Event and Fault Trees

NeqSim provides two complementary risk-quantification engines under neqsim.process.safety.risk:

Class Purpose Standard
EventTreeAnalyzer Forward propagation of an initiating event through binary branches IEC 62502 (2010)
FaultTreeAnalyzer Top-down decomposition of a top event via AND / OR / k-of-N gates IEC 61025 (2006)

Event tree

EventTreeAnalyzer eta = new EventTreeAnalyzer("Gas leak", 1.0e-4);
eta.addBranch("Immediate ignition",   0.10);
eta.addBranch("Delayed ignition",     0.20);
eta.addBranch("Unfavourable wind",    0.50);

double fJet = eta.outcomeFrequency(new boolean[] { true,  false, false }); // jet fire
double fVCE = eta.outcomeFrequency(new boolean[] { false, true,  true  }); // VCE
String tree = eta.toTextTree();

Fault tree

FaultTreeNode b1 = FaultTreeNode.basic("PT fail",  1.0e-2);
FaultTreeNode b2 = FaultTreeNode.basic("LT fail",  1.0e-2);
FaultTreeNode g  = FaultTreeNode.or("Sensor failure", b1, b2)
                                .withCCF(0.10);          // β-factor
FaultTreeNode top = FaultTreeNode.and("ESD fails",
    g, FaultTreeNode.basic("Solver fail", 5.0e-3));

double pTop = FaultTreeAnalyzer.topEventProbability(top);
List<List<String>> cuts = FaultTreeAnalyzer.minimalCutSets(top, 3);

// k-of-N voting
FaultTreeNode v = FaultTreeNode.voting("2oo3 PT", 2,
    FaultTreeNode.basic("PT-1", 1e-2),
    FaultTreeNode.basic("PT-2", 1e-2),
    FaultTreeNode.basic("PT-3", 1e-2));

β-factor common-cause semantics

Per IEC 61508 Part 6, a β-factor models the fraction of failures that are common-cause. NeqSim uses a convex combination:

\[P_{\text{gate, CCF}} \;=\; (1-\beta)\,P_{\text{indep}} \;+\; \beta\,\max_i P_{\text{basic}_i}\]

The directional effect differs between gate types:

Gate Independent only With β > 0 Reason
AND $\prod_i P_i$ — small larger Common cause defeats redundancy → failures coincide
OR $1 - \prod_i (1-P_i)$ — slightly above $\max P_i$ smaller Replaces independent disjunction with single correlated event

For redundant safety systems (AND gates) β-factor increases the top-event probability — this is the dominant CCF mechanism. For series systems (OR gates) the convex combination simply caps probability at max P_i.

See also