Analytical simulation of water system capacity reliability 2. A Markov chain approach and verification of the models

A reliability model for water supply systems is presented which represents demand changes, failures and repairs of capacity components, and streamflows as independent Markov chains. Finished water storage is simulated using an operating policy that depends on the system state. Reliability statistics, including system unavailability, expected unserved demand, and the frequency and duration of failures are obtained from the transition probabilities and resulting steady state probabilities. Both the Markov model and another analytical simulation approach, the modified frequency-duration method, are applied to an actual water supply system. Their results are compared to those of a more realistic Monte Carlo simulation in order to verify that analytical simulation yields useful estimates of reliability indices. A procedure for interfacing models of capacity reliability with simulation models of large reservoirs is proposed.