My estimation might be off by an order of magnitude but I have seen the number of about 20 million Note 7 devices shipped. My guess is that the total number of incidents is probably 200 at most. That is a ratio of 1:100'000. If they cannot narrow it down further (eg, to production batches) that is a tough nut to crack. They might be getting clues by examining damaged devices but also might not get anything out of that given the extent of the destruction. They will be examining the whole production process to see if they can find anything there that is out of spec. They might be stress testing full phones and individual components but if the failure is truly random, even if the stress testing accelerates the failure process, they would be testing a lot of devices before they see a failure in the lab given the 1:100'000 ratio.
On the one side this is process of just looking for anything that could point them into the right direction. And on the other side this is developing theories and (a) testing to confirm or rule them out and (b) if they have some confidence in their theory, even if they cannot prove it, implement countermeasures into the production process. And these two sides naturally inform each other.