Two-level factorial designs with extreme numbers of level changes

Abstract

The construction of run orders of two-level factorial designs with extreme (minimum and maximum) numbers of level changes is considered. Minimizing the number of level changes is mainly due to economic considerations, while the problem of maximizing the number of level changes arises from some recent results on trend robust designs. The construction is based on the fact that the $2^k$ runs of a saturated regular fractional factorial design for $2^k -1$ factors can be ordered in such a way that the numbers of level changes of the factors consist of each integer between 1 and $2^k -1$. Among other results, we give a systematic method of constructing designs with minimum and maximum numbers of level changes among all designs of resolution at least three and among those of resolution at least four. It is also shown that among regular fractional factorial designs of resolution at least four, the number of level changes can be maximized and minimized by different run orders of the same fraction.