Abstract
This paper presents three kinds of balanced fractional 3m factorial designs
such that the general mean and all the main effects are estimable, and furthermore
(A) the linear by linear components of the two-factor interaction are estimable, and
the factorial effects of the quadratic by quadratic and linear by quadratic ones of the
two-factor interaction are confounded with each other, (B) the quadratic by quadratic
ones of the two-factor interaction are estimable, and the effects of the linear by linear
and linear by quadratic ones of the two-factor interaction are confounded with each
other, and (C) the linear by quadratic ones of the two-factor interaction are estimable,
and the effects of the linear by linear and quadratic by quadratic ones of the two-factor
interaction are confounded with each other, where the three-factor and higher-order
interactions are assumed to be negligible and the number of assemblies is less than the
number of non-negligible factorial effects. These designs are concretely given by the
indices of a balanced array of full strength, which is called a simple array.
