Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
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A Statistical Methodology to Estimate the Economical Replacement Time of Water Pipes

상수관로의 경제적 교체시기를 산정하기 위한 통계적 방법론

  • Park, Su-Wan (Dept. of Civil and Env. Eng., Pusan National Univ.)
  • 박수완 (부산대학교 공과대학 사회환경시스템공학부)
  • Published : 2009.06.30
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Abstract

This paper proposes methodologies for analyzing the accuracy of the proportional hazards model in predicting consecutive break times of water mains and estimating the time interval for economical water main replacement. By using the survival functions that are based on the proportional hazards models a criterion for the prediction of the consecutive pipe breaks is determined so that the prediction errors are minimized. The criterion to predict pipe break times are determined as the survival probability of 0.70 and only the models for the third through the seventh break are analyzed to be reliable for predicting break times for the case study pipes. Subsequently, the criterion and the estimated lower and upper bound survival functions of consecutive breaks are used in predicting the lower and upper bounds of the 95% confidence interval of future break times of an example water main. Two General Pipe Break Prediction Models(GPBMs) are estimated for an example pipe using the two series of recorded and predicted lower and upper bound break times. The threshold break rate is coupled with the two GPBMs and solved for time to obtain the economical replacement time interval.

본 논문에서는 상수관로의 파손자료를 이용하여 관로의 위험률을 산정하기 위해 사용되는 비례위험모형의 관로의 순차적 파손시간 예측정확도를 분석하고 이를 이용하여 관로의 경제적 교체 시간구간을 산정할 수 있는 방법론을 제시하였다. 비례위험모형에 기초한 생존함수를 이용하여 연구대상 관로들의 순차적 파손시간을 예측하고 이들을 기록된 파손시간과의 차이를 분석하였다. 이를 통하여 비례위험모형의 파손시간 예측 오차를 최소화하는 생존확률은 0.70인 것으로 결정되었으며, 세 번째 파손으로부터 일곱 번째 파손에 대한 모형만이 관로의 파손시간을 예측하는데 적합한 것으로 분석되었다. 생존확률 0.70과 순차적 파손사건에 대한 생존함수의 하한 및 상한을 이용하여 예제로 사용된 관로에 대해 예측된 파손시간의 95% 신뢰구간의 하한 및 상한을 추정하였다. 예측된 파손시간의 95% 신뢰 구간의 하한과 상한을 이용하여 관로 파손 경향모형인 General Pipe Break Prediction Models(GPBM)을 구축하고 이들을 관로의 한계파괴율과 결합하여 시간에 대한 해를 구하므로써 경제적 교체 시간구간을 산정하였다.

Keywords

References

  1. 박수완 (2009). '상수관로에 대한 시간종속형 공변수를 포함한 포괄적 비례위험모형.' 한국수자원학회논문집, 한국수자원학회, 제42권, 제6호, pp. 445-455 https://doi.org/10.3741/JKWRA.2009.42.6.445
  2. Clark, R.M., Stafford, C.L. & Goodrich, J.A. (1982). 'Water distribution systems: A spatial and cost evaluation.' Journal of Water Resources Planning and Management-ASCE, Vol. 108, No. 3, pp. 243-256
  3. Cox, D. R. (1972). 'Regression Models and Life Tables.' Journal of Royal Statistic Society, Vol. 34(B), pp. 187-220
  4. Dandy, G.C. and Engelhardt, M. (2001). 'Optimal scheduling of water pipe replacement using genetic algorithms.' Journal of Water Resources Planning and Management-ASCE, Vol. 127, No. 4, pp. 214-223 https://doi.org/10.1061/(ASCE)0733-9496(2001)127:4(214)
  5. de Schaetzen, W., Randall-Smith, M.J., Savic, D. and Walters, G.A. (1998). 'A Genetic algorithm approach for rehabilitation in water supply systems.' Proc. Int. Conf. on Rehabilitation Technol. for Water Industry, pp. 1-11
  6. Deb, A.K., Hasit, Y.J., Grablutz, F.M. and Herz, R.K. (1998). Quantifying future rehabilitation and replacement needs of water mains. AWWA Research Foundation
  7. Halhal, D., Walters, G.A., Ouzar, D. and Savic, D.A. (1997). 'Water network rehabilitation with a structured messy genetic algorithm.' Journal of Water Resources Planning and Management-ASCE, Vol. 123, No. 3, pp. 137-146 https://doi.org/10.1061/(ASCE)0733-9496(1997)123:3(137)
  8. Kim, J.H. and Mays, L.W. (1994). 'Optimal rehabilitation model for water-distribution systems.' Journal of Water Resources Planning and Management-ASCE, Vol. 120, No. 5, pp. 674-692 https://doi.org/10.1061/(ASCE)0733-9496(1994)120:5(674)
  9. Kleiner, Y., Adams, B.J. and Rogers, J.S. (1998). 'Selection and scheduling of rehabilitation alternatives for water distribution systems.' Water Resources Research, Vol. 34, No. 8, pp. 2053-2061 https://doi.org/10.1029/98WR01281
  10. Kleiner, Y. and Rajani, B. (2001). 'Comprehensive review of structural deterioration of water mains: statistical models.' Urban Water, Vol. 3, pp. 131-150 https://doi.org/10.1016/S1462-0758(01)00033-4
  11. Lansey, K.E., Basnet, C., Mays, L.W. and Woodburn, J. (1992). 'Optimal maintenance scheduling for water distribution systems.' Civil Engineering Systems, E & FN Spon, London, Vol. 9, pp. 211-256 https://doi.org/10.1080/02630259208970650
  12. Loganathan, G.V., Park, S. and Sherali, H.D. (2002). 'A threshold break rate for pipeline replacement in water distribution systems.' Journal of Water Resources Planning and Management-ASCE, Vol. 128, No. 4, pp. 271-279 https://doi.org/10.1061/(ASCE)0733-9496(2002)128:4(271)
  13. Male, J.W., Walski, T.M. and Slutsky, A.H. (1990). 'Analyzing water main replacement policies.' Journal of Water Resources Planning and Management-ASCE, Vol. 116, No. 3, pp. 362-374 https://doi.org/10.1061/(ASCE)0733-9496(1990)116:3(362)
  14. Park, S. and Loganathan, G.V. (2002). 'Optimal pipe replacement analysis with a new pipe break prediction model.' Journal of the Korean Society of Water and Wastewater, Vol. 16, No.6, pp. 710-716
  15. Park, S., Kim, J.W., Agbenowosi, N. and Jun, H. (2007). 'A methodology to estimate economically optimal replacement time interval of water distribution pipes.' Water Science and Technology: Water Supply, Vol. 7, No. 5, pp. 149-155 https://doi.org/10.2166/ws.2007.103
  16. Ramos, W.L. (1985). 'Benefit/cost analysis procedure for determining water main replacement.' Proc. AWWA Conf. Symp., pp. 125-133
  17. Shamir, U. and Howard, C.D.D. (1979). 'An analytic approach to scheduling pipe replacement.' Journal American Water Works Association, Vol. 71, No. 5, pp. 248-258
  18. Walski, T.M. and Pelliccia, A. (1982). 'Economic analysis of water main breaks.' Journal American Water Works Association, Vol. 74, No. 3, pp. 140-147