Fault Tree Overview

# Fault Tree Overview

A fault tree is a hierarchical model that is used to analyze risk. Typically, a particular risk can be broken down into component faults or failures. The fault tree provides a graphic representation of this breakdown and describes all interactions of the components. These interactions are defined by AND gates () and OR gates (), which behave similarly to the corresponding logical operators. AND gates and OR gates are the functional glue of the fault tree.

A noncoherent fault tree includes NOT gates as well, which behave similarly to the logical operator NOT. A coherent fault tree contains only AND gates and OR gates. DPL Fault Tree is equipped to handle both coherent and noncoherent fault trees.

The motivation for modeling a risk with a fault tree is based on the assumption that each component fault has a probability of occurrence that is easier to assess than the more general fault. In this way, the model serves as a probability expression, which can then be evaluated by DPL Fault Tree.

Fault trees are unique in their ability to gracefully handle graphic representations of large scale problems. The fault tree helps to provide a better understanding of what risks are involved in a particular system. This helps to make a more accurate probability assessment of the overall risk.

A fault tree is both an analytical and a communication tool. Basic events for which probabilities are assessed directly are typically at the bottom of the tree. Derived events are arranged above the basic events and are connected by gates. In a fully formed fault tree, there is only one top level event that has no successors. This event is referred to as the top event or the root. The root of a fault tree is the event that represents the most general statement of the risk. The top level event in a fault tree is defined by either an AND gate or OR gate.

The next level down from the root consists of a set of events that feed into the gate at the root. These events contribute to the probability of occurrence of the top level event according to the type of gate.

This structure continues down the tree. A node at any level in the tree is the root of the subtree below it. At some point as you descend down the hierarchy of the tree, the events become specific enough so that they can be assessed directly. Typically events higher up in the hierarchy are more difficult to assess directly. Once you have reached the point where the events are specific enough to assess directly, the tree should end. These endpoints are referred to as basic events.

Creating Events and Values

• Select FAULT TREE | Node | Binary Event or Value from the ribbon ( and , respectively).
• Click in the fault tree where you would like the node placed. The Node Definition dialog appears.
• Name the node, annotate it and give it data as desired.
• Note: clicking on another node when placing the event/value creates a connection from the new node to the node you clicked on. See Connections for more information about connections.
• Click OK to close the Node Definition dialog.
Creating Gates

• Select FAULT TREE | Gate | AND or OR from the ribbon ( and , respectively).
• Click in the diagram where you would like the object placed.

See Gates for information on creating NOT gates.

Documenting Fault Tree Models

There are a number of ways to add documentation to a fault tree. You can:

You can categorize nodes by placing markers beside them.

Place a marker beside a node as follows.

• Select one or more nodes.
• Drop down FAULT TREE | Node | Markers & Legends.
• Select the marker style for the node.
There are 16 marker styles. Delete a marker as follows.
• Select one or more nodes.
• Drop down FAULT TREE | Node | Markers & Legends.
• Select Remove.

Create a legend for the markers as follows.

• Drop down FAULT TREE | Node | Markers & Legends.
• Select Legend. The Marker Legend dialog comes up.
• Give names to the marker styles. Note: marker styles that you put a name beside will show up in the legend.
• If desired, select Show Legend. The legend will appear in the fault tree window as a text box and it can be moved to where you like.
• If desired, select Border.

# Fault Tree Analysis Overview

There are three main analyses that are performed on fault trees:

• Calc Prob: Reports the likelihood of an event in the fault tree.
• Minimal Cut Sets: Enumerates the minimal cut sets for the selected event.
• Partial Derivatives: Determines the impact of each event on the likelihood of the top event.
Versions: DPL Fault Tree