Delineamento Fatorial Duplo.

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.