Selection of non-regular fractional factorial designs when some two-factor interactions are important

Introduction: Non-regular two-level fractional factorial designs, such as Placket-Burman designs, are becoming popular choices in many areas of scientific investigation due to their run size economy and flexibility. The run size of non-regular two-level factorial designs is a multiple of 4. They fill the gaps left by the regular two-level fractional factorial designs whose run size is always a power of 2 (4, 8, 16, 32, ...). In non-regular factorial designs each main effect is partially confounded with all the two-factor interactions not involving itself. Because of this complex aliasing structure, non-regular factorial designs had not received sufficient attention until recently. ... In practical applications of non-regular designs, it is often in the case that some of the two-factor interactions are important and need to be estimated in addition to the main effects. In this article, we consider how to select non-regular two-level fractional factorial designs when some of the two-factor interactions are presumably important. We propose and study a method to select the optimal non-regular two-level fractional factorial designs in the situation that some of the two-factor interactions are potentially important. We then discuss how to search for the best designs according to this method and present some results for the Plackett-Burman design of 12 runs.