account in properly assessing the optimal setting of the control factors. For 2^t factorial parameter designs, we develop some new designs for the control factors by using a partially balanced array. These designs are characterized by a small number of runs and some balancedness property of the variance-covariance matrix of the estimates of main effects and two-factor interactions. Methods of analyzing the new designs are also developed. For 3^t factorial parameter designs, a detection procedure consisting of two stages is developed by using a sequential method in order to reduce the number of runs needed to detect influential two-factor interactions. In this paper, an extension of the parameter design to several quality characteristics is also developed by devising suitable statistics to be analyzed, depending on whether a proper loss function can be specified or not. / Ph. D.

Let V be an n-dimensional vector space over the field of q elements. By a geometric t-[q^n, k, λ] design we mean a collection D of k-dimensional subspaces of V, called blocks, such that every t-dimensional subspace T of V appears in exactly λ blocks in D. A large set, LS [N] [t, k, q^n], of geometric designs is a collection on N disjoint t-[q^n, k, λ] designs that partitions [V K], the collection of k-dimensional subspaces of V. In this work we construct non-isomorphic large sets using methods based on incidence structures known as the Kramer-Mesner matrices. These structures are induced by particular group actions on the collection of subspaces of the vector space V. Subsequently, we discuss and use computational techniques for solving certain linear problems of the form AX = B, where A is a large integral matrix and X is a {0,1} solution. These techniques involve (i) lattice basis-reduction, including variants of the LLL algorithm, and (ii) linear programming. Inspiration came from the 2013 work of Braun, Kohnert, Ostergard, and Wassermann, [17], who produced the first nontrivial large set of geometric designs with t ≥ 2. Bal Khadka and Michael Epstein provided the know-how for using the LLL and linear programming algorithms that we implemented to construct the large sets. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 116-121). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 116-121). Also available on the Internet.

Submitted by Lucas Augusto Moisés (lucasaugustomoises@hotmail.com) on 2018-11-12T14:28:19Z No. of bitstreams: 1 Dissertação Lucas Augusto Moisés_2.pdf: 2728995 bytes, checksum: 4372fefa9820f84b2816df79babc8610 (MD5) / Approved for entry into archive by Adriana Aparecida Puerta null (dripuerta@rc.unesp.br) on 2018-11-13T18:12:17Z (GMT) No. of bitstreams: 1 moises_la_me_rcla.pdf: 2728995 bytes, checksum: 4372fefa9820f84b2816df79babc8610 (MD5) / Made available in DSpace on 2018-11-13T18:12:18Z (GMT). No. of bitstreams: 1 moises_la_me_rcla.pdf: 2728995 bytes, checksum: 4372fefa9820f84b2816df79babc8610 (MD5) Previous issue date: 2018-09-11 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / No presente trabalho produziram-se filmes finos transparentes de ZnO depositados pela técnica de spray-pirólise com objetivo de estudar o comportamento de suas propriedades elétricas durante a incidência de luz UV e após a incidência de luz (no escuro). Para tal, foram propostos três designs experimentais do tipo fatorial de dois níveis, um do tipo fatorial fracionário com base no modelo de Plackett-Burman e dois fatoriais completos. Na realização desses experimentos, variou-se parâmetros de produção do filme e também parâmetros experimentais no momento da realização da medida, sendo nove parâmetros no total. Através dos dados obtidos nesses experimentos, obteve-se respostas experimentais. Em cima disso foram realizadas analises estatísticas. Assim, através dessas análises se conheceu quais os fatores experimentais tiveram maior influência em cada uma dessas respostas e os resultados obtidos tiveram um bom acordo com a teoria, indicando a eficácia dos experimentos fatoriais de dois níveis realizados. Por fim, foi realizado medidas de predição e comparado as respostas obtidas nessas medidas com os dados estatísticos obtidos. Através dessa comparação, foi encontrado uma resposta reprodutível, indicando assim a possibilidade aplicação de filmes de ZnO na área de sensores / In the present work, transparent thin films of ZnO deposited by the spray - pyrolysis technique were used to study the behavior of their electrical properties during the incidence of UV light and after the incidence of light (in the dark). For that, three experimental designs of the two - level factorial type were proposed, one of the fractional factorial type based on the Plackett - Burman model and two complete factorials. In the performance of these experiments, parameters of production of the film were varied as well as experimental parameters at the moment of the measurement, being nine parameters in total. Through the data obtained in these experiments, experimental responses were obtained. Statistical analyzes were performed on top of this. Thus, through these analyzes it was known which experimental facto rs had the greatest influence on each one of these responses and the results obtained had a good agreement with the theory, indicating the effectiveness of the two - level factorial experiments performed. Finally, prediction measures were performed and the r esponses obtained in these measurements were compared with the statistical data obtained. Through this comparison, a reproducible response was found, thus indicating the possibility of applying ZnO films in the area of sensors

Box-Behnken designs are used to estimate parameters in a second-order response surface model (Box and Behnken, 1960). These designs are formed by combining ideas from incomplete block designs (BIBD or PBIBD) and factorial experiments, specifically 2^k full or 2^k-1 fractional factorials. In this dissertation, a more general mathematical formulation of the Box-Behnken method is provided, a general expression for the coefficient matrix in the least squares analysis for estimating the parameters in the second order model is derived, and the properties of Box-Behnken designs with respect to the estimability of all parameters in a second-order model are investigated when 2^kfull factorials are used. The results show that for all pure quadratic coefficients to be estimable, the PBIB(m) design has to be chosen such that its incidence matrix is of full rank, and for all mixed quadratic coefficients to be estimable the PBIB(m) design has to be chosen such that the parameters λ₁, λ₂, ...,λ_m are all greater than zero. In order to reduce the number of experimental points the use of 2^k-1 fractional factorials instead of 2^k full factorials is being considered. Of particular interest and importance are separate considerations of fractions of resolutions III, IV, and V. The construction of Box-Behnken designs using such fractions is described and the properties of the designs concerning estimability of regression coefficients are investigated. Using designs obtained from resolution V factorials have the same properties as those using full factorials. Resolutions III and IV designs may lead to non-estimability of certain coefficients and to correlated estimators. The final topic is concerned with Box-Behnken designs in which treatments are applied to experimental units sequentially in time or space and in which there may exist a linear trend effect. For this situation, one wants to find appropriate run orders for obtaining a linear trend-free Box-Behnken design to remove a linear trend effect so that a simple technique, analysis of variance, instead of a more complicated technique, analysis of covariance, to remove a linear trend effect can be used. Construction methods for linear trend-free Box-Behnken designs are introduced for different values of block size (for the underlying PBIB design) k. For k= 2 or 3, it may not always be possible to find linear trend-free Box-Behnken designs. However, for k ≥ 4 linear trend-free Box-Behnken designs can always be constructed. / Ph. D.

A method is presented for analysing a 2 x 2 factorial experiment in which the data consist cf relative rankings in pairwise comparisons. Maximum likelihood estimates are developed for the ratings of the various levels of each factor und for the treatment combinations. Likelihood ratio tests of the most important hypotheses likely to arise are derived in detail. The large sample approximations are used. In addition, the method is presented in a manner such that tests of other hypotheses in which the experimenter might be interested can easily be derived. The equations for the analysis of a factorial design of arbitrary size are presented, It can be seen, however, that the complexity of these equations render an attempt at their solution impractical in most cases and more work must be done if a useful method of analysing experiments of this, type is to be found. / Master of Science

Robert J. Taylor and Herbert A. David developed a new experimental approach in the screening of prospective drugs to be used in the treatment of cancer. The procedure is a sequential one, where the allocation of patients to drugs is based upon the performance of the drugs in immediately previous periods. Taylor further developed a computer program to study the effectiveness of the procedure by means of simulated trials. The purpose of this paper has been to study the sequential allocation procedure further by means of simulation in the form of a factorial experiment. Of primary concern has been the behavior of different weighting functions operating under varying experimental conditions. Response variables have been studied as a means for evaluating the effectiveness of the procedure. The results of this experiment are comparable with the findings originally presented by Taylor and David. / Master of Science

O presente trabalho teve como objetivo o estudo de experimentos em delineamentos em esquema fatorial duplo com tratamento adicional do tipo testemunha. Para este esquema usa-se a notação A x B +1, em que A representa o primeiro fator com i níveis (i = 1, 2, ..., a) e B representa o segundo fator com j níveis (j = 1, 2, ..., b) com a adição do tratamento adicional. Para a análise de variância deste caso, consideraram-se os modelos lineares yijk = μ + αi + βj + γij + εijk e yh = μ + τ + εh; relacionados, em que yijk é a variável observada no i-ésimo nível do fator α com o j-ésimo nível do fator β da k-ésima repetição (k = 1, 2, ..., r), μ é a média amostral, αi é o efeito do i-ésimo nível do primeiro fator, βj é o efeito do j-ésimo nível do segundo fator, γij é o efeito da interação do i-ésimo nível do fator α com o j-ésimo nível do fator β, εijk é o erro associado independente e identicamente distribuído, εijk~N(0,σ2), yh é a variável observada na h-ésima repetição do tratamento adicional, τ é o efeito do tratamento adicional e εh é o erro associado ao tratamento adicional, independente e identicamente distribuído εh~N(0,σ2). Considerou-se os delineamentos experimentais inteiramente casualizado e blocos casualizados. Para a análise do delineamento em blocos ao acaso, a adição do efeito de blocos λv (v = 1, 2, ..., w) aos modelos, se fez necessária. Foi realizada a dedução da soma de quadrados de tratamentos e sua decomposição para os efeitos dos fatores, sua interação e o contraste com o tratamento adicional. Os graus de liberdade foram deduzidos a partir do posto da matriz núcleo da forma quadrática das somas de quadrados. A técnica do diagrama de Hasse também foi adotada para dedução das somas de quadrados e graus de liberdade. Uma ilustração do método obteve os mesmos resultados da análise de variância do pacote ExpDes no programa R. Curvas de regressão linear foram ajustadas considerando o tratamento controle como um nível de fatores quantitativos. O teste de Dunnett foi empregado para comparar as médias do fatorial com o tratamento controle. / The present study aimed to study the experiments in two-way factorial designs with additional treatment of type control. For this scheme uses the notation A x B +1, where A represents the first factor levels with i (i = 1, 2, ..., a) and B is the second factor with levels j (j = 1 , 2, ..., b) with the addition of one more treatment. For the analysis of variance of this case, we considered the linear models yijk = μ + αi + βj + γij + εijk and yh = μ + τ + εh; related, wherein yijk is the variable observed in the ith level of factor α with the jth level of factor β of k-th iteration (k = 1, 2, ..., r), μ is the sample mean, αi is the effect of the ith level of the first factor, βj is the effect of the jth level of the second factor, γij is the interaction effect of the ith level of factor α with the jth level of factor β, εijk is the error associated with independent and identically distributed, εijk~N(0,σ2), yh is the variable observed in the hth repetition of the additional treatment, τ is the effect of the additional treatment and εh is the error associated to the additional treatment, independent and identically distributed εh~N(0,σ2). It was considered the completely experimental designs and randomized block design. For the analysis of the randomized block design, the addition of blocks effect λv (v = 1, 2, ..., w) to the models, was necessary. Was performed the deduction of the sum of squares of treatments and their decomposition to the effects of the factors, their interaction and the contrast with the additional treatment. The degrees of freedom were deducted from the posto of the matrix core of the quadratic form of sums of squares. The Hasse diagram technique has also been adopted for deduction of sums of squares and degrees of freedom. An illustration of the method has obtained the same results of analysis of variance program package ExpDes in R. Linear regression analysis was fitted control treatment as a level of the quantitative factors. The Dunnett test was used to compare the means of the factorial with the control treatment.

O presente trabalho teve como objetivo o estudo de experimentos em delineamentos em esquema fatorial duplo com tratamento adicional do tipo testemunha. Para este esquema usa-se a notação A x B +1, em que A representa o primeiro fator com i níveis (i = 1, 2, ..., a) e B representa o segundo fator com j níveis (j = 1, 2, ..., b) com a adição do tratamento adicional. Para a análise de variância deste caso, consideraram-se os modelos lineares yijk = μ + αi + βj + γij + εijk e yh = μ + τ + εh; relacionados, em que yijk é a variável observada no i-ésimo nível do fator α com o j-ésimo nível do fator β da k-ésima repetição (k = 1, 2, ..., r), μ é a média amostral, αi é o efeito do i-ésimo nível do primeiro fator, βj é o efeito do j-ésimo nível do segundo fator, γij é o efeito da interação do i-ésimo nível do fator α com o j-ésimo nível do fator β, εijk é o erro associado independente e identicamente distribuído, εijk~N(0,σ2), yh é a variável observada na h-ésima repetição do tratamento adicional, τ é o efeito do tratamento adicional e εh é o erro associado ao tratamento adicional, independente e identicamente distribuído εh~N(0,σ2). Considerou-se os delineamentos experimentais inteiramente casualizado e blocos casualizados. Para a análise do delineamento em blocos ao acaso, a adição do efeito de blocos λv (v = 1, 2, ..., w) aos modelos, se fez necessária. Foi realizada a dedução da soma de quadrados de tratamentos e sua decomposição para os efeitos dos fatores, sua interação e o contraste com o tratamento adicional. Os graus de liberdade foram deduzidos a partir do posto da matriz núcleo da forma quadrática das somas de quadrados. A técnica do diagrama de Hasse também foi adotada para dedução das somas de quadrados e graus de liberdade. Uma ilustração do método obteve os mesmos resultados da análise de variância do pacote ExpDes no programa R. Curvas de regressão linear foram ajustadas considerando o tratamento controle como um nível de fatores quantitativos. O teste de Dunnett foi empregado para comparar as médias do fatorial com o tratamento controle. / The present study aimed to study the experiments in two-way factorial designs with additional treatment of type control. For this scheme uses the notation A x B +1, where A represents the first factor levels with i (i = 1, 2, ..., a) and B is the second factor with levels j (j = 1 , 2, ..., b) with the addition of one more treatment. For the analysis of variance of this case, we considered the linear models yijk = μ + αi + βj + γij + εijk and yh = μ + τ + εh; related, wherein yijk is the variable observed in the ith level of factor α with the jth level of factor β of k-th iteration (k = 1, 2, ..., r), μ is the sample mean, αi is the effect of the ith level of the first factor, βj is the effect of the jth level of the second factor, γij is the interaction effect of the ith level of factor α with the jth level of factor β, εijk is the error associated with independent and identically distributed, εijk~N(0,σ2), yh is the variable observed in the hth repetition of the additional treatment, τ is the effect of the additional treatment and εh is the error associated to the additional treatment, independent and identically distributed εh~N(0,σ2). It was considered the completely experimental designs and randomized block design. For the analysis of the randomized block design, the addition of blocks effect λv (v = 1, 2, ..., w) to the models, was necessary. Was performed the deduction of the sum of squares of treatments and their decomposition to the effects of the factors, their interaction and the contrast with the additional treatment. The degrees of freedom were deducted from the posto of the matrix core of the quadratic form of sums of squares. The Hasse diagram technique has also been adopted for deduction of sums of squares and degrees of freedom. An illustration of the method has obtained the same results of analysis of variance program package ExpDes in R. Linear regression analysis was fitted control treatment as a level of the quantitative factors. The Dunnett test was used to compare the means of the factorial with the control treatment.