Evaluation of Large Fault-Trees with Repeated Events Using an Efficient Bottom-Up Algorithm

In current fault-tree analysis of systems, the usual algorithms for evaluation of fault-trees with repeated events apply the method of minimal cuts. Since the number of minimal cuts increases exponentially with the number of system components, truncation as well as optimization techniques have to be performed for the evaluation of large fault-trees. This paper presents an algorithm which combines the bottom-up algorithm for fault-trees without repeated events with the bottom-up algorithm for establishing the structure function of a fault-tree with repeated events. It allows convenient modeling and evaluation of large fault-trees with repeated events and it computes the exact reliability characteristics, such as steady-state and time-dependent system unavailability and failure rate for repairable and nonrepairable systems. This algorithm has been implemented by a computer program and has been in use at the Power Engineering and Automation Group of Siemens AG. The program includes many features for the description and modular structuring of fault-trees, eg, 1. Definition of fault-tree modules, which can also be declared as repeated transmission trees. 2. A subtree can be used several times as a transmission tree, representing many modules of the system. 3. Repeated events with respect to a subtree level. A great advantage is that the user of the program need not concern himself with a repeated event which appears in different subtrees. The structure of the system can be carried over into a system of subsidiary fault-trees which can be mutually dependent, analogous to the system features.