Journal of Korean Society on Water Environment (한국물환경학회지)

Korean Society on Water Environment (한국물환경학회)
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The Proportional Hazards Modeling for Consecutive Pipe Failures Based on an Individual Pipe Identification Method using the Characteristics of Water Distribution Pipes

상수도 배수관로의 특성에 따른 개별관로 정의 방법을 이용한 파손사건 사이의 비례위험모델링

  • Park, Suwan (Department of Civil Engineering, Pusan National University) ;
  • Kim, Jung Wook (Department of Civil Engineering, Pusan National University) ;
  • Jun, Hwan Don (Department of Civil and Environmental Engineering, Korea University)
  • 박수완 (부산대학교 공과대학 토목공학과) ;
  • 김정욱 (부산대학교 공과대학 토목공학과) ;
  • 전환돈 (고려대학교 공과대학 BK21 글로벌 리더 사업단)
  • Received : 2006.11.20
  • Accepted : 2006.12.08
  • Published : 2007.01.30
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Abstract

In this paper a methodology of identifying individual pipes according to the internal and external characteristics of pipe is developed, and the methodology is applied to a case study water distribution pipe break database. Using the newly defined individual pipes the hazard rates of the cast iron 6 inch pipes are modeled by implementing the proportional hazards modeling approach for consecutive pipe failures. The covariates to be considered in the modeling procedures are selected by considering the general availability of the data and the practical applicability of the modeling results. The individual cast iron 6 inch pipes are categorized into seven ordered survival time groups according to the total number of breaks recorded in a pipe to construct distinct proportional hazard model (PHM) for each survival time group (STG). The modeling results show that all of the PHMs have the hazard rate forms of the Weibull distribution. In addition, the estimated baseline survivor functions show that the survival probabilities of the STGs generally decrease as the number of break increases. It is found that STG I has an increasing hazard rate whereas the other STGs have decreasing hazard rates. Regarding the first failure the hazard ratio of spun-rigid and spun-flex cast iron pipes to pit cast iron pipes is estimated as 1.8 and 6.3, respectively. For the second or more failures the relative effects of pipe material/joint type on failure were not conclusive. The degree of land development affected pipe failure for STGs I, II, and V, and the average hazard ratio was estimated as 1.8. The effects of length on failure decreased as more breaks occur and the population in a GRID affected the hazard rate of the first pipe failure.

Keywords

Acknowledgement

Supported by : 한국학술진흥재단

References

  1. 박재빈, 생존분석 이론과 실제, 신광출판사, 서울, pp. 181-187 (2006)
  2. Andreou, S. A., Marks, D. H. and Clark, R. M., A New Methodology for Modeling Break Failure Patterns in Deteriorating Water Distribution Systems: Applications, Advances in Water Resources, 10, pp. 11-20 (1987) https://doi.org/10.1016/0309-1708(87)90013-3
  3. Collet, D., Modelling Survival Data in Medical Research, Chapman & Hall/CRC, Boca Raton, U.S.A., pp. 80-87 (2003)
  4. Constantine, A. G. and Darroch, J. N., In S. Osaki, D. N. P. Murthy (Eds.), Pipeline Reliability: Stochastic Models in Engineering, Technology and Management, World Scientific, Singapore (1993)
  5. Cox, D. R., Regression Models and Life Tables, Journal of Royal Statistic Society, 34(B), pp. 187-220 (1972)
  6. Kalbfleisch, J. D. and Prentice, R. L., Marginal Likelihoods Based on Cox's Regression and Life Model, Biometrika, 60, pp. 267-278 (1973) https://doi.org/10.1093/biomet/60.2.267
  7. Klein, J. P. and Moeschberger, M. L., Survival Analysis: Techniques for Censored and Truncated Data, Springer, New York, U.S.A., pp. 276-287 (2003)
  8. Kleiner, Y. and Rajani, B., Comprehensive Review of Structural Deterioration of Water Mains: Statistical Models, Urban Water, 3, pp. 131-150 (2001) https://doi.org/10.1016/S1462-0758(01)00033-4
  9. Li, D. and Haims, Y. Y., Optimal Maintenance-related Decision Making for Deteriorating Water Distribution Systems 1. Semi-Markovian model for a water main, Water Resources Research, 28(4), pp. 1053-1061 (1992) https://doi.org/10.1029/91WR03035
  10. Male, J. W., Walski, T. M. and Slutski, A. H., Analyzing Watermain Replacement Policies, Journal of Water Resources Planning and Management, ASCE, 116(3), pp. 363-374 (1990)
  11. Park, S., Identifying the Hazard Characteristics of Pipes in Water Distribution Systems by using the Proportional Hazards Model: 1. Theory, KSCE Journal of Civil Engineering, 8(6), pp. 663-668 (2004) https://doi.org/10.1007/BF02823557
  12. Rajani, B. and Kleiner, Y., Comprehensive Review of Structural Deterioration of Water Mains: Physically based Models, Urban Water, 3, pp. 151-164 (2001) https://doi.org/10.1016/S1462-0758(01)00032-2
  13. Shamir, U. and IToward, C. D. D., An Analytic Approach to Scheduling Pipe Replacement, Journal of American Water Works Asociation, 71(5), pp. 248-258 (1979) https://doi.org/10.1002/j.1551-8833.1979.tb04345.x
  14. Walski, T. M. and Pelliccia, A., Economic Analysis of Water Main Breaks, Journal of American Water Works Asociation, 74(3), pp. 140-147 (1982) https://doi.org/10.1002/j.1551-8833.1982.tb04874.x