Use of Binary Decision Diagrams in Importance Analysis Based on Minimal Cut Vectors

Reliability is a key characteristic of any technical system. A current issue in reliability engineering is analysis of complex systems consisting of many components. Examples of such systems are various network systems, such as distribution networks, telecommunication networks, and computer networks. Investigation of these and similar systems in a reasonable time requires a mathematical description of the system that can be efficiently processed by a computer. One of the prospective approaches is to express the structure of the system using a decision diagram. Application of this data structure in reliability analysis allows developing efficient algorithms for calculation of various reliability characteristics, such as importance measures, which permit evaluating influence of individual components of the system on its operation. In this paper, we focus on one special measure, known as Fussell-Vesely's importance, which quantifies how a failure of a component contributes to the failure of the entire system. This measure can be defined using the concept of minimal cut vectors whose identification might not be an easy task. Therefore, in this paper, we develop a new method for calculation of Fussell-Vesely's importance through binary decision diagrams. The method is illustrated on an example of a distributed computing system.