Fault Tree Inversion Overview

DPL Fault Tree provides two forms of fault tree inversion. Both are in the FAULT TREE | Alter group on the ribbon.

Gates Only

This option replaces all AND gates with OR gates and replaces all OR gates with AND gates.

All (logical inverse of fault tree)

This option replaces the tree with its logical inverse. The logical inverse of a fault tree is equivalent to the original fault tree with a NOT gate placed above the top event. The probability of the inverted fault tree equals one minus the probability of the original fault tree.

To modify the active fault tree, select FAULT TREE | Alter | Gates Only or FAULT TREE | Alter | All.

DeMorgan's Laws

When inverting all, the logical inverse is restructured following DeMorgan's laws (see below) so that the NOT gates are moved as far down the tree as possible.

NOT(A AND B) is equivalent to (NOT A) OR (NOT B)

NOT(A OR B) is equivalent to (NOT A) AND (NOT B)

Versions: DPL Fault Tree

See Also

Fault Trees Overview