Efeitos dos pontos axiais e centrais sobre a eficiência do delineamento composto central

• Ano de defesa: 2010
• Autor(a) principal: Perázio, Bráulia Aparecida de Almeida
• Orientador(a): Ribeiro Junior, José Ivo
• Banca de defesa: Silva, Fabyano Fonseca e , Lopes, Jaques Silveira
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Viçosa
• Programa de Pós-Graduação: Mestrado em Estatística Aplicada e Biometria
• Departamento: Estatística Aplicada e Biometria
• País: BR
• Palavras-chave em Português: Superfície de resposta; Delineamento de tratamentos; Qualidade de ajuste
• Palavras-chave em Inglês: Response surface; Treatment designs; Quality of fitting
• Área do conhecimento CNPq: CNPQ::CIENCIAS AGRARIAS
• Link de acesso: http://locus.ufv.br/handle/123456789/4029

In the analysis of problems in which the response variable of interest is influenced by many factors and whose goal is to optimize, it's it intended to use designs for the response surface. One of the highlights is the central composite design (CCD), which is a randomized second-order and may have characteristics of rotational and / or orthogonality. These designs are simple, economical, promising and very flexible. These are consisted of factorial points, axial and central. This way, using simulation data, the objective was to investigate, by means of simulation data, the effects of axial points and the number of central points on the quality of fitting of the area response surfaces obtained through this design for two factors studied, when the great is well centered or not in the intervals studied, trying to indicate more appropriated analysis strategies in different cases. For this purpose, the full factorial was used as a witness. For the two factors study, we established a complete 9x9 factorial design with nine replicates per treatment, according to a completely randomized design, it also has been established two responses areas one with a critical point near the midpoint and the other with a critical point away from central. Defined the values of the axial points (α) equal to 1; 1,4142; 2 and 3 and the number of repetitions at the central point equal to 1, 3, 6 and 9. The 16 CCDs observations were obtained from the first repetition of the respective treatments (factorial points, axial and central) contained in the full factorial. For different simulations, it was determined the coefficients of variation equal to 5, 10, 20 and 30%. Five simulations were done by variation coefficient and response surface, totaling 640 data files. To evaluate the of approximation degree of the response surface adjusted, compared to the real one, was used as a measure, the absolute difference between the values of true and estimated coefficients (Δβi) and the absolute difference related to critical points (ac and bc) from the responses surfaces (Δac and Δbc) in relation to the factors A and B, and to measure the fit degree of each response surface, we used the mean absolute percentage error (EPMA) and the linear correlation coefficient between the fitted values and true Y (rŷyv). However, different values of α provided better estimates of the measures evaluated and, as α = 1,4142 is closer to them all, it was concluded that this value is probably among the best for treatment planning. The value of α = 1,4142, which has the property rotatability and the increase in number of repetitions at the central point provided the best fit response surface, however, the residual variance increase is not good for this estimates. Therefore, the conclusion is that the rotational CCD must be recommended for experiments under more controlled conditions, and compared with the full factorial had low efficient. In addition, the CCD presented similar results for the two surfaces of simulated responses.