Two-Level Factorial and Fractional Factorial Designs in Blocks of Size Two

Abstract

When two-level designs are split into blocks of size two, the traditional method is to use mirror-image (foldover) pairs of runs, in which the signs of the factors are completely changed in the second run of the pair. This enables the estimation of all main effects clear of blocks, but of nothing else. We point out that by employing more runs, but still using blocks of size two, all the available effects can be estimated free of blocks. This is useful to know in situations where runs are cheap but the response varies over time, batch, or some other characteristic external to the experimental factors. In general, for a basic 2^k-p design (p ≥ 0), (k - p) 2^k-p runs are needed, with equal replications for all treatment combinations.

• Blocking
• Factorial Designs
• Fractional Factorial Designs

Additional information

Notes on contributors

Norman R. Draper

Dr. Draper is a Professor of Statistics. He is a Fellow of ASQC.

Irwin Guttman

Dr. Guttman is a Professor of Statistics.