The Fault Tree is made up out of Basic Events (BEs, the boxes), AND gates, OR gates, and k/N (k out of N) gates. Basic Events represent elemental failures of components of the overall system. Gates are used to describe how these elemental failures interact with each other, leading to the eventual failure of the overall system. Every gate has 2 or more connections to other gates or Basic Events. The OR gate models something has failed if any of the connected gates/BEs has failed. The AND gate describes something has failed if all the connected gates/BEs have failed. The k/N gate describes something has failed if k out of the N connected gates have failed.
The failure probability of the Basic Events and gates is described with a value from 0 to 1 (0% to 100%). The probabilities of the Basic events in the model can be adjusted with the sliders under the Basic Events.
The example below illustrates the potential total failure of a road trip:
- The road trip fails if the car fails and the phone fails, since road side assistance can’t be called.
- The car fails if the engine fails, or the tires fail.
- The tires fail if 2 out of 5 of the individual, identical tires (4 used normally and 1 spare) fail.
- The cell phone fails if its power fails, or the connection fails.
- The cell phone runs out of power if its battery fails, or the car engine fails, since it can’t be charged by the alternator.
This example illustrates the results through statistical model checking. A random state (failed/working) is generated for each Basic Event based on the given probability, also known as Monte Carlo Simulation. The effects of this state are then proagated through the Fault Tree, calculating the state of each gate based on their children. This is done for 100 separate runs.
Given enough runs, due to the law of large numbers, the proportion of runs where a Basic Event or Gate is in the failed state will aproximate the expected failure failure probability (P) of that Basic Event/Gate.