Optimal blocking Schemes for Two-level and Three-level Fractional Factorial Designs

Abstract

Blocking is commonly used in design of experiments to reduce the systematic variation and increase the precision of estimations of effects. For 2n-k fractional factorial design in 2p blocks, Sun, Wu and Chen (1997), Sitter, Chen and Feder (1997) study the confounding pattern between blocking factors and treatment factors and propose some criteria to choose optimal blocking schemes. Their criteria are primarily based on the word lengths of the defining contrast subgroup. We point out some weakness of these criteria and suggest several modifictaions which allow more lower order effects to be estimable. Extensions to 3-level fractional factorial design are also considered. (This work is joint with C. F. Jeff Wu)