The logical interpretation was favored by logicians, such as Keynes, Reichenbach, and Carnap, and is currently out of vogue. The relative frequency interpretation is used by many statisticians and is currently the most favored. The personalistic interpretation is more universal and incorporates engineering and other knowledge. This interpretation is popular in many applications, including risk analysis and safety analysis. All the interpretations of probability have a common set of axioms that tell us how to combine probabilities of different events.
Fault trees are similar to block diagrams of a system.
This is the subject of reliability analysis wherein mathematical models, expert judgment, failure data, and maintenance come into play. Consider the following cases. The assumption of independence is an idealization often made routinely because it simplifies the analysis, but the consequences can be severe. For example, Figure E-5 illustrates the possibility that a failure in one engine could prompt the flight crew to shut down the functional engine, which would result in the loss of both engines even though only one engine malfunctioned. Clearly, the two probabilities are different.