Proportional hazards models (PHMs) for the times between consecutive pipe breaks were constructed using case study water main break data. The 150 mm individual cast iron pipes in the case study water distribution system were categorized into seven groups according to the past break history to construct a distinct PHM for each group. During the modeling process the assumption of the proportional hazards of covariates was examined to include the time-dependent effects of covariates on the failure hazard in the models. By analyzing the baseline hazard rates, the hazards of the third through the seventh break were found to follow a form similar to a bath-tub. The estimated regression coefficients and the hazard ratios of the selected covariates were used to analyze the variations in the factors and their effects, including the timedependent effects on the pipe failures. The changes in the relative hazards of the covariates were also analyzed according to the number of breaks. The constructed PHMs were verified by analyzing the deviance residuals of each model.
In this paper a systematic methodology is developed to estimate economically optimal replacement time interval of a water distribution pipe using the proportional hazards modeling approach. To maximize the full potential of the proportional hazards model (PHM) the pipes in a case study area are redefined so that the pipes have consistent internal and external characteristics along their newly defined lengths. The survival functions of the PHMs are constructed for the six ordered survival time groups of cast iron 6 inch pipes in the area and subsequently used to estimate the intervals of future failure times of a pipe. The recorded and predicted future failure time intervals are used to model the trend of pipe failure using the General Pipe Break Prediction Model (GPBM). The equivalence relationship between the GPBM and the threshold break rate of a pipe is used to estimate the economically optimal replacement time interval of a pipe.
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