Reliability HotWire: eMagazine for the Reliability Professional
Reliability HotWire

Issue 44, October 2004

Reliability Basics

Comparison of RBD and Fault Tree Simulation

The slightly modified constructs in BlockSim FTI erase the distinction between reliability block diagrams (RBD) and fault trees. Given this, any analysis that is possible in a BlockSim RBD (including throughput analysis) is also available when utilizing fault trees. In this article, the simulation of an RBD and its corresponding fault tree will be compared.

 

Example

Consider the RBD shown in Figure 1 and its equivalent fault tree representation in Figure 2.

RBD for a repairable system

Figure 1: RBD for a repairable system

Fault tree equivalent for the RBD shown in Figure 1

Figure 2: Fault tree equivalent for the RBD shown in Figure 1

In addition, 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.

Figure 3 shows a sample table of simulation results for up to t = 1,000 using simulations for each diagram and an identical seed.

Sample simulation results

Figure 3: Sample simulation results

 

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 utilized by both diagrams, the results are not always expected to be identical. 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. Therefore, 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 FTI) may be utilized.

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