  Several Open Source Software (OSS) projects depend on the continuity of their
development communities to remain sustainable. Understanding how developers
become inactive or why they take breaks can help communities prevent
abandonment and incentivize developers to come back. In this paper, we propose
a novel method to identify developers' inactive periods by analyzing the
individual rhythm of contributions to the projects. Using this method, we
quantitatively analyze the inactivity of core developers in 18 OSS
organizations hosted on GitHub. We also survey core developers to receive their
feedback about the identified breaks and transitions. Our results show that our
method was effective for identifying developers' breaks. About 94% of the
surveyed core developers agreed with our state model of inactivity; 71% and 79%
of them acknowledged their breaks and state transition, respectively. We also
show that all core developers take breaks (at least once) and about a half of
them (~45%}) have completely disengaged from a project for at least one year.
We also analyzed the probability of transitions to/from inactivity and found
that developers who pause their activity have a ~35-55\% chance to return to an
active state; yet, if the break lasts for a year or longer, then the
probability of resuming activities drops to ~21-26%, with a ~54% chance of
complete disengagement. These results may support the creation of policies and
mechanisms to make OSS community managers aware of breaks and potential project
abandonment.
