Estimation of Maximum Cut‐Set Size for Water Network Failure

Abstract

Assessment of the reliability of a water distribution system through evaluation of all possible combinations of mechanical (pipe) failure is computationally intensive. It is nonpolynomial (NP) hard. An approach is proposed in which the probability of varying levels of simultaneous pipe breaks and the probability that the various levels of simultaneous breaks will cause network failure are combined to obtain estimates of overall network reliability. The probability Of a fixed number of simultaneous failures occurring is derived from analyses of historical data. The probability that a particular number of simultaneous failures will cause a system failure is estimated from simulation analyses. In analyzing the historical data, both the maximum number of simultaneous failures and the distribution of the varying levels of simultaneous pipe failures are analyzed for different sizes of a distribution network. A sample application of the procedure is presented, using the pipe failure data from the city of Winnipeg and a smaller scale sample network taken from the literature.