Evaluating the economic residual life of water pipes using the proportional hazards model

This paper provides a method for evaluating the residual lives of water pipes using the proportional hazards model (PHM) based on the economically optimal replacement times of pipes. The survival times, which are used in the proportional hazards modeling process, were defined as the economically optimal replacement times of pipes. The break rate of an individual pipe is estimated using the General Pipe Break Model (GPBM). The optimal replacement time of a pipe is obtained using the equivalence relationship between the GPBM and threshold break rate. In order to use the GPBM effectively, the process of estimating the GPBM has been modified in this paper by utilizing additional break data for the time of installation and adjusting the value of the weighting factor (WF) in the GPBM. The residual lives and hazard ratios of the case study pipes, of which the cumulative number of breaks was at least one, were estimated using the estimated survivor function of the constructed PHM. The time-dependency of the pipe material covariate caused the hazard rate of the cast iron pipes to become lower than the hazard rate of the steel pipes after 19 years since installation. The methodology developed in this paper may help utilities identify important factors related to the economics of water pipe maintenance and; therefore more efficiently maintain their water pipes.