A method for identifying a minimal set of test conditions in 2k experimental design

A primary task of the analysis of a 2k factorial design is to estimate the 2k unknown effects/interactions. When some of these interactions are known to be zero or negligible, a full 2k factorial design may no longer be necessary. In general, when only M effects/interactions are non-zero, only M test conditions are required for the estimation. Both fractional factorial design and Taguchi's method typically require 2n test conditions, n=2,3,4,…, and hence do not take full advantage of this fact. We first demonstrate that when there are M non-zero effects/interactions in a 2k model, not every set of M test conditions out of the 2k test conditions would suffice for estimating the M unknowns. We then propose an algorithm to find a set of M test conditions that suffices. The proposed algorithm can be used to identify all such minimal sets of test conditions. In this paper, we report two such minimal sets for all possible scenarios of interest for 23 and 24 designs. If the assumed zero interactions are indeed zero, confounding is not an issue. Moreover, such assumptions can be double-checked via ANOVA.