Time dependent fault trees are used most often for FTA. The results of basic events in the tree are propagated to next higher-level events, such as intermediate events or top events. The results for individual events are calculated using their failure and repair distributions and a time period for analysis, which is usually referred to as mission time. Because event calculations use mission time, they are time-specific, which is why the trees themselves are called time dependent fault trees.

You can classify a time dependent tree as either static or dynamic. The types of gates you insert in a tree determines its classification.

You can further classify static trees as coherent or noncoherent. In a coherent tree, each component in the system is relevant, and the structure function is monotonically increasing (non-decreasing). All trees that contain independent events and only AND or OR gates are coherent.

When you introduce NOT logic into a static tree, it can become noncoherent. Not logic includes NOT, NOR, NAND, and XOR gates as well as disjoint and dependent events. For more information, see NOT Logic Gates.

A static tree is noncoherent when both component failures and successes (positive and negative events) can cause the top event to occur. For example, system failure might occur due to the recovery of a failed component. Or, while the system is in a failed state, the failure of an additional component may bring the system to a good state.

Because trees that contain NOT, NOR, NAND, or XOR logic are typically noncoherent, these types of gates are often referred to as noncoherent gates.

Methods for analyzing coherent systems are based on special properties of monotonic structure functions. Thus, these methods are not applicable for noncoherent systems. This makes qualitative analysis more difficult. Instead of using the MOCUS algorithm for cut set generation, prime-implicants must be used.

For additional information specific to constructing and calculating time dependent trees, see: