Exposition and comparison of two kinds of a posteriori analysis of fault trees

Abstract EN

Fault trees are top-down formal deductive analytic tools with diverse applications in many fields such as reliability, safety and security.

Forward fault tree analysis (FTA) can be termed a priori analysis since it predicts the top-event probability in terms of basic-event probabilities.

This paper offers a tutorial exposition and a detailed comparison of two kinds of backward or a posteriori FTA that are implemented in the probability domain and in the Boolean domain, respectively.

For the probability-domain a posteriori FTA, it is assumed that the top event probability is known.

For example, when the top event is presumed to have occurred, then it has a probability of one.

The analysis proceeds recursively in the probability domain to assess the probabilities of lower events under certain realistic assumptions such as mutual exclusiveness or statistical independence of the input events for a specific gate, and with the utilization of educated guesses on certain ratios of probabilities of such events.

This paper offers a detailed mathematical procedure for implementing this a posteriori FTA that makes the most of the concept of duality.

The procedure is demonstrated via a detailed illustrative example.

The paper also considers the a posteriori FTA in the Boolean domain.

Such an analysis is available in the literature in terms of the very powerful tool of Bayesian Networks (BNs).

We demonstrate here that in many cases this analysis is still possible via elementary faulttree manipulations that use the concept of a Boolean quotient to effectively implement Bayes’ Theorem in the Boolean domain.

Again, a demonstrative example is given to illustrate the Boolean a posteriori FTA, explain its details, and show that the power of BNs is not really warranted in simple cases.

A detailed comparison between the two kinds of a posteriori FTA is also given to identify their similarities and differences.