Time dependent Classification problem I am trying to solve a decision making problem. In it, information evolves and increases with time for each event observed, and the history of the event may be useful.

The problem is as follows: in an electric network at time $t_0$ there is signal that automatically triggers the possible need of a technical intervention in a network to correct the problem. The system at $t_0$ has a large set of general indicators describing the state of the network based on which I'd like to determine whether to proceed with an intervention at $t_{0}$. 

It's possible to carry specific measurements at the point where the problem was detected (this takes some time $\Delta t$). At this stage we can again ask whether the intervention is necessary or not? We can iterate this procedure a few times. Then, my question is, which is the machine learning method best suited for this classification problem? Can it be formulated as a Survival problem?
From the description of the problem, you can just choose whatever classification algorithm you like to classify the need of intervention at  $t_{0}$.

The general rule for choosing a classifier for this is to start simple--e.g., by using nearest neighbor and iterate to more powerful classifiers until you get enough accuracy.

If additional measurements at $t_{0}$ can be made a classifier can be used to determine the necessity of intervention without this additional data, then based on the probability output of this classifier and a threshold the additional measurements can be triggered. Based on this measurements another probability can be output which hopefully uses more informative features.

If you care about $\Delta t$, you should think about wether there is a real time dependency. Does the need of intervention depend upon the series of classifications? Is the order of determining interventions as necessary important for you? 

In my opinion, you do not have to care about ordering for this application.
Rather, I would suggest pooling classifications for one instance according to the most frequent label or something like that.