Modeling Correlations in Rail Line Construction

AbstractThe 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 ...

[1]  Bruce W. Schmeiser,et al.  Bivariate Gamma Random Vectors , 1982, Oper. Res..

[2]  Kw Chau.  The validity of the triangular distribution assumption in Monte Carlo simulation of construction costs: empirical evidence from Hong Kong , 1995 .

[3]  John N. Tsitsiklis,et al.  Introduction to Probability , 2002 .

[4]  Shane G. Henderson,et al.  Behavior of the NORTA method for correlated random vector generation as the dimension increases , 2003, TOMC.

[5]  R. Clemen,et al.  Correlations and Copulas for Decision and Risk Analysis , 1999 .

[6]  Joseph L. Hammond,et al.  Generation of Pseudorandom Numbers with Specified Univariate Distributions and Correlation Coefficients , 1975, IEEE Transactions on Systems, Man, and Cybernetics.

[7]  P. Embrechts,et al.  Chapter 8 – Modelling Dependence with Copulas and Applications to Risk Management , 2003 .

[8]  Herbert H. Einstein,et al.  Updating the Decision Aids for Tunneling , 2002 .

[9]  P. Embrechts,et al.  Risk Management: Correlation and Dependence in Risk Management: Properties and Pitfalls , 2002 .

[10]  Bruno Rémillard,et al.  Goodness‐of‐fit Procedures for Copula Models Based on the Probability Integral Transformation , 2006 .

[11]  A. Touran.  Probabilistic Cost Estimating with Subjective Correlations , 1993 .

[12]  Sidney Newton,et al.  Methods of analysing risk exposure in the cost estimates of high quality offices , 1992 .

[13]  Ali Touran,et al.  Monte Carlo Technique with Correlated Random Variables , 1992 .

[14]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[15]  Roger M. Cooke,et al.  Uncertainty Analysis with High Dimensional Dependence Modelling: Kurowicka/Uncertainty Analysis with High Dimensional Dependence Modelling , 2006 .

[16]  Louis Y. Pouliquen,et al.  Risk analysis in project appraisal , 1970 .

[17]  Gary T. Fry,et al.  Defining Triangular Probability Distributions from Historical Cost Data , 2000 .

[18]  Herbert H. Einstein,et al.  Experience in Expert Estimation of Probabilities and Correlations for Rail Line Construction , 2012 .

[19]  Yvonne Moret,et al.  Modeling cost and time uncertainty in rail line construction , 2011 .

[20]  Philip M. Lurie,et al.  An Approximate Method for Sampling Correlated Random Variables From Partially-Specified Distributions , 1998 .

[21]  Roger M. Cooke,et al.  Uncertainty Analysis with High Dimensional Dependence Modelling , 2006 .

[22]  R. Iman,et al.  A distribution-free approach to inducing rank correlation among input variables , 1982 .

[23]  P. Friederichs,et al.  Multivariate non-normally distributed random variables in climate research - introduction to the copula approach , 2008 .