I basically have a timespan from January until August (or any other timespan) which is divided into active periods (denoted by a red line in the plot) and inactive periods (the rest).
What I want to compute from these periods is a measure of temporal spread (couldn't think of a better name).
I've already come up with a very simple measure, the percentage of active periods, but this doesn't tell me whether active periods are spread all over the timespan. For example, both plots below have a percentage of active periods of about 50%, but the latter should have more "continuity", or temporal spread.
In the last plot, the overall percentage is even lower than 50%, but spread should be the highest of all three, because there are also active periods in May or June.
As you can see, I don't know what I am looking for exactly, so I was wondering whether there exists some sort of standard measure for this problem.