Long rant coming. Sorry ‘bout that..
Yes, this is a situation that might be modeled mathematically. Plenty of people know how to do this. I’ve even done a little bit of that myself.
It would most likely involve many variables, and thousands of simulations run with separate probability distributions and cross correlations on each of the variables. You would most likely want to make multiple runs using different underlying assumptions as a way of testing the sensitivity of the results to the various estimates used. The final result would be a sensitivity analysis and an outcome probability distribution.
Caveat: The outcome would certainly look “scientific,” but the “garbage in, garbage out” rule would still apply. Anyone who knows how to do this could skew the result if they were so inclined. Spotting what they did would require knowledge of the underlying engineering issues plus knowledge of the model specifics.
I hope someone is actually doing this type of analysis, and the data they use is unbiased. If they are, there seem to be enough things that might go wrong, and a high enough probability associated with each, that the combined risk profile an analysis like this would generate might not look so good... The public would never see it.
HOWEVER...
You don’t need advanced math and a computer to know that the more things that MIGHT go wrong, the higher the odds are that at least one of them WILL go wrong.
You don’t need advanced math and a computer to figure out that if you don’t fix something it is likely to get worse.
You don’t need advanced math and a computer to know that if a dam is leaking enough to create a large green spot you should dam sure figure out why.
The giant underlying exogenous variable is the weather. If this winter is as wet as last winter, then the spillway will again be needed, and the gates/tendons/pillars will again be put to the test. Absent repairs, sooner or later they will fail that test.
Even if the spillway is not used this winter, the green spot will be an issue whenever the lake rises to a level high enough for more water to leak out. This does NOT seem to be a self-sealing leak..
In a complex system, any single point of failure must be considered a failure if there is no "redundancy" as a backup. In true "worst case analysis" of High Risk Systems there is no "Monte Carlo" applied.
DWR is required to do FERC Part 12D Potential Failure Mode Analysis (PFMA) exercises but the problem has been they have been effectively using "assumed" data rather than KNOWN* data. Worse yet, the Dam industry has been warning for years of the potential of blowouts of spillways from Stagnation Pressure. The Main spillway had all of the classic sign and symptoms but this was overlooked or not understood. So yes, it became a GIGO (garbage in - garbage out) analysis scenario.
From what has been uncovered in FERC database documentation (before it became "hidden") on the Anchor Tendon crack analysis, DWR revealed that they were playing "number games" and fudging (changing over time) what was a critical verses a minor steel tendon crack in a failure risk.
So this Safety Risk Analysis of the Dam & complex becomes an issue that should concern the public. What is needed is an outside independent analysis of the real information (that DWR may or may not have but is keeping ALL critical documents CEII secret where you cannot distinguish either).
Bottom line, a Safe system can be proven in every piece of the system by worst case analysis showing margin with a factor of safety margin above.
(btw- I prefer straight numbers rather than the translation into probability coefficients. This allows identifying any assumptions or critical analysis issues much quicker rather than having it condensed into a final number or numbers).
*(proven, tested, verified, data with known industry time tested methods)