This produces both shear stress (i.e. stress that promotes sliding on the fault) and normal stress (i.e. stress that resist sliding on the fault due to friction).
One common manifestation of the elastic rebound theory says that there is some relatively fixed stress ratio at which the shear stress overcomes the frictional resistance to slip and the fault slides rapidly in an earthquake. The basic assumption (which is supported by data for some well-studied faults such as the San Andreas) is that the rates of strain accumulation are generally constant through time, and therefore earthquakes on a fault are quasiperiodic in time and have more or less similar magnitudes. These are called 'characteristic earthquakes'.
In this situation, then the likelihood of an earthquake on a given part of a fault does increase with time since the last earthquake. I wrote a blog post quantifying this for the southern San Andreas Fault [1], using data from the geologic record and only a few assumptions (basically just that the geologic record contains all of the earthquakes).
However, though very few researchers disagree with the fundamental principles of elastic rebound theory, there is an ongoing scientific debate over whether earthquakes are periodic and characteristic, or more or less random. Many statistical seismologists believe that they are the common form of 'random', i.e. that the likelihood of an earthquake doesn't change with time since the last earthquake. Some faults (and especially larger fault systems) seem to behave in this fashion, but for an individual fault this implies very different earthquake physics. There are huge fights in places like California between senior scientists over this topic when doing seismic hazard modeling. Additionally there are other statistical distributions than either characteristic/quasiperiodic and random (Poissonian) that produce different behavior [2,3]--with some models, the longer it's been since the last earthquake, the longer it will be until the next, and with others after some time for stress to renew on the fault, it becomes basically random.
For storms, floods, etc. the likelihood of a big event happening in a given year is more or less equal every year and therefore 'random' with the exception of some multiyear cycles such as El Niño. However, over shorter timescales, they aren't. Big storms are more likely to occur during rainy seasons rather than dry seasons, and big floods are more likely soon after previous big floods (i.e. days to weeks) because the meterological conditions that generate them may be persistent and the groundwater is still high, which means that it takes less rain to get the same river levels.
[1]: http://rocksandwater.net/blog/2016/07/wrightwood-recurrence/ [2]: https://pdfs.semanticscholar.org/3071/de51c5abc4f770b0b11ede... [3]: http://windofweef.jp/library/o_m/disaster_prevention/img/10....