Efficient Analysis of Fault Trees with Voting Gates

The voting gate, or k-out-of-n (k/n) gate, is a standard logic gate used in fault trees modelling fault-tolerant systems. It is traditionally expanded into a combination of AND and OR gates, and this expansion may result in combinatorial explosion problem in the calculation of minimal cut sets (MCSs) of the fault tree for even a not very big n, especially when the voting gate inputs are intermediate rather than basic events. In this paper we propose a set of reduction rules to simplify the voting gates without direct expanding, and also propose a concept of minimal cut vote (MCV) denoting a k/n gate whose inputs are all basic events and whose k-combinations are all MCSs of the fault tree. With the proposed reduction rules and MCV concept, the MCSs of fault trees can be evaluated and weeded more efficiently and the result can be represented in a more compact form. The results of experiments on practical fault trees with voting gates show that our method not only outperforms conventional MCS evaluation methods by several orders of magnitude but also provides performance comparably to that provided by binary decision tree (BDD) based algorithms.