Generalized Activities and Reliability

The analysis of the Tutte polynomial of a matroid using activities is associated with a shelling of the family of spanning sets. We introduce an activities analysis of the reliability of a system specified by an arbitrary clutter, associated with an \( \mathcal{S} \)-partition rather than a shelling. These activities are related to a method of constructing Boolean interval partitions developed by Dawson in the early 1980s.