The following speed statistics were updated in July 2017, and courtesy of the crowd-sourced journal review website Scirev.
In 2015 Daniel Himmelstein published a great speed comparison blog post based on his in-depth analysis of a range of journals. The image below shows how PeerJ stacks up against other leading journals:
Please note that the 24 hour publication time assumes your article passes editorial staff checks first time (most do). If these checks identify changes to be made, this may delay publication of your Preprint.