How to estimate when next event occurs? From a series of binary machine failure events, say occured on 
20. Feb. 2013
18. Aug. 2013
03. Jun. 2014
04. Dec. 2014
09. Oct. 2015
14. May 2016

I would like to estimate when the next failure will occur as per today. In my understanding, since from to day to the last failure (May 2016) more time has passed than since May to Oct. 2015, the next failure actually is overdue (assuming no maintenance has been done in the meanwhile).
What are standard methods for scenarios like these?
 A: Have a look at this excellent post on using Weibull distributions in a sequential network.
https://ragulpr.github.io/2016/12/22/WTTE-RNN-Hackless-churn-modeling/
This contains by far the best illustration of how to think (and visualize) about time to event prediction / survival analysis I have come across.  It also has an applied example at end of jet engine failures ( akin to your machine failure example).
For your problem in particular the RNN might be overkill. Just a marginal Weibull distribution estimate based on time between failures already gets you to an answer about "what's the chance this machine will fail in next n days?" Using standard probability / survival analysis methodology . See https://bookdown.org/mpfoley1973/data-sci/survival-curve-estimation.html for a tutorial with examples in R.
I didn't see any mention of covariates in your example, so being overdue is just based on when prob("survived until now" | model at day 0) becomes less likely than a threshold specified based on your risk tolerance.
Note: With continually measured covariates / features of each machine (e.g. temperature, noise) this becomes a bit more tricky and it's not clear to me how to define - let alone predict - a notion of 'being overdue conditioned on constantly updated features' in a meaningful way.
