World Tunnel Congress 2015
Dubrovnik
Quantitative Risk Analysis –
Fallacy of the Single Number
Dubrovnik, 27.05.2015
Philip Sander
Alfred Mörgeli
John Reilly
sander@riskcon.at
alfred.moergeli@moergeli.com
john@johnreilly.us
Technikerstr. 32
6020 Innsbruck
Austria
Rosengartenstr. 28
Schmerikon
Switzerland
1101 Worchester Road
Framingham MA 01701
USA
www.riskcon.at
www.moergeli.com
www. johnreilly.us
Overview
1. Uncertainty
2. Probabilistic and Deterministic Approach
3. Examples from Real Projects
4. Summary
Quantitative Risk Analysis – Fallacy of the Single Number
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Slide 2
Uncertainty – Distinguish Between Basic Elements and Risk
Uncertainty
in predictions
Basic Elements
Risk
(Cost, Time, etc.)
 Will always occur
(e.g. elements in a cost estimation)
 Exact price or time is uncertain
Quantitative Risk Analysis – Fallacy of the Single Number
 Has a probability of occurrence
 Consequences (costs, time, etc.)
are uncertain
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Slide 3
Uncertainty in a 14 Day Weather Forecast
Example temperatures (German television):
Munich Temperatures
Increasing deviation
Exemplary risk:
No construction works
below 2°C
 Additional probability
that risk will occur
Date
Quantitative Risk Analysis – Fallacy of the Single Number
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Slide 4
Information re Deterministic Versus Probabilistic Method in Project Development
Deterministic approach:
– single figure (sharply defined):



Planning
Approval
Cost Uncertainty
Determined (no range)
Has high uncertainty
Appears accurate but is not!
Probabilistic approach:
–bandwidth represents the
range of potential values


Construction
Goal:
Best possible cost estimate
during project
development over time
Uses ranges
Degree of certainty changes
according to project progress
 large range for large uncertainties
 narrower range for smaller uncertainties
Quantitative Risk Analysis – Fallacy of the Single Number
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Slide 5
Probabilistic and Deterministic
Approach
Quantitative Risk Analysis – Fallacy of the Single Number
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Slide 6
Comparisons of Deterministic and Probabilistic Method
Deterministic Method
Single number:
probability of occurrence times impact
Distribution:
probability of occurrence and several values
for the impact (e.g., minimum, most likely,
and maximum)
50 % &
10k
USD
50k
USD
 Uncertainty not considered
 Considers uncertainty
A simple mathematical addition to give the
aggregated consequence for all risks. This
results in an expected consequence for the
aggregated risks.
Simulation methods produce a probability
distribution based on thousands of realistic
scenarios.
Distribution Function (Impact in kUSD)
7%
100%
90%
6%
80%
Rtotal   pi * Ii
5%
Relative Frequency
Result
Overall
risk potential
20k
USD
70%
60%
4%
50%
3%
40%
Value at Risk
Input
Single risk
50 % X 20k USD
=
10k USD
Probabilistic Method
30%
2%
20%
1%
10%
Quantitative Risk Analysis – Fallacy of the Single Number
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10,000
7,500
5,000
2,500
0%
1,000
0%
Slide 7
Fallacy of the Deterministic Approach (1)
A deterministic method can give
 equal weight
to risks that have a
 low probability of occurrence and high impact
and risks that have a
 high probability of occurrence and low impact
using a
 simple multiplication of probability and impact.
This approach is incorrect.
Quantitative Risk Analysis – Fallacy of the Single Number
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Slide 8
Fallacy of the Deterministic Approach (2) - Example
5
Very Likely
4
Likely
3
Possible
2
Unlikely
1
Very
Unlikely
5
 Give equal weight to completely
different scenarios.
Flat tire
 By multiplying the two elements of
probability and impact, these values are
no longer independent.
 Loosing the probability
information
 Loosing the scenario impact
information
Negligible
1
Minor
2
Moderate
3
TBM fire
5
Significant
Severe
4
5
 The actual impact will definitely deviate
from the deterministic value (i.e., the
mean)  see following example.
Example deterministic calculation:
Tire damage mine dumper:
80% x 10,000 $ = 8,000 $
TBM fire:
NPP accident:
Quantitative Risk Analysis – Fallacy of the Single Number
(1/500) x 4,000,000 $ = 8,000 $
(1/10,000,000) x 80.000,000,000 $ = 8,000 $
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Slide 9
Examples from Real Projects
Applying the Probabilistic Method
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Slide 10
Examples from Current Projects
Koralm Base Tunnel (Southern Austria)
With a total length of 32.8 km and a maximum cover of 1.250 m the base tunnel will traverse the Koralpe mountain
range. The tunnel system is designed with two single-track tubes (approx. 66-71 m² per tube) and cross drifts at
intervals of 500 m. Excavation for the Koralm tunnel is executed by two double shield TBM’s for long distances.
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Slide 11
Example 1: Customized Distribution Function – The Scenario
Scenario:
A tunnel with 1,000 m of TBM excavation is designed without a final lining as
a result of expected favorable geological conditions.
However, a final lining may become necessary in some sections if geological
conditions turn out to be less favorable.
If it will be necessary to excavate 700 m or more with a final lining, final lining
will be implemented for the full length of 1,000 m.
Quantitative Risk Analysis – Fallacy of the Single Number
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Slide 12
Example 1: Individual Distribution Function – Estimation and Result
The quantity is modeled by
the individual distribution.
Quantitative Risk Analysis – Fallacy of the Single Number
The financial impact is modeled by
a deterministic value: 2,000 USD
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Slide 13
Examples from Current Projects
Hydro Electric Power Plant
Spullersee (Vorarlberg /Austria)
Planned in 3 scenarios
2 surface scenarios
1 subsurface scenario
For comparison consider basic costs
and risks for each scenario.
 Ground risks
subsurface scenario
 Production outage
surface scenario
Quantitative Risk Analysis – Fallacy of the Single Number
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Slide 14
Example 2: Event Tree Analysis – Scenario Description
Scenario:
Access road to the construction site of the reservoir
Probability of 40% that the access road will not be permitted (nature reserve)
 In this case (risk does occur) there will be 2 alternatives:
1. Extension of the existing public road to the reservoir.
Estimated probability for permission only 20%
2. No permission for the public road => new cableway for material transport
Most expensive scenario (80%)
The whole scenario can be modeled by an event tree.
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Slide 15
Example 2: Event Tree Analysis – The Model
20%
8%
80%
32%
40%
60%
60%
Costs for the access road are estimated to be 1,000,000.
If there will be no permission, the costs for the access road are saved in a first step.
Triangle
Most likely
Min
Omitted access road
Extension of public road
8%
Omitted access road
Cableway for material transport
Quantitative Risk Analysis – Fallacy of the Single Number
32%
Max
-1,000,000
-1,000,000
-1,000,000
467,500
550,000
880,000
-1,000,000
-1,000,000
-1,000,000
1,912,500
2,250,000
2,925,000
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Slide 16
Example 2: Event Tree Analysis – The Result
After simulation the result is a probability distribution that displays the overall risk potential.
There is a probability of 60% that the risk will not occur (see red distribution function).
Cost bandwidth
scenario public road
(opportunity)
Cost bandwidth
scenario
cableway for material
transport
Deterministic Approach:
8% x (-1,000,000 + 550,000) + 32% x (-1,000,000 + 2,250,000) + 60% x 0
= -36,000 + 400,000 + 0
364,000 will not occur in reality
Quantitative Risk Analysis – Fallacy of the Single Number
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Slide 17
Example 2: Event Tree Analysis – Risk Administration and Analysis Tool (RIAAT)
http://riaat.riskcon.at
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Slide 18
Summary
 Every cost estimate for future events comes with significant uncertainties.
 The probabilistic method delivers comprehensive information
• range of probable cost
• probability information
• specifics of potential risk event
 In particular, probabilistic methods support owners and contractors to better
understand their risks.
• allowing contractors to price their work knowing those risks
• allowing owners to budget accordingly
Distribution Function (Impact in kUSD)
7%
100%
90%
6%
80%
70%
60%
4%
50%
3%
40%
Value at Risk
Relative Frequency
5%
e.g. 80%
risk potential
coverage
30%
2%
20%
1%
10%
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10,000
7,500
5,000
2,500
0%
1,000
0%
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Slide 19