Reliability Indices for Water Supply Systems

Abstract
In the design of hydraulic structures for flood control, it has become standard practice to employ the average return period of a flood as the design event. This study introduces an analogous index for the design of a water supply system: the average return period of a reservoir system failure, defined as the expected number of years until the first reservoir system failure. Here a failure is defined as a year in which the prespecified yield could not be delivered by a water supply system. The mean and variance of the time until the first reservoir system failure are derived, as are the mean and variance of the duration of a reservoir system failure for a simple Markov failure model. Other indices of the reliability of a water supply system are also introduced. The assumption that sequences of reservoir surplus and failures can be represented by a two‐state Markov chain is validated for the Pacific Northwest Hydroelectric Power System.