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

Detalhes bibliográficos
Autor(a) principal: Perázio, Bráulia Aparecida de Almeida
Data de Publicação: 2010
Tipo de documento: Dissertação
Idioma: por
Título da fonte: LOCUS Repositório Institucional da UFV
Texto Completo: http://locus.ufv.br/handle/123456789/4029
Resumo: 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.
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spelling Perázio, Bráulia Aparecida de Almeidahttp://lattes.cnpq.br/7556927554031300Santos, Nerilson Terrahttp://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4782537A2Martins Filho, Sebastiãohttp://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4723282T5Ribeiro Junior, José Ivohttp://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4723282Y6Silva, Fabyano Fonseca ehttp://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4766260Z2Lopes, Jaques Silveirahttp://lattes.cnpq.br/16056989458524482015-03-26T13:32:09Z2011-06-082015-03-26T13:32:09Z2010-02-24PERÁZIO, Bráulia Aparecida de Almeida. Effects of central and axial points on the efficiency of central composite design. 2010. 68 f. Dissertação (Mestrado em Estatística Aplicada e Biometria) - Universidade Federal de Viçosa, Viçosa, 2010.http://locus.ufv.br/handle/123456789/4029In 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.Na análise de problemas nos quais a variável resposta de interesse é influenciada por diversos fatores e cujo objetivo é otimizá-la, propõe-se utilizar delineamentos para superfície de resposta. Dentre eles, destaca-se o Delineamento Composto Central (DCC), que é um delineamento de segunda ordem, podendo apresentar características de rotacionalidade e/ou ortogonalidade. Tais delineamentos são simples, econômicos, promissores e bastante flexíveis. Estes são constituídos de pontos fatoriais, axiais e central. Deste modo, o objetivo deste trabalho foi de investigar, por meio da simulação de dados, os efeitos dos pontos axiais e do número de pontos centrais sobre a qualidade dos ajustes das superfícies de reposta obtidas, por meio desse delineamento para dois fatores estudados, quando a região ótima está ou não bem centralizada nos intervalos estudados, buscando assim, indicar estratégias de análises mais adequadas em diferentes casos. Para tanto, utilizou-se como testemunha, o fatorial completo. Para o estudo de dois fatores, foi estabelecido um fatorial completo 9x9 com nove repetições por tratamento, segundo o delineamento inteiramente casualizado, estabeleceu-se também duas superfícies de respostas, uma com ponto crítico próximo ao ponto central e a outra com ponto crítico afastado do ponto central. Definiu-se os valores dos pontos axiais (α) iguais a 1; 1,4142; 2 e 3 e do número de repetições no ponto central iguais a 1, 3, 6 e 9. As observações dos 16 DCCs, foram obtidas a partir da primeira repetição dos respectivos tratamentos (pontos fatoriais, axiais e central) contidos no fatorial completo. Para as diferentes simulações, foi especificado os coeficientes de variação iguais a 5, 10, 20 e 30%. Realizou-se cinco simulações por coeficiente de variação e por superfície de resposta, totalizando 640 arquivos de dados. Para avaliação do grau de aproximação da superfície de resposta ajustada, em relação à verdadeira, utilizou-se como medida a diferença absoluta entre os valores dos coeficientes verdadeiros e estimados (Δβi) e a diferença absoluta relacionada aos pontos críticos (ac e bc) das superfícies de respostas (Δac e Δbc) em relação aos fatores A e B, e para medir o grau de ajuste de cada superfície de resposta utilizou-se o erro percentual médio absoluto (EPMA) e o coeficiente de correlação linear entre os valores ajustados e verdadeiros de Y ( rŷyv ). Contudo, diferentes valores de α proporcionaram melhores estimativas das medidas avaliadas e, como α = 1,4142 está mais próxima de todas elas, concluiu-se que esse valor está, provavelmente entre os melhores para o planejamento dos tratamentos. O valor de α = 1,4142, que possui a propriedade de rotacionalidade, e o aumento do número de repetições no ponto central proporcionou melhor ajuste da superfície de resposta, porém, o aumento da variância residual prejudicou tais estimativas. Portanto, conclui-se que o DCC rotacional deve ser recomendado para experimentos sob condições mais controladas, e quando comparado com o fatorial completo apresentou-se menos eficiente. Além disso, o DCC apresentou resultados similares para as duas superfícies de respostas simuladas.application/pdfporUniversidade Federal de ViçosaMestrado em Estatística Aplicada e BiometriaUFVBREstatística Aplicada e BiometriaSuperfície de respostaDelineamento de tratamentosQualidade de ajusteResponse surfaceTreatment designsQuality of fittingCNPQ::CIENCIAS AGRARIASEfeitos dos pontos axiais e centrais sobre a eficiência do delineamento composto centralEffects of central and axial points on the efficiency of central composite designinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccessreponame:LOCUS Repositório Institucional da UFVinstname:Universidade Federal de Viçosa (UFV)instacron:UFVORIGINALtexto completo.pdfapplication/pdf1306121https://locus.ufv.br//bitstream/123456789/4029/1/texto%20completo.pdfa37665a647e350c65a7c8f5fa7dc4f7bMD51TEXTtexto completo.pdf.txttexto completo.pdf.txtExtracted texttext/plain98396https://locus.ufv.br//bitstream/123456789/4029/2/texto%20completo.pdf.txt37852f0b4dc26baea87c217143623ae8MD52THUMBNAILtexto completo.pdf.jpgtexto completo.pdf.jpgIM Thumbnailimage/jpeg3685https://locus.ufv.br//bitstream/123456789/4029/3/texto%20completo.pdf.jpge2740e7b9d522b35287e4bba0833696eMD53123456789/40292016-04-09 23:17:54.447oai:locus.ufv.br:123456789/4029Repositório InstitucionalPUBhttps://www.locus.ufv.br/oai/requestfabiojreis@ufv.bropendoar:21452016-04-10T02:17:54LOCUS Repositório Institucional da UFV - Universidade Federal de Viçosa (UFV)false
dc.title.por.fl_str_mv Efeitos dos pontos axiais e centrais sobre a eficiência do delineamento composto central
dc.title.alternative.eng.fl_str_mv Effects of central and axial points on the efficiency of central composite design
title Efeitos dos pontos axiais e centrais sobre a eficiência do delineamento composto central
spellingShingle Efeitos dos pontos axiais e centrais sobre a eficiência do delineamento composto central
Perázio, Bráulia Aparecida de Almeida
Superfície de resposta
Delineamento de tratamentos
Qualidade de ajuste
Response surface
Treatment designs
Quality of fitting
CNPQ::CIENCIAS AGRARIAS
title_short Efeitos dos pontos axiais e centrais sobre a eficiência do delineamento composto central
title_full Efeitos dos pontos axiais e centrais sobre a eficiência do delineamento composto central
title_fullStr Efeitos dos pontos axiais e centrais sobre a eficiência do delineamento composto central
title_full_unstemmed Efeitos dos pontos axiais e centrais sobre a eficiência do delineamento composto central
title_sort Efeitos dos pontos axiais e centrais sobre a eficiência do delineamento composto central
author Perázio, Bráulia Aparecida de Almeida
author_facet Perázio, Bráulia Aparecida de Almeida
author_role author
dc.contributor.authorLattes.por.fl_str_mv http://lattes.cnpq.br/7556927554031300
dc.contributor.author.fl_str_mv Perázio, Bráulia Aparecida de Almeida
dc.contributor.advisor-co1.fl_str_mv Santos, Nerilson Terra
dc.contributor.advisor-co1Lattes.fl_str_mv http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4782537A2
dc.contributor.advisor-co2.fl_str_mv Martins Filho, Sebastião
dc.contributor.advisor-co2Lattes.fl_str_mv http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4723282T5
dc.contributor.advisor1.fl_str_mv Ribeiro Junior, José Ivo
dc.contributor.advisor1Lattes.fl_str_mv http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4723282Y6
dc.contributor.referee1.fl_str_mv Silva, Fabyano Fonseca e
dc.contributor.referee1Lattes.fl_str_mv http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4766260Z2
dc.contributor.referee2.fl_str_mv Lopes, Jaques Silveira
dc.contributor.referee2Lattes.fl_str_mv http://lattes.cnpq.br/1605698945852448
contributor_str_mv Santos, Nerilson Terra
Martins Filho, Sebastião
Ribeiro Junior, José Ivo
Silva, Fabyano Fonseca e
Lopes, Jaques Silveira
dc.subject.por.fl_str_mv Superfície de resposta
Delineamento de tratamentos
Qualidade de ajuste
topic Superfície de resposta
Delineamento de tratamentos
Qualidade de ajuste
Response surface
Treatment designs
Quality of fitting
CNPQ::CIENCIAS AGRARIAS
dc.subject.eng.fl_str_mv Response surface
Treatment designs
Quality of fitting
dc.subject.cnpq.fl_str_mv CNPQ::CIENCIAS AGRARIAS
description 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.
publishDate 2010
dc.date.issued.fl_str_mv 2010-02-24
dc.date.available.fl_str_mv 2011-06-08
2015-03-26T13:32:09Z
dc.date.accessioned.fl_str_mv 2015-03-26T13:32:09Z
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dc.identifier.citation.fl_str_mv PERÁZIO, Bráulia Aparecida de Almeida. Effects of central and axial points on the efficiency of central composite design. 2010. 68 f. Dissertação (Mestrado em Estatística Aplicada e Biometria) - Universidade Federal de Viçosa, Viçosa, 2010.
dc.identifier.uri.fl_str_mv http://locus.ufv.br/handle/123456789/4029
identifier_str_mv PERÁZIO, Bráulia Aparecida de Almeida. Effects of central and axial points on the efficiency of central composite design. 2010. 68 f. Dissertação (Mestrado em Estatística Aplicada e Biometria) - Universidade Federal de Viçosa, Viçosa, 2010.
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