Determining the Set of the Most Critical System Components—Optimization Approach

The aim of this paper is to propose a new approach for determining the set of the most critical system components. Importance measures, commonly used for this purpose, first rank each individual component and afterward form a set of the most critical components due to their ranking. In this paper, we propose a new approach based on optimization so the whole set of the most critical components could be determined simultaneously. By taking into account interdependence of components, sets of the most critical system components with different cardinalities does not have to share any of the components. The proposed approach uses optimization over minimal cut sets of the observed system. The greater the number of minimal cut sets in which a component appears, the greater is its importance. The problem of determination of the minimal number of components which appear in all minimal cut sets is considered and formulated as set covering problem. The optimization problem is solved using available optimization software and original heuristic algorithm. Experiments were performed on a group of benchmark fault trees, and the results are compared with the results obtained by commonly used importance measures.