Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andreou SA, Marks DH, Clark RM (1987) A new methodology for modeling break failure patterns in deteriorating water distribution systems: applications. Adv Water Resour 10:11–20
Allison PD (1996) Survival Analysis using SAS: a practical guide. Cary, NC, SAS Institute Inc., pp 173–174
Brémond B (1997) Statistical modeling as help in network renewal decision, European commission co-operation on science and technology (COST). Committee C3—diagnostics of urban infrastructure. Paris, France
Cox DR (1972) Regression models and life tables. J R Stat Soc, R Stat Soc 34(B):187–220
Eisenbeis P (1994) Modélisation statistique de la prévision des défaillances sur les conduites d’eau potable. Ph.D. thesis, University Louis Pasteur of Strasbourg, collection Etudes Cemagref No. 17, France
Klein JP, Moeschberger ML (2003) Survival Analysis: techniques for censored and truncated data. Springer, New York, pp 374–381
Kleiner Y, Rajani B (2001) Comprehensive review of structural deterioration of water mains: statistical models. Urban Water, Taylor and Francis 3:131–150
Lei J (1997) Statistical approach for describing lifetimes of water mains—Case Trondheim Municipality. SINTEF Civil and Environmental Engineering, Report No. 22F007.28, Trondheim, Norway
Marks DH et al (1985) Predicting urban water distribution maintenance strategies: a case study of New Haven Connecticut. US Environmental Protection Agency (cooperative agreement R8 1 0558-01–0)
Marks HD, Andreou S, Jeffrey L, Park C, Zaslavski A (1987) Statistical models for water main failures. US Environmental Protection Agency (Cooperative Agreement CR8 1 0558) M.I.T. Office of Sponsored Projects No. 94211. Boston, MA
Park S, Jun H, Kim BJ, Im GC (2008) Modeling of water main failure rates using the log-linear ROCOF and the power law process. Water Resour Manag 22:1311–1324
Rajani B, Kleiner Y (2001) Comprehensive review of structural deterioration of water mains: physically based models. Urban Water, Taylor and Francis 3:151–164
SAS Institute Inc (2009) http://www.sas.com/index.html
Therneau TM, Grambsch PM, Fleming TR (1990) Martingale-based residuals for survival models. Biometrika, Oxford Journals 77:147–160
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Park, S., Jun, H., Agbenowosi, N. et al. The Proportional Hazards Modeling of Water Main Failure Data Incorporating the Time-dependent Effects of Covariates. Water Resour Manage 25, 1–19 (2011). https://doi.org/10.1007/s11269-010-9684-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11269-010-9684-y