Analytical simulation of water system capacity reliability: 1. Modified frequency‐duration analysis

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Abstract
The problem addressed is the computation of the unavailability and expected unserved demand of a water supply system having random demand, finished water storage, and unreliable capacity components. Examples of such components include pumps, treatment plants, and aqueducts. Modified frequency‐duration analysis estimates these reliability statistics by, first, calculating how often demand exceeds available capacity and, second, comparing the amount of water in storage with how long such capacity deficits last. This approach builds upon frequency‐duration methods developed by the power industry for analyzing generation capacity deficits. Three versions of the frequency‐duration approach are presented. Two yield bounds to system unavailability and unserved demand and the third gives an estimate of their true values between those bounds.