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
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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
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3. The Nemesis of Cost Overruns
• Decision-makers are over • Deceptive actions to ensure
optimistic about the outcome of projects proceed
planned actions
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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
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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.
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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
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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
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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
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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).
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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.
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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
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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!
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