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


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


The Nemesis of Cost Overruns

• Deceptive actions to ensure projects proceed

• Decision-makers are over optimistic about the outcome of planned actions


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


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.


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


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


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):

)(,

1)(max

1ii

nixF

n

i

n

ixFD

n

iini xFInxInFi

nnA

11)(1)()12(

12

k

i i

ii

E

EO

1

22


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

PDF

CDF

xxxf exp)(

1

x

xf exp)(


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


For the 101 construction and engineering projects with a contract range of $11 to $50M at Four Parameter Burr Distribution

1

1

1

)(

k

yx

yxk

xF

k

yxxF

11)(

PDF =

CDF =


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!


Conclusion

probability distribution fitting of cost overrun profiles

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