Fault Tree Analysis Considerations and Special Cases

In order to permit analysis, all fault tree diagrams created in BlockSim must conform to the following constraints:

  • A diagram must contain a top gate and at least one event.
  • All blocks in the diagram must be connected.
  • An event can have only one output event, and no input events or gates.
  • Additional gates are not allowed below a load sharing gate or standby gate.
  • The inputs to negative gates (i.e., NOT, NAND and NOR gates) must be fixed probabilities, or evaluate to fixed probabilities; this is checked at analysis, and any input that evaluates to a time-varying model will result in an error, indicated with a flag applied to the gate.

Fault Tree Analysis Types

As of Version 2023, there are three analysis types available for use with analytical fault trees. These are based on two analysis engines.

  • The Equation analysis type, which is based on the original engine that has been used by all versions of BlockSim, generates a reliability equation to calculate results.

  • The newer Binary Decision Diagram (BDD) engine generates a binary decision diagram from the fault tree to calculate results. This can handle scenarios that the equation method cannot and generally has better performance. There are two analysis types based on this engine:

    • In the exact BDD analysis type (typically referred to as just Binary Decision Diagram or BDD), when you click Analyze, a binary decision diagram is constructed based on the fault tree and is stored. This is then used to calculate results.

    • In the BDD Approximation analysis type, the binary decision diagram is not constructed upon analysis. Instead, it is calculated when a specific numeric result (e.g., failure rate, reliability, etc.) is requested, using the reliability values for events at the time specified. The result is a BDD that has been trimmed of branches of logic that are redundant or statistically insignificant to the overall end calculation. The BDD is not stored, as it cannot be assumed that any subsequent requested value will be at the same point in time.

Which Analysis Type Should I Choose?

Your choice of analysis type will depend on the overall size of your fault tree(s), the kinds of results you're looking for and any additional analyses that you might want to perform.

The Equation analysis type:

  • Is best suited for fault trees with up to a few thousand elements.

  • Can handle "hybrid" scenarios where a fault tree has RBD subdiagrams.

  • Allows you to perform allocation analysis based on the fault tree analysis results.

  • Offers the full range of analytical plots.

The Binary Decision Diagram analysis type:

  • Is well suited to fault trees with up to about 20,000 elements.

  • Can calculate cut sets in scenarios where there are multiple subdiagrams using the same mirrored event blocks.

  • Can provide accurate numeric and cut set results in a variety of scenarios where the Equation analysis type fails (often involving mirrors or containers).

  • Offers the full range of analytical plots.

The BDD Approximation analysis type:

  • Is the best choice for extremely large fault trees.

  • Like the BDD analysis type, can calculate cut sets in scenarios where there are multiple subdiagrams using the same mirrored event blocks and can provide accurate numeric and cut set results in a variety of scenarios where the Equation analysis type fails (often involving mirrors or containers).

  • Demands less memory and is "lighter" in the database than the BDD analysis type due to its on-demand nature.

  • Takes longer to generate results than the Equation analysis type or the BDD analysis type.

  • Offers only Static Reliability Importance plots.

  • Introduces higher uncertainty in numeric calculations due to inherently ignoring some branches of the fault tree.

Fault Tree Special Cases

For analytical fault trees, the ways in which duty cycles and mirrored event blocks interact differ depending on the analysis type used. Consequently, analysis results will differ. Consider the following example:

Here, assume that a duty cycle has been applied to one subdiagram; the FaultTree1 subdiagram block on the left has a duty cycle of 1, while the FaultTree1 subdiagram block on the right has a duty cycle of 4. If you use the Equation analysis type, the duty cycle will be applied to the right subdiagram but not the left. If you use a Binary Decision Diagram (BDD) analysis type, the duty cycle will be ignored entirely due to the mirrored event block in the subdiagram, and specifically due to the fact that the mirroring is not wholly contained within the subdiagram.

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