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Master's Dissertation
DOI
https://doi.org/10.11606/D.11.1984.tde-20220208-045553
Document
Author
Full name
Sueli Costa e Silva
Institute/School/College
Knowledge Area
Date of Defense
Published
Piracicaba, 1984
Supervisor
Title in Portuguese
Delineamento de três parâmetros
Keywords in Portuguese
DELINEAMENTO EXPERIMENTAL
ENSAIO FATORIAL
EXPERIMENTAÇÃO AGRONÔMICA
MODELOS MATEMÁTICOS
SUPERFÍCIES DE RESPOSTA
Abstract in Portuguese
Um novo tipo de delineamento foi desenvolvido para permitir ajustar aos dados um polinômio do segundo grau com duas variáveis independentes, usando três parâmetros: ẟ, ϒ e P. O delineamento e constituí do por um fatorial 2x2, onde os· níveis codificados das variáveis são -1 e +1, acrescido dos pontos codificados (ẟ, 0), (-ẟ, 0), (0, ϒ), (0, -ϒ) (0, 0) onde o ponto central é repetido P vezes. Fórmulas que permitem a ortogonalização deste delineamento foram conseguidas, sendo que quando ẟ= ϒ, o delineamento torna-se um Composto Central Ortogonal com P pontos centrais. Foram determinadas fórmulas das estimativas dos coeficientes polinomiais e suas respectivas somas de quadrados e variâncias. Pesquisando-se as variâncias das estimativas dos coeficientes, chegou-se à conclusão que quando ẟ= 1, as variâncias das estimativas de β1 e β12 são mínimas se P=1 e a variância da estimativa de β11 é mínima quando P=4. Por outro lado, quando ϒ=1, as variâncias das estimativas de β2 e β12 são mínimas se P= 1 e a variância da estimativa de β22 é mínima quando P=4. Se o pesquisador quiser adotar somente um ponto central, recomenda-se o delineamento fatorial 3x3. Para mais um ponto central, recomenda-se para o fator mais importante o valor de ẟ=1 se este fator estiver representado em X1 e ϒ= 1 se este fator estiver representado em X2. Finalmente, foi verificado que quando P e maior do que um, as variâncias das estimativas de β1, β11 e β12 são mínimas quando ẟ= 1 do que quando o delineamento transforma-se em composto central ortogonal e as variâncias das estimativas de β2, β22 e β12 são mínimas quando ϒ=1 do que quando o delineamento transforma-se em Composto Central Ortogonal.
Title in English
A three parameters design
Abstract in English
A new design was developed for fitting to data a second-degree polynomial equation with two factors and three parameters ẟ, ϒ and P. There were 8+P treatment combinations, four from the 2x2 Factorial Design were the coded levels of the X-variables were -1 and + 1 , and additi ona 1 trea tment combinations (ẟ, 0), (-ẟ, 0), (0, ϒ), (0, -ϒ), and P central points. Formulas to make the destgn orthogonal were detemined, and when ẟ= ϒ the design becomes to a Orthogonal Central Composite Design with P central points. It were determined formulas to estimate the polynomial regression coeftcients and its sums of squares and variances. It was verified when ẟ= 1 the variances of the β1 and β12 estimated coefficients are smallest if P=l and the variance of the β11 estirnated coefficient is smallest if P=4. It also verified when ϒ=1, the variances of the β2 and β12 estimated coefficients are smallest if P=1 and the variance of the β22 estimated coefficient is smallest if P=4. For one central point it is better to use a 3x3 Factorial Design and for P grea ter than one, for the mos t important fator it may to use ẟ=1 if this factor lies in X1 -axis or ϒ= 1 if this factor lies in X2 -axis . Finally, it was verified that when P is greater than one, for ẟ= 1 the variances of the β1, β11 and β12 esti'mated coefftcients are smaller than when the design becomes a Orthogonal Central Composite Design and for ϒ= 1 the variances of β2, β22 e β12 estimated coefficiénts·are -.: smaller than when the design becomes a Orthogonal Central Composite Design.
 
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Publishing Date
2022-02-08
 
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