Analysing no-confounding designs using the Dantzig selector

No-confounding designs in 16 runs for 6, 7 and 8 factors are non-regular fractional factorial designs that have been suggested as attractive alternatives to the regular minimum aberration resolution IV designs because they do not completely confound any two-factor interactions with each other. These designs allow for potential estimation of main effects and a few two-factor interactions without the need for follow-up experimentation. Analysis methods for non-regular designs are areas of ongoing research, because standard variable selection techniques such as stepwise regression may not always be the best approach. We investigate the use of the Dantzig selector for analysing no-confounding designs. Through a series of examples we show that this technique is very effective for identifying the set of active factors in no-confounding designs when there are three of four active main effects and up to two active two-factor interactions.