Pfadmengen

Pfadmengen, also known as path sets, are a concept used in reliability engineering and system analysis. They represent collections of basic events that, if all occur simultaneously, will lead to a specific top-level system failure. In essence, a pfadmenge is a minimal cut set where the minimal aspect refers to the fact that no subset of the events in the set can cause the system failure. If any event within a pfadmenge does not occur, the system will not fail due to that specific combination.

The identification and analysis of pfadmengen are crucial for understanding the failure modes of complex systems. By determining these critical combinations of basic events, engineers can pinpoint vulnerabilities and implement appropriate preventive measures. This often involves strategies to reduce the probability of occurrence of the individual events within the pfadmengen or to introduce redundancy so that the failure of multiple components does not necessarily lead to system failure.

The process of finding pfadmengen is typically performed using fault tree analysis (FTA). A fault tree starts with a top-level undesired event (e.g., system failure) and breaks it down into increasingly basic events through logical gates (AND, OR, etc.). The minimal cut sets, or pfadmengen, are then derived from this tree structure. Understanding these sets allows for a quantitative assessment of system reliability by calculating the probability of system failure based on the probabilities of the basic events within the identified pfadmengen.