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Master's Dissertation
DOI
https://doi.org/10.11606/D.11.1974.tde-20240301-152728
Document
Author
Full name
Laede Maffia de Oliveira
Institute/School/College
Date of Defense
Published
Piracicaba, 1974
Supervisor
 
Title in Portuguese
Eficiência de delineamentos para ajustamento de superfícies de resposta
Keywords in Portuguese
DELINEAMENTO EXPERIMENTAL
MODELOS MATEMÁTICOS
SUPERFÍCIES DE RESPOSTA
Abstract in Portuguese
O presente trabalho visa a comparar a precisão das estimativas dos coeficientes dos modelos do grupo fatorial 3k para k = 2, 3, 4, relativamente às estimativas correspondentes, obtidas dos modelos de delineamento composto central rotativo para k = 2, 3, 4, usando-se um ou mais pontos no centro. A metodologia usada baseia-se nos trabalhos de BOX e WIIBON (1951), CANPOS (1967), PIMENTEL GOMES e CAMPOS (1972). Para cada delineamento, tendo em vista as diversas equações comumente utilizadas, foram obtidas as respectivas matrizes de dispersão. Pela comparação dos termos destas matrizes, após conseguir-se conveniente equivalência de escala, obtivemos as variâncias seguintes, com i ≠ j: 1 – Para k = 2: 1.1 – Fatorial: (descrito no resumo); 1.2 – Composto central rotativo: (descrito no resumo). 2 – Para k = 3: 2.1 – Fatorial: (descrito no resumo); 2.2 - Composto central rotativo: (descrito no resumo). 3 – Para k = 4: 3.1 – Fatorial fracionado: (descrito no resumo); 3.2 - Composto central rotativo: (descrito no resumo). Logo, o grupo fatorial 3k, para k = 2, 3, 4 é mais eficiente para o ajustamento de superfícies de resposta do que os delineamentos compostos centrais rotativos correspondentes, pois fornece variâncias das estimativas muito menores.
Abstract in English
This study aims at comparing the precision of the estimates of the coefficients from the models of factorial series 3k for k = 2, 3, 4 with the correspondi.ng estimates obtained from models of central composite rotatable design for k = 2, 3, 4, using one or more points in the center. The methodology used was based on the works of BOX and WILSON (1951), CAMPOS (1967), PIMENTEL GOMES and CAMPOS (1972). For each design, considering the various equations usually used, the respective dispersion matrices were obtained. The variances for i Ͱ j, after comparing the terms of the matrices and obtaining convenient equivalence of scale were: 1 - For k = 2: 1.1 – Factorial: (described in the summary); 1.2 - Central composite rotatable: (described in the summary). 2 – For k = 3: 2.1 - Factorial: (described in the summary); 2.2. – Central composite rotatable: (described in the summary). 3 – For k = 4: 3.1 – Fractional replication: (described in the summary); 3.2 - Central composite rotatable: (described in the summary). It is concluded that the factorial series 3k for k = 2, 3, 4 is more efficient than the corresponding central composite rotatable design because the estimates have smaller variance.
 
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Publishing Date
2024-03-14
 
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