Determination of formulas on the orthogonal central composite design (Box)

Detalhes bibliográficos
Autor(a) principal: Batista, Lauro Boechat
Data de Publicação: 2014
Outros Autores: Silva, Sueli Costa e
Tipo de documento: Artigo
Idioma: por
Título da fonte: Pesquisa Agropecuária Brasileira (Online)
Texto Completo: https://seer.sct.embrapa.br/index.php/pab/article/view/16760
Resumo: A theoretical study was devised to determine the formula of ʆ which makes orthogonal the central composite design (Box), with P + 1 central points and maximum of four factors. The following expressions of α was obtained: α = [-2k-1+ [22k-2 + 2k-2 (2k + 1 + P)]1/2]1/2 it was equally verified that in the case of the orthogonal central composite design, with P + 1 central points, the formulas which estimated the variances of the estimates of the polynomial equation coefficients, could be calculated through the following expressions:V (βi) = 1/r (2k+ 2α2) *α-2 V (βij) = 1/r2k *α-2 V (βii) = 1/r * [2k+ 2α4 - (2k+ 2α2)2/2k+ 2k + 1 + P]-1*α-2   Finally, it was verified that when the orthogonal central composite design has eight central points, the coefficients βii of the squared terms are estimated as precise as the coefficients βi and more precise than the coefficients βij.
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spelling Determination of formulas on the orthogonal central composite design (Box)Determinações de fórmulas no delineamento composto central ortogonal (Box)Experimental Design or Response SurfaceEstatística Experimental ou Superfície de RespostaA theoretical study was devised to determine the formula of ʆ which makes orthogonal the central composite design (Box), with P + 1 central points and maximum of four factors. The following expressions of α was obtained: α = [-2k-1+ [22k-2 + 2k-2 (2k + 1 + P)]1/2]1/2 it was equally verified that in the case of the orthogonal central composite design, with P + 1 central points, the formulas which estimated the variances of the estimates of the polynomial equation coefficients, could be calculated through the following expressions:V (βi) = 1/r (2k+ 2α2) *α-2 V (βij) = 1/r2k *α-2 V (βii) = 1/r * [2k+ 2α4 - (2k+ 2α2)2/2k+ 2k + 1 + P]-1*α-2   Finally, it was verified that when the orthogonal central composite design has eight central points, the coefficients βii of the squared terms are estimated as precise as the coefficients βi and more precise than the coefficients βij.No presente trabalho foi feito um estudo teórico visando as determinações da fórmula α que torna ortogonal o delineamento composto central (Box) e das fórmulas das estimativas das variâncias das estimativas dos coeficientes de um polinômio do segundo grau, quando ajustamos o polinômio aos dados provenientes de um delineamento composto central ortogonal, com P + 1 pontos centrais e com um máximo de quatro fatores, como também o estudo da precisão das estimativas dos coeficientes. Verificou-se que a fórmula de α que torna ortogonal o delineamento composto central, com P + 1 pontos centrais e para um máximo de quatro fatores, é dada pela expressão: α = [-2k-1 + [22k-2 + 2k-2(2k + 1 + P)]1/2]1/2 Foi também verificado que as fórmulas das estimativas das variâncias das estimativas dos coeficientes do polinômio do segundo grau, quando ajustamos esse polinômio a dados provenientes do delineamento composto central ortogonal, com P + 1 pontos centrais e um máximo de quatro fatores, são dadas pelas expressões:V (βi) = 1/r (2k+ 2α2) *α-2 V (βij) = 1/r2k *α-2 V (βii) = 1/r * [2k+ 2α4 - (2k+ 2α2)2/2k+ 2k + 1 + P]-1*α-2  Verificou-se, ainda, que, quando são usados oito pontos centrais, isto é, quando P = 7, a estimativa de βii é tão precisa quanto a estimativa de βi e mais eficiente do que a estimativa de βij.Pesquisa Agropecuaria BrasileiraPesquisa Agropecuária BrasileiraBatista, Lauro BoechatSilva, Sueli Costa e2014-04-15info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://seer.sct.embrapa.br/index.php/pab/article/view/16760Pesquisa Agropecuaria Brasileira; v.13, n.2, fev. 1978; 39-47Pesquisa Agropecuária Brasileira; v.13, n.2, fev. 1978; 39-471678-39210100-104xreponame:Pesquisa Agropecuária Brasileira (Online)instname:Empresa Brasileira de Pesquisa Agropecuária (Embrapa)instacron:EMBRAPAporhttps://seer.sct.embrapa.br/index.php/pab/article/view/16760/11087info:eu-repo/semantics/openAccess2014-04-15T19:14:28Zoai:ojs.seer.sct.embrapa.br:article/16760Revistahttp://seer.sct.embrapa.br/index.php/pabPRIhttps://old.scielo.br/oai/scielo-oai.phppab@sct.embrapa.br || sct.pab@embrapa.br1678-39210100-204Xopendoar:2014-04-15T19:14:28Pesquisa Agropecuária Brasileira (Online) - Empresa Brasileira de Pesquisa Agropecuária (Embrapa)false
dc.title.none.fl_str_mv Determination of formulas on the orthogonal central composite design (Box)
Determinações de fórmulas no delineamento composto central ortogonal (Box)
title Determination of formulas on the orthogonal central composite design (Box)
spellingShingle Determination of formulas on the orthogonal central composite design (Box)
Batista, Lauro Boechat
Experimental Design or Response Surface
Estatística Experimental ou Superfície de Resposta
title_short Determination of formulas on the orthogonal central composite design (Box)
title_full Determination of formulas on the orthogonal central composite design (Box)
title_fullStr Determination of formulas on the orthogonal central composite design (Box)
title_full_unstemmed Determination of formulas on the orthogonal central composite design (Box)
title_sort Determination of formulas on the orthogonal central composite design (Box)
author Batista, Lauro Boechat
author_facet Batista, Lauro Boechat
Silva, Sueli Costa e
author_role author
author2 Silva, Sueli Costa e
author2_role author
dc.contributor.none.fl_str_mv

dc.contributor.author.fl_str_mv Batista, Lauro Boechat
Silva, Sueli Costa e
dc.subject.por.fl_str_mv Experimental Design or Response Surface
Estatística Experimental ou Superfície de Resposta
topic Experimental Design or Response Surface
Estatística Experimental ou Superfície de Resposta
description A theoretical study was devised to determine the formula of ʆ which makes orthogonal the central composite design (Box), with P + 1 central points and maximum of four factors. The following expressions of α was obtained: α = [-2k-1+ [22k-2 + 2k-2 (2k + 1 + P)]1/2]1/2 it was equally verified that in the case of the orthogonal central composite design, with P + 1 central points, the formulas which estimated the variances of the estimates of the polynomial equation coefficients, could be calculated through the following expressions:V (βi) = 1/r (2k+ 2α2) *α-2 V (βij) = 1/r2k *α-2 V (βii) = 1/r * [2k+ 2α4 - (2k+ 2α2)2/2k+ 2k + 1 + P]-1*α-2   Finally, it was verified that when the orthogonal central composite design has eight central points, the coefficients βii of the squared terms are estimated as precise as the coefficients βi and more precise than the coefficients βij.
publishDate 2014
dc.date.none.fl_str_mv 2014-04-15
dc.type.none.fl_str_mv
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://seer.sct.embrapa.br/index.php/pab/article/view/16760
url https://seer.sct.embrapa.br/index.php/pab/article/view/16760
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv https://seer.sct.embrapa.br/index.php/pab/article/view/16760/11087
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Pesquisa Agropecuaria Brasileira
Pesquisa Agropecuária Brasileira
publisher.none.fl_str_mv Pesquisa Agropecuaria Brasileira
Pesquisa Agropecuária Brasileira
dc.source.none.fl_str_mv Pesquisa Agropecuaria Brasileira; v.13, n.2, fev. 1978; 39-47
Pesquisa Agropecuária Brasileira; v.13, n.2, fev. 1978; 39-47
1678-3921
0100-104x
reponame:Pesquisa Agropecuária Brasileira (Online)
instname:Empresa Brasileira de Pesquisa Agropecuária (Embrapa)
instacron:EMBRAPA
instname_str Empresa Brasileira de Pesquisa Agropecuária (Embrapa)
instacron_str EMBRAPA
institution EMBRAPA
reponame_str Pesquisa Agropecuária Brasileira (Online)
collection Pesquisa Agropecuária Brasileira (Online)
repository.name.fl_str_mv Pesquisa Agropecuária Brasileira (Online) - Empresa Brasileira de Pesquisa Agropecuária (Embrapa)
repository.mail.fl_str_mv pab@sct.embrapa.br || sct.pab@embrapa.br
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