Double Factorial Design.

Double Factorial Design.

Authors

  • Lauro Boechat Batista Universidade Federal Rural do Rio de Janeiro.
  • Eliza Helena de Souza Faria Universidade Federal Rural do Rio de Janeiro.
  • Maria Eunice O C Rodrigues Universidade Federal Fluminense.
  • Kellen Moreira Batista Universidade Federal Rural do Rio de Janeiro.
  • Vandeir Francisco Guimarães Universidade Federal Rural do Rio de Janeiro.

DOI:

https://doi.org/10.5433/1679-0375.1994v14n4p346

Keywords:

Response surface, Second-order polynomial equations.

Abstract

This design was developed for fitting to data a second-degree polynomial equation with two variables, denominated Double Factorial Design. The purpose was to make it orthogonal when five levels of each of the factors were involved. In this design there are 17 treatment combinations, and 9 of them belong to a 32 factorial design where the coded levels of the X-variables were -1, 0, and +1, and the others added to the (0, 0) central point make a 32 factorial design where the coded levels of the X-variables were -a, 0, and +a . It was verified that if a= 0,780776406, the design becomes orthogonal. In this design, each level of the X1-variable must have 3 or 5 different levels of the other X2-variable and vice-versa. Several formulas were determinated, like the formulas to make the design orthogonal, to estimate the polynomial equation coefficients, to estimate the variances of the polynomial regression coefficients, and so on. It was verified that the Double Factorial Design is less efficient than the 32 Factorial Design and more efficient than the 52 and 72 Factorial Designs, for all regression coefficients, when adopting PIMENTEL GOMES & CAMPOS'S METHOD, and in case of using the same total area for all the compared designs.

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Author Biographies

Lauro Boechat Batista, Universidade Federal Rural do Rio de Janeiro.

Departamento de Matemática.

Eliza Helena de Souza Faria, Universidade Federal Rural do Rio de Janeiro.

Departamento de Matemática.

Maria Eunice O C Rodrigues, Universidade Federal Fluminense.

Departamento de Saúde da Comunidade do Centro de Ciências Médicas.

Kellen Moreira Batista, Universidade Federal Rural do Rio de Janeiro.

Aluna do Curso de Agronomia da UFRRJ.

Vandeir Francisco Guimarães, Universidade Federal Rural do Rio de Janeiro.

Aluno do Curso de Agronomia da UFRRJ e ex-bolsista do CNPq.

Published

2004-12-15

How to Cite

Batista, L. B., Faria, E. H. de S., Rodrigues, M. E. O. C., Batista, K. M., & Guimarães, V. F. (2004). Double Factorial Design. Semina: Ciências Exatas E Tecnológicas, 14(4), 346–359. https://doi.org/10.5433/1679-0375.1994v14n4p346

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