Probability Distribution Fitting of Cost Overrun Profiles

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Probability Distribution Fitting of Cost Overrun Profiles

  1. 1. Royal Institution of Chartered Surveyors Legal Research Symposium,COBRA 2010, September 11th -13th, Las Vegas, Nevada USAProbability Distribution Fitting of CostOverrun Profiles Professor Peter ED Love Curtin University is a trademark of Curtin University of Technology CRICOS Provider Code 00301J
  2. 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 errorsCurtin University is a trademark of Curtin University of TechnologyCRICOS Provider Code 00301J
  3. 3. The Nemesis of Cost Overruns• Decision-makers are over • Deceptive actions to ensure optimistic about the outcome of projects proceed planned actionsCurtin University is a trademark of Curtin University of TechnologyCRICOS Provider Code 00301J
  4. 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. 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 TechnologyCRICOS Provider Code 00301J
  6. 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 controlCurtin University is a trademark of Curtin University of TechnologyCRICOS Provider Code 00301J
  7. 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 outcomesCurtin University is a trademark of Curtin University of TechnologyCRICOS Provider Code 00301J
  8. 8. Research ApproachProbability 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 nexamined using the 1 A2 n (2i 1) InF ( xi ) In 1 F ( xn i 1 ) n i 1Maximum Likelihood Chi-squared statistic (χ2):Estimates k 2 2 Oi Ei i 1 EiCurtin University is a trademark of Curtin University of TechnologyCRICOS Provider Code 00301J
  9. 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 TechnologyCRICOS Provider Code 00301J
  10. 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 WakebyThe 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. 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 DistributionCurtin University is a trademark of Curtin University of TechnologyCRICOS Provider Code 00301J
  12. 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 TechnologyCRICOS Provider Code 00301J
  13. 13. ConclusionCurtin University is a trademark of Curtin University of TechnologyCRICOS Provider Code 00301J

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