A Note on Small Orthogonal Main-Effect Plans for Factorial Experiments

Abstract

Methods for obtaining orthogonal main-effect plans for factorial experiments in which the number of trials is at least as small as that of any corresponding plans previously developed are described in papers by Addelman and Kempthorne [11 and Addelman [2]. This note shows by example that orthogonal main-effect plans smaller than those obtainable by the Addelman and Kempthorne procedures do exist in some instances. The example used to show this fact is a fraction of a 37 factorial containing only 16 trials which is slightly smaller than the 18 trials in their smallest plan for the 37 factorial experiment. (The particular plan for the 37 in 18 trials had been developed previously by Burman [3] and by Bose and Bush [4].) The orthogonal main-effect plan with 16 trials for the 37 factorial experiment is developed from the Plackett-Burman [3] plan,