Recursive reliability assessment of radial lifeline systems with correlated component failures

The increasing susceptibility of lifeline systems to failure due to aging and external hazards requires efficient methods to quantify their reliability and related uncertainty. Monte Carlo simulation techniques for network-level reliability and uncertainty assessment accommodate component correlations and topological complexity without high computational demands but at the expense of reduced accuracy. In contrast, available analytical approaches provide accurate reliability assessments but for limited topologies with component correlations at the expense of high computational complexity. This study introduces a recursive closed-form technique to obtain the entire probability distribution of a reliability metric of customer service availability (CSA) for radial lifeline systems with component failure correlations. The flexibility of correlation inclusion is enabled by a novel recursive algorithm that does not perform the recursive operations explicitly, but rather it recursively transfers knowledge about which operations need to be performed. This approach halves the computation time relative to a naive reliability assessment implementation. In addition, this study demonstrates that correlation inclusion transforms a problem solvable in polynomial time as a function of problem size into a problem only solvable in exponential time. Such tool for radial topologies applies to other systems upon pertinent modifications, including bridges and wind turbines, while providing infrastructure owners an efficient tool to inform operation and maintenance decision making under uncertainty.