Fractional Factorial Designs for Estimating Main Effects Orthogonal to Two-Factor Interactions: (3 Superscript N) and (2 Superscript M) X (3 Superscript N) Series.

摘要

Fractional factorial designs are considered of the (3 superscript n) and (2 superscript m) x (3 superscript n) series, and of resolution IV, i.e. where one desires to estimate only the main effects but the 2- factor interactions are not negligible. Such designs are needed both for uniresponse and multiresponse experiments. The presently known designs are usually of uneconomic size and therefore cumbersome. Here it is shown that for the 3n series, a necessary and sufficient condition that a design be of resolution IV (i.e. where main effects are estimable orthogonal to other effects) is that it be an orthogonal array of strength 3. Similar conditions are obtained for the (2 superscript m) x (3 superscript n) series. (Author)