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Partial Derivatives

Partial Derivatives

Partial Derivatives are a form of sensitivity analysis that is specific to fault trees. Partial derivatives offer a method of determing the events that have a significant impact on the select top event. The results are generated for individual events (as opposed to Minimal Cut Sets, whose results are generated for sets).

Generating Partial Derivatives

  • Select Fault Tree | Analysis | Partial Derivatives. DPL displays the Partial Derivatives dialog.
  • Specify the Partial Derivative Event for which partial derivatives will be calculated.
  • Specify with respect to which event or leave blank for all.
  • Choose how you would like the derivatives sorted.

For more information on these settings, see Partial Derivatives dialog. The results of the run are displayed in a bar chart or written to the Session Log.

Interpreting Partial Derivatives

The partial derivatives tell you how much a change in the probability of each basic event affects the probability of the partial derivative event. This value depends on the structure of the model and the probabilities of other events but not the probability of the event in question.

The Maximum Impact shows how much the probability of the partial derivative event can be reduced by setting the probability of each basic event to zero. For example, if a particular basic event is part of every cut set for the partial derivative event, the Maximum Impact of that event will equal the probability of the partial derivative event.

Versions: DPL Fault Tree

See Also

Partial Derivatives dialog

Analyzing Fault Trees

Minimal Cut Sets