Question 1

What is a minimal cut set?

Accepted Answer

A minimal cut set (MCS) is the smallest collection of basic events whose simultaneous occurrence causes the top event. First-order MCSs represent single-point failures (a single failure that causes system failure) and are the highest priority for design improvement. Lower-order MCSs indicate greater system vulnerability.

Question 2

What is the difference between Fussell-Vesely importance and Birnbaum importance?

Accepted Answer

Birnbaum importance I_B_i = ∂Q_top/∂Q_i measures how sensitive the top event probability is to changes in the probability of basic event i. Fussell-Vesely importance FV_i = Q_i × I_B_i / Q_top represents the fraction of the top event probability contributed by basic event i, and is used to prioritize risk reduction. The sum of FV values may exceed 1 when cut sets are shared.

Question 3

How do OR gate and AND gate probability calculations differ?

Accepted Answer

OR gate (top event occurs if at least one input occurs): Q = 1 − ∏(1−Qi). AND gate (top event occurs only if all inputs occur): Q = ∏Qi. For example, with two basic events (Q1=0.1, Q2=0.2): OR: Q=1−(0.9×0.8)=0.28; AND: Q=0.1×0.2=0.02. AND gates represent redundancy (parallel systems) and are effective for improving reliability.

Question 4

How can this tool be used in CAE and safety design?

Accepted Answer

The tool can be used for preliminary analysis to meet FTA requirements of IEC 61508 (functional safety) and MIL-STD-1629A, for pre-analysis of ISO 26262 ASIL evaluation in automotive applications, for integration with Process Hazard Analysis (PHA) in process plants, and as a complement to FMEA (FMEA is bottom-up; FTA is top-down).

Fault Tree Analysis & Cut Set Calculator

Theory