A "a non-common cause engine failure" implies more than one engine failing, right ?
So do you mean the relative probability of multiple engine failures on a quad vs a twin ?
Or do you mean, given multiple engine failures, the relative probability of an accident ? Nobody could possibly argue that that's higher with 2 remaining engines than with none.
Perhaps I didn't express that very well, but it is what I meant. Most engine failures are benign - the engine quits making thrust or the flight crew sees something abnormal and shuts it down. Since all currently certified jet airliners can operate safely with one engine out, the aircraft continues flying and lands safely.
However, there is a small subset of engine failures that are not benign - uncontained disc failures, engine fires, etc. While we design to minimize the threat, these non-benign failures have resulted in a number of crashes over the years. What I was trying to say was, the greater the number of engines on an aircraft, the greater the risk of experiencing one of these non-benign engine failures that would result in a catastrophic outcome.
The reason I brought in 'non common cause' is that common cause failures - by definition - can affect all engines on an aircraft so it really doesn't matter how many engines you have. If the mechanic leaves the o-rings out of all the engines, your fuel load is so contaminated that the engines can't function properly, or you fly through volcanic ash and all the engines flame out, 4 vs. 2 doesn't matter much.