To answer the first question, you use a fault tree analysis to predict potential failure starting points (like a broken component) and then describe how those failures will propagate through the system.
https://en.wikipedia.org/wiki/Fault_tree_analysis
For an example, say I'm building a system that needs to hold a block of aluminum at 550C, 99% of the time. Okay, so you add a thermocouple and a heater to it, easy.
What if the thermocouple fails?
Well, if the thermocouple fails open then the temperature will read infinity and the heater will shut down and probably produce a non-catastrophic failure.
If the thermocouple fails closed, the temperature will read room temp and the heater will blast full on until the aluminum melts at 660C, which is a catastrophic failure.
If the relay in the temperature controller fails, the furnace probably turns off but theoretically could fail on if the relay switch gets fused.
Okay, so I can see that there is an unlikely but possible chain of events that could cause a catastrophic failure. So I add a second thermocouple to act as a safety shutoff using a second redundant relay and controller if it reads a temperature above 600C.
Total probability then is estimated by either using real world performance metrics or best-guesses. I'd say the odds of a thermocouple failing in 10 years of operation at 550C is nearly 100%, so this failure will nearly certainly occur.
Or consider an LED array with 10 of them in parallel. If one blows open, the remaining 9 each get 10% more current so are more likely to fail. So your first branch of the tree might be that the odds are 10% that an LED will fail at design current within five years. That may well not qualify as a failure, especially since the other 9 LEDs are ~10% brighter due to the higher-than-spec current. But now your probability for the next failure is 20% within five years. So you do need to define different outcomes, usually by severity of impact and probability of outcome in event of a predicted possible failure point.