Reliability Measure of a Sewer Network

Introduction: the ramified sewerage system for receiving and transferring household and industrial sewage typical for a large city is considered. Consideration is restricted to the sub-system of sewage conveyance (sewer network). Methods and materials: the relative raw sewage volume that could be potentially discharged to the environment as a result of component failures in the sewer network is proposed as a measure of overall system reliability. Results: a simple method for quick and proper calculation of this volume is presented. The problem reduced to finding of the raw sewage volume potentially discharged from the sewer network, and is solved using the following assumptions and limitations: mathematically, an urban sewer network is a simply connected, acyclic, oriented graph (so-called tree-like graph); of a pipe fails, its capacity becomes equal to zero; all specific peculiarities of a pipe (material, diameter, age, operating conditions, etc.) manifest itself in its failure rate; the network pumping stations are taken absolutely reliable. The basis for this method is a representation of the sewer network by a combination of structure-forming fragments. Each such fragment is formally substituted by a fictitious equivalent sewer that has a failure rate leading to the same output for the same input. Conclusion: as a result, the problem reduces to a sequential consideration of elementary sub-problems the solution of which is easily accomplished.