Branch-and-bound algorithm for efficient reliability analysis of general coherent systems

Abstract

Branch and bound algorithms have been developed for reliability analysis of coherent systems. They exhibit a set of advantages; in particular, they can find a computationally efficient representation of a system failure or survival event, which can be re-used when the input probability distributions change over time or when new data is available. However, existing branch-and-bound algorithms can handle only a limited set of system performance functions, mostly network connectivity and maximum flow. Furthermore, they run redundant analyses on component vector states whose system state can be inferred from previous analysis results. This study addresses these limitations by proposing branch and bound for reliability analysis of general coherent systems} (BRC) algorithm: an algorithm that automatically finds minimal representations of failure/survival events of general coherent systems. Computational efficiency is attained by dynamically inferring importance of component events from hitherto obtained results. We demonstrate advantages of the BRC method as a real-time risk management tool by application to the Eastern Massachusetts highway benchmark network.

Figures (11)

• Figure 1: Illustrative example
• Figure 2: The BRC algorithm consisting of rule evaluation (upper left-hand side), decomposition (right-hand side), and reliability evaluation (lower left-hand side).
• Figure 3: Procedures of the BRC algorithm applied for the system in Fig. \ref{['subfig:toy']}. System failure probability is defined as disconnectivity between node 1 and 3. A component event $X_n$, $n=1,2,3$ represents the binary state of edge $e_n$, where $P(x_1^0)=0.1$, $P(x_2^0)=0.2$, and $P(x_3^0)=0.3$. In the figures, specified branches are marked gray and their $\Bar{\mathcal{R}}$ are not specified as they do not require further decomposition. At each iteration, the selected state for system simulation is marked red; the system simulation result and the newly obtained rule is also marked red.
• Figure 4: The network for two-terminal maximum flow reliability analysed in JanLai08. The origin and the destination nodes are 10 and 12, respectively.
• Figure 5: Results of the BRC algorithm for the example network in Fig. \ref{['fig:mf_net']}.