Fault Trees and Simulation

The slightly modified constructs in BlockSim erase the distinction between RBDs and fault trees. Given this, any analysis that is possible in a BlockSim RBD (including throughput analysis) is also available when using fault trees.

Example of Fault Trees and Simulation

Consider the RBD shown in Figure 10.44 and its equivalent fault tree representation, as shown in Figure 10.45.

Figure 10.44: RBD for a repairable system.

Figure 10.45: Fault tree equivalent of the repairable system shown in Figure 10.44.

Furthermore, assume the following basic failure and repair properties for each block and event:

Block A:

Failure Distribution: Weibull; β = 1.5; η = 1,000.
Corrective Distribution: Weibull; β = 1.5; η = 100.

Block B:

Failure Distribution: Exponential; μ = 10,000.
Corrective Distribution: Weibull; β = 1.5; η = 20.

Block C:

Failure Distribution: Normal; μ = 1,000; σ = 200.
Corrective Distribution: Normal; μ = 6; σ = 2.

Block D:

Failure Distribution: Weibull; β = 1.5; η = 10,000.
Corrective Distribution: Exponential; μ = 10.

Block E:

Failure Distribution: Weibull; β = 3; η = 1,000.
Corrective Distribution: Weibull; β = 1.5; η = 20.

Block F:

Failure Distribution: Weibull; β = 1.5; η = 5,000.
Corrective Distribution: Weibull; β = 1.5; η = 100.

Block G:

Failure Distribution: Exponential; μ = 100,000.
Corrective Distribution: Weibull; β = 1.5; η = 10.

Block H:

Failure Distribution: Normal; μ = 5,000; σ = 50.
Corrective Distribution: Normal; μ = 10; σ = 2.

A sample table of simulation results is given next for up to t = 1,000, using simulations for each diagram and an identical seed.

As expected, the results are equivalent (within an expected difference due to simulation) regardless of the diagram type used. It should be pointed out that even though the same seed was used by both diagrams, the results are not always expected to be identical because the order in which the blocks are read from a fault tree diagram during the simulation may differ from the order in which they are read in the RBD; thus using a different random number stream for each block (e.g. block G in the RBD may receive a different sequence of random numbers than event block G in the FT).

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