You can use the Sony camcorder diagnosis in some instances.
Years ago, when camcorders shrunk in size, Sony used the same pesky surface mount electrolytic capacitors. When units began failing, a bulletin was released advising to use a hairdryer to gently heat the capacitors and re-test. If the unit began working, the diagnosis was that the capacitors were beginning to fail.
That's why when a Mac Classic first goes "checkerboard", leaving it on for about 20 minutes and then switching it off and back on immediately would often make the machine spring back to life.
Eventually, the capacitors would completely fail and the gentle warmth trick would no longer work and tracks would begin to be etched by the leaked electrolyte.
Of course, a gentle heat can also reveal cracked/dry solder joints, but these are unlikely to occur on the logic board. However, they do occur on the analog board.
As for statistics, it's not that easy, especially if tracks have been etched through. The difficulty is finding them, especially if they are under an IC. My personal experience is about a 75% success rate.
Also, replacing the surface mount capacitors is IMHO, is a priority. Especially on boards that don't appear to have leaking caps. These horrible caps will eventually leak & etch tracks which makes repair even more difficult.
Replacing them with surface mount tantalum capacitors is my recomendation. They don't leak and if they fail, they generally short and blow a pin size hole in themselves, making them easy to find.