Probability Distribution Fitting of Cost Overrun Profiles
- 1. Royal Institution of Chartered Surveyors Legal Research Symposium, COBRA 2010, September 11th -13th, Las Vegas, Nevada USA Probability Distribution Fitting of Cost Overrun Profiles Professor Peter ED Love Curtin University is a trademark of Curtin University of Technology CRICOS Provider Code 00301J
- 2. Cost Overruns: A Pervasive Problem • Unrealistic estimate (optimum bias) • Changes in scope • Completion date determined before the project’s scope had been defined • Inadequate project governance • Inappropriate procurement method (risk allocation) • Documentation errors Curtin University is a trademark of Curtin University of Technology CRICOS Provider Code 00301J
- 3. The Nemesis of Cost Overruns • Decision-makers are over • Deceptive actions to ensure optimistic about the outcome of projects proceed planned actions Curtin University is a trademark of Curtin University of Technology CRICOS Provider Code 00301J
- 4. The Fallacy of Cost Overruns • 2004 budget was $420m • 320% cost overrun ? Construction on time and budget • Where do you measure from? • Need to distinguish between factors that increase project cost and those affect the accuracy of estimates Curtin University is a trademark of Curtin University of Technology CRICOS Provider Code 00301J
- 5. Comparing Apples with Oranges • Reference class forecasting: Projects in a statistical distribution of outcomes from class of reference points • Projects of the same ilk experience similar degrees of optimism bias and overruns • Research has shown there is NO significance between cost overruns (% contract value) with project type, procurement etc. Curtin University is a trademark of Curtin University of Technology CRICOS Provider Code 00301J
- 6. Does Contract Size Matter? • Larger projects experience smaller overruns (Vice versa) • Larger projects are better managed and longer completion times provide an opportunity to facilitate cost control Curtin University is a trademark of Curtin University of Technology CRICOS Provider Code 00301J
- 7. Convenience of the Normal Distribution • A Normal distribution is symmetric about its mean value and therefore cannot be used to accurately model left or right skewed data. • The selection of an inappropriate statistical distribution can produce incorrect probabilities, which can adversely affect decision-making and therefore lead to negative outcomes Curtin University is a trademark of Curtin University of Technology CRICOS Provider Code 00301J
- 8. Research Approach Probability Density Goodness of Fits Test: Function, CDF and Kolmogorov-Smirnov statistic (D): distribution parameters D max F ( xi ) i 1 i , F ( xi ) for continuous 1 i n n n Anderson-Darling statistic (A2): distributions were n examined using the 1 A2 n (2i 1) InF ( xi ) In 1 F ( xn i 1 ) n i 1 Maximum Likelihood Chi-squared statistic (χ2): Estimates k 2 2 Oi Ei i 1 Ei Curtin University is a trademark of Curtin University of Technology CRICOS Provider Code 00301J
- 9. Results Frechet 3P • Mean overall cost overrun (n=276) PDF f ( x) 1 exp x x 12.22% of contract value • Civil engineering projects (n=115) 12.56% • Building (n=161) 11.76% • ANOVA revealed no significant differences between types of project, procurement method, and CDF f ( x) exp x size (contract value) • The likelihood that a project does not exceed a cost overrun of 12.22% is 60% (P (X < X1) = .60). Curtin University is a trademark of Curtin University of Technology CRICOS Provider Code 00301J
- 10. Distribution by Contract Value 0.44 PDF <$1M PDF $11-$50M • <$1M and $51 to $100M (Cauchy) 0.4 Probability of Cost Overrun 0.36 0.32 0.28 0.24 1 2 0.2 x 0.16 PDF = f ( x) 1 0.12 0.08 0.04 0 -10 -5 0 5 10 15 20 25 Percentage of Cost Overrun 1 x % Cost Overrun Cauchy CDF = F ( x) arctan 0 .5 1 PDF > $100M PDF $1-$10M Probability of Cost Overrun 0.8 • $1 to $10M and >$100M (Wakeby) 0.6 0.4 Wakeby distribution is defined by the quantile function 0.2 (inverse CDF): 0 -0.2 -150 -100 -50 0 50 100 150 CDF = x( F ) 1 1 F 1 1 F Percentage of Cost Overrun % Cost Overrun Wakeby The quantile function it is an alternative to the probability density or mass function, the cumulative distribution function and the characteristic function. Curtin University is a trademark of Curtin University of Technology CRICOS Provider Code 00301J
- 11. 1 x y k F ( x) PDF = x y k 1 1 k x y CDF = F ( x) 1 1 For the 101 construction and engineering projects with a contract range of $11 to $50M at Four Parameter Burr Distribution Curtin University is a trademark of Curtin University of Technology CRICOS Provider Code 00301J
- 12. Contingency • Most projects will experience cost increases from the determine of budget and contract award • Design errors, omission and changes (identifiable risks) • Assumption of 3 to 5% for construction contingency • In excess of 12.22% cost contingency needed! Curtin University is a trademark of Curtin University of Technology CRICOS Provider Code 00301J
- 13. Conclusion Curtin University is a trademark of Curtin University of Technology CRICOS Provider Code 00301J