Advantages of a modular representation of fault trees

Fault trees together with event trees have become a wide-spread tool in the field of reliability analyses and probabilistic risk assessment. A quantitative evaluation is often carried out in terms of minimal cut sets (MCS). Unfortunately the number of MCS can exceed a limit value determined by the storage capacity of the computer used. The usual way to reduce the number of MCS in fault tree evaluation is either to introduce supercomponents or cut-off procedures, i.e., all MCS with contributions lower than a defined value are neglected. This is done efficiently by estimating non-minimal, not fully developed cut sets. However, the total number of terms neglected this way remains unknown, so the case cannot be excluded that the sum of all neglected terms is no longer negligible. Simple supercomponents are the OR gates in the above example. These composite events can be chosen arbitrarily large and complex, if only all basic events of one special supercomponent do not occur in the remainder of the fault tree, i.e., if one looks at the two sets of events, they have to be mutually exclusive. This is a very familiar concept of modularization of a fault tree. The method described in this paper also makes use of this supercomponent type of modularization, but only applied to subsets of MCS or subtrees