  We introduce several statistics on ordered partitions of sets, that is, set
partitions where the blocks are permuted arbitrarily. The distribution of these
statistics is closely related to the q-Stirling numbers of the second kind.
Some of the statistics are generalizations of known statistics on set
partitions, but others are entirely new. All the new ones are sums of two
statistics, inspired by statistics on permutations, where one of the two
statistics is based on a certain partial ordering of the blocks of a partition.
