Minimal Cut Sets

Minimal Cut Sets are a form of sensitivity analysis that is specific to fault trees.

In any fault tree, the top event will be true for some combination of basic events. That is, there will be some set of basic events such that if each event in the set occurs, the top event will also occur. Such a combination of basic events is called a cut set. Elements of a cut set may be basic events or negations of basic events (the event NOT A is denoted in DPL Fault Tree as ~A). A fault tree can have many possible cut sets. A minimal cut set is a cut set such that if any event is removed, the remaining events are no longer a cut set. The minimal cut sets, along with their associated probabilities and costs, help identify the most likely or the lowest cost ways for the top event to occur. When generating cut sets, you may select for which event you'd like minimal cut sets produced. The remainder of this topic will use the term "top event" to mean the selected event for which cuts were produced.

Using the Cut Set Viewer

It is instructive to view cut sets in a circuit diagram to see how the basic events interact to cause the top event to be true. If all of the basic events in a cut set are set to true (or false if NOT gates exist), the circuit will be broken, since this set of events causes the top event to be true. The Cut Set Viewer window is created by running a minimal cut set analysis. When it is first displayed, it appears as a circuit diagram with the first minimal cut set (either most likely or least costly) displayed (i.e., the elements in the cut set set to true/false as appropriate).

In the Cut Set Viewer window, you can scroll through the minimal cut sets in the circuit diagram using the up or down arrows.

To see the list of cut sets, double-click anywhere on the background of the Cut Set Viewer window or select FAULT TREE | Display | Select Cut Set. The Select Cut Set dialog appears with the list of minimal cut sets and each cut set's probability of occurrence (and cost, if available). Use the dialog to select a cut set to display.

The Cut Set Viewer window is not saved with the Workspace file. Minimal cut sets need to be regenerated if you close and open a Workspace file.

Interpreting cut sets in the Session Log

The probability of the cut set begins each line followed by the cost of the cut set (if the fault tree contains cost data). The last column displays a list of all the events in the cut set using variable names. The list of cut sets is sorted by probability or cost as specified in the Minimal Cut Sets dialog.

Versions: DPL Fault Tree

See Also

Minimal Cut Sets dialog

Select Cut Set dialog

Analyzing Fault Trees

Circuit Diagrams

Entering Probability and Cost Data