Techniques for Constructing Fractional Replicate Plans

This paper is a review of techniques for obtaining the treatment combinations that comprise a fraction of a factorial arrangement. Several procedures for constructing fractional replicate plans, which in their original form appear to be different, are presented in a manner which illustrates their similarities. The techniques discussed include orthogonal and non-orthogonal plans for both symmetrical and asymmetrical factorial experiments. The plans developed range from those that permit estimation of main effects only, to those that permit estimation of main effects and all two-factor interaction effects.