The increased susceptibility of lifeline systems to failure requires efficient methods to quantify their reliability and uncertainty. Monte Carlo simulation techniques for network-level reliability assessment usually require large computational experiments. Also, available analytical approaches apply mainly to simple network topologies and are limited to providing average values or confidence bounds of reliability metrics. Hence, this study introduces a closed form technique to obtain the entire probability distribution of a reliability metric of customer service availability (CSA) for radial looped systems. These systems have main feeders emanating from a source point and reach customers through lateral branches from the main feeders, while there are normally open switches at the end of the feeders that automatically close to provide redundant paths. The theoretical development of CSA imposes no restrictions on the number of branching points per feeder or laterals per branch, although there are practical computational limitations for large systems. However, the structure of the formulation reveals that it is possible to find recursive algorithms to cope with computational complexity in the future. The proposed reliability assessment equation and resulting probability distribution provide infrastructure owners with critical insights for informed operation and maintenance decision making under uncertainty.
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