For time dependent fault trees, the FTA module supports four dynamic gates: priority AND, spare, sequence enforcing, and functional dependency. If you run exact calculations for a tree with a dynamic gate, parts of the tree are converted to equivalent Markov models. On the FTA > Advanced page in the Calculate window, you specify the precision that the Markov calculation engine is to use.

Exact calculations first identify the independent modules in the tree. The probabilities of each of these modules are then calculated using conditional probabilities in the same manner as they are for BDDs (binary decision diagrams).

A module is classified as either static or dynamic. A dynamic module contains at least one dynamic gate. The top gate of a dynamic module does not have to be a dynamic gate. This typically happens when repeated events are present in the module. First, dynamic modules are calculated using the Markov calculation engine; then, static models are calculated using an exact method based on pivotal decomposition. Once the results for all modules are obtained, the results for the top gate are calculated using an exact method based on a bottom-up approach.

Because Markov models are required for exact calculations of dynamic modules, all event behaviors in a dynamic module should be specified using failure and repair rates. Therefore, Failure rate/MTBF or Failure rate with repair are the only models allowed. Generally, the events in a dynamic module are non-repairable. Therefore, failure rate or MTBF values are the inputs used in most systems.

With repairable components/events, no industry standard exists for the behavior of dynamic gates (dynamic trees). Hence, standard calculation methods are also unavailable. First, the FTA module generates a Markov model corresponding to a dynamic module without considering the repairs of the events. Then, it adds the repair information to the Markov diagram to compute the final results for the dynamic module.