Importance Functions from Minimal Cut Sets Sample Clauses

Importance Functions from Minimal Cut Sets. The compositional importance function of [3] is defined per gate (and BE) type. The key concept is that, in general, importance should reflect proximity to the rare event. For fault trees this means that the importance of a gate should increase as the gate approaches its own failure. Note that the type of a gate defines how, as its children fail, the gate approaches its own failure. This is used in [3] to define a local importance function for each gate, which assigns an importance to the gate based on its type and on the state of its children. For instance, AND gates fail when all its children fail, so the importance of an AND should increase with the failure of every child. Thus, the local importance function of ANDs is a summation of the importance of its children. By the same argument, the importance of an OR is the max importance among its children. Basic events are the base case of this recursion: BEs and SBEs essentially have a binary state, failed or not,1 which are assigned importance 1 and 0 resp. Δ Δ Δ In [3] this recursive construction starts from the leaves of the tree and ends in the top gate, thus deriving a function FT that considers every single gate in the original ft . Instead, here we work on the mcs re-write ∗, for which the three cases described above suffice. ∗ consists of the top OR, potentially some ANDs, and the base BEs and SBEs: the importance function assigned to such tree is a max (OR) over the summation (ANDs) of every basic event in an mcs. Table 1 gives the mathematical expression of this formula, which we denote { } I Δ