Probability Distribution Fitting of Cost Overrun Profiles
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Transcript of Probability Distribution Fitting of Cost Overrun Profiles
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Professor Peter ED Love
Probability Distribution Fitting of Cost Overrun Profiles
Royal Institution of Chartered Surveyors Legal Research Symposium, COBRA 2010, September 11th -13th, Las Vegas, Nevada USA
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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
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The Nemesis of Cost Overruns
• Deceptive actions to ensure projects proceed
• Decision-makers are over optimistic about the outcome of planned actions
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The Fallacy of Cost Overruns
• Where do you measure from?
• Need to distinguish between factors that increase project cost and those affect the accuracy of estimates
• 2004 budget was $420m
• 320% cost overrun ?
Construction on time and budget
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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.
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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
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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
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Research Approach
Probability Density Function, CDF and distribution parameters for continuous distributions were examined using the Maximum Likelihood Estimates
Goodness of Fits Test:Kolmogorov-Smirnov statistic (D):
Anderson-Darling statistic (A2):
Chi-squared statistic (χ2):
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Results
• Mean overall cost overrun (n=276) 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 size (contract value)
• The likelihood that a project does not exceed a cost overrun of 12.22% is 60% (P (X < X1) = .60).
Frechet 3P
CDF
xxxf exp)(
1
x
xf exp)(
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Distribution by Contract Value
• <$1M and $51 to $100M (Cauchy)
• $1 to $10M and >$100M (Wakeby)
The quantile function it is an alternative to the probability density or mass function, the cumulative distribution function and the characteristic function.
12
1)(
x
xfPDF =
CDF = 5.0arctan1
)(
xxF
CDF =
FFFx 1111)(
PDF <$1M
% Cost Overrun Cauchy
Percentage of Cost Overrun2520151050-5-10
Prob
abili
ty o
f Cos
t Ove
rrun
0.440.4
0.36
0.32
0.28
0.24
0.20.16
0.12
0.08
0.04
0
PDF $11-$50M
% Cost Overrun Wakeby
Percentage of Cost Overrun150100500-50-100-150
Prob
abili
ty o
f Cos
t Ove
rrun
1
0.8
0.6
0.4
0.2
0
-0.2
PDF $1-$10M
Wakeby distribution is defined by the quantile function (inverse CDF):
PDF > $100M
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For the 101 construction and engineering projects with a contract range of $11 to $50M at Four Parameter Burr Distribution
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1
1
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k
yx
yxk
xF
k
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11)(
PDF =
CDF =
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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!
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Conclusion