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.