Efficient Two-Level Designs for Estimating All Main Effects and Two-Factor Interactions

Regular designs for a large number of factors require many more treatment combinations than there are lower order effects to be estimated. For example, 29−2 = 128 treatment combinations are required to estimate only nine main effects and their 36 two-factor interactions. Nonregular orthogonal designs as well as nonorthogonal designs provide attractive alternatives in such cases. This article reviews the literature regarding alternatives to the usual orthogonal resolution V designs and suggests questions for future research. The topic is illustrated with a ballistic missile simulation application requiring estimation of main effects and two-factor interactions for 47 factors. For such large examples, run-size efficiency is more important than variance efficiency.