Modeling Correlations in Rail Line Construction
Publication: Journal of Construction Engineering and Management
Volume 138, Issue 9
Abstract
The total construction cost and time of projects are often overrun. It is known that when positive correlations between costs are disregarded, the range of possible total construction costs is underestimated. A model is needed to estimate the effect of correlations on the probability distributions of total cost and total time. Four cost–cost and one cost–time correlations in the construction of rail lines were identified, two of which were investigated in detail using a model applicable to the construction of any networked system. This paper presents the theoretical background of the model, the correlations occurring in rail line construction, and the analysis of the impact of such correlations in two case studies including several scenarios and one sensitivity analysis. The results clearly show that the standard deviation of the total cost increases with the magnitude of the correlation and, most importantly, it dramatically increases with the number of costs that are correlated; it also depends on the type of correlation matrix. Correlation between costs must be modeled to capture the wide range of the possible total cost; otherwise, the total construction cost of projects will continue being significantly underestimated.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writers would like to acknowledge that the data for the viaduct and the tunnel case studies were made available by Rede ferroviária de Alta Velocidade(RAVE) and Gabinete de Estructuras e Geotecnia(GEG). The first author is also thankful for the support by the MIT Portugal Program and the Berger Fellowship Foundation.
References
Back, W. E., Boles, W. W., and Fry, G. T. (2000). “Defining triangular probability distributions from historical cost data.” J. Constr. Eng. Manage., 126(1), 29–37.
Bertsekas, D. P., and Tsitsiklis, J. N. (2002). Introduction to probability, Athena Scientific, Belmont, MA.
Cario, M. C., and Nelson, B. L. (1997). “Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix.” Technical report, Northwestern Univ., Evanston, IL.
Chau, K. W. (1995). “The validity of the triangular distribution assumption in Monte Carlo simulation of construction costs: Empirical evidence from Hong Kong.” Constr. Manage. Econ., 13(1), 15–21.
Clemen, R. T., and Reilly, T. (1999). “Correlations and copulas for decision and risk analysis.” Manage. Sci., 45(2), 208–224.
Embrechts, P., Lindskog, F., and McNeil, A. (2003). “Modelling dependence with copulas and applications to risk management.” Handbook of heavy tailed distributions in finance,Svetlozar, T. R., ed., North-Holland, Amsterdam, The Netherlands 329–384.
Embrechts, P., McNeil, A. J., and Straumann, D. (2002). “Correlation and dependence in risk management: Properties and pitfalls.” Risk management: Value at risk and beyond, Dempster, M. A. H., ed., Cambridge University Press, Cambridge, New York, 176–223.
Genest, C., Quessy, J.-F., and Remillard, B. (2006). “Goodness-of-fit procedures for copula models based on the probability integral transformation.” Scand. J. S., 33(2), 337–366.
Ghosh, S., and Henderson, S. G. (2003). “Behavior of the NORTA method for correlated random vector generation as the dimension increases.” ACM Trans. Model. Comput. Simul., 13(3), 276–294.
Haas, C., and Einstein, H. H. (2002). “Updating the decision aids for tunneling.” J. Constr. Eng. Manage., 128(1), 40–48.
Iman, R. L., and Conover, W. J. (1982). “A distribution-free approach to inducing rank correlation among input variables.” Commun. Stat. Simul. Comput., 11(3), 311–334.
Kurowicka, D., and Cooke, R. (2006). Uncertainty analysis with high dimensional dependence modelling, Wiley, Chichester, UK.
Li, S. T., and Hammond, J. L. (1975). “Generation of pseudorandom numbers with specified univariate distributions and correlation coefficients.” IEEE Trans. Syst. Man Cybern., SMC-5(5), 557–561.
Lurie, P. M., and Goldberg, M. S. (1998). “An approximate method for sampling correlated random variables from partially-specified distributions.” Manage. Sci., 44(2), 203–218.
Moret, Y. (2011). “Modeling cost and time uncertainty in rail line construction.” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
Moret, Y., and Einstein, H. H. (2012). “Experience in expert estimation of probabilities and correlations for rail line construction.” J. Constr. Eng. Manage., 138(9).
Newton, S. (1992). “Methods of analyzing risk exposure in the cost estimates of high quality offices.” Constr. Manage. Econ., 10(5), 431–449.
Pouliquen, L. Y. (1970). “Risk analysis in project appraisal.” World Bank staff occasional papers, Johns Hopkins Univ. Press, Baltimore.
Rede ferrovíária de Alta Velocidade (RAVE). (2006a). “Ligacao ferroviaria de alta velocidade entre porto e vigo, lote1a, troco aeroporto francisco sa carneiro—braga/barcelos, estudo previo, volume 08—obras de arte: Pontes e viaductos.” Technical report, Lisbon, Portugal.
Rede ferrovíária de Alta Velocidade (RAVE). (2006b). “Ligacao ferroviaria de alta velocidade entre porto e vigo, lote1a, troco aeroporto francisco sa carneiro—braga/barcelos, estudo previo, volume 09—obras de arte: Tuneis.” Technical report, Lisbon, Portugal.
Robert, C. P., and Casella, G. (2004). Monte Carlo statistical methods, 2nd Ed., Springer, New York.
Schmeiser, B. W., and Lal, R. (1982). “Bivariate gamma random vectors.” Oper. Res., 30(2), 355–374.
Schöelzel, C., and Friederichs, P. (2008). “Multivariate non-normally distributed random variables in climate research—Introduction to the copula approach.” Nonlinear Processes Geophys., 15(5), 761–772.
Touran, A. (1993). “Probabilistic cost estimating with subjective correlations.” J. Constr. Eng. Manage., 119(1), 58–71.
Touran, A., and Wiser, E. P. (1992). “Monte Carlo technique with correlated random variables.” J. Constr. Eng. Manage., 118(2), 258–272.
Information & Authors
Information
Published In
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Dec 19, 2009
Accepted: Nov 2, 2011
Published online: Nov 4, 2011
Published in print: Sep 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.