Methodology for economically optimal replacement of pipes in water distribution systems: 1. Theory

While the idea of critical breaks rate (defined as the break rate after which it is no longer economical to continuously repair) of water distribution pipeline has been accepted in the literature and among practicing engineers, the formula to obtain the critical break rate has remained elusive. In this paper, an equation for identifying the critical break rate of a pipe is preseted. The Threshold (or critical) Break Rate equation gives an accurate criterion for pipe replacement decision. Input variables to obtain the Threshold Break Rate of a pipe are repair and replacement costs, interest rate, and the length and diameter of a pipe. The newly developed Threshold Break Rate equation does not involve time variable in its form resulting in incapability of predicting future optimal replacement time. This disadvantage of the Threshold Break Rate equation is overcome by establishing relations of equivalence between the Threshold Break Rate and other failure rate models such as the ROCOF (rate of occurrence of failure) and hazard function.