Computing for Fault-Tree Analysis

Building and quantifying logical trees that trace an undesired event back to the combinations of failures that could cause it.

What a fault tree is

A fault tree starts from an undesired top event and works backward through logic gates to the basic failures that could cause it. AND gates mean all inputs must fail together; OR gates mean any one suffices. The tree makes explicit how component failures combine into system failure, and it can be quantified to estimate the top event's probability.

Reading the logic

The table above shows an AND gate: the output fails only when both inputs fail. An OR gate, by contrast, outputs failure if either input fails. Real trees nest many such gates, and the same basic failure can appear in several branches, which the analysis must handle correctly.

Minimal cut sets

The key computed result is the set of minimal cut sets: the smallest combinations of basic failures that, together, cause the top event. A cut set of size one is a single point of failure and a design red flag. Enumerating cut sets in a large tree is computationally demanding, which is why fault-tree analysis is a computing task, not a paper exercise, for real systems.

def top_probability(cut_sets, p):
    # rare-event approximation: sum of cut-set probabilities
    total = 0.0
    for cs in cut_sets:
        prod = 1.0
        for basic in cs:
            prod *= p[basic]
        total += prod
    return total

Its limits

Fault trees assume failures are reasonably independent and that the analyst enumerated the right events. Common-cause failures, where one root defeats several 'independent' safeguards at once, must be modeled explicitly or they are missed. The tree is only as good as the imagination that built it.

Kronos framing

Fault-tree analysis is part of the safety case for the Hyperion breeder, ahead of construction in the second quarter of 2027, focused on the real fusion hazards of tritium, activation, and stored energy.