The Proportional Hazards Modeling of Water Main Failure Data Incorporating the Time-dependent Effects of Covariates

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 time-dependent 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.