Framework of Quantitative Risk Assessment. ⢠Consequence Score. ⢠Likelihood Score. ⢠Risk Score & Risk Matrix Approach. ⢠Framework for Multiple Threats/ ...
A Practical Approach to Quantitative Risk Assessment Xun Guo Lin & Richard Jarrett Division of Mathematical and Information Sciences Canberra & Melbourne Risk Conference, Wellington, 2009
Darwin after Cyclone Tracy 1974
Category 4 Cyclone with
Max speed 240km/hr (66.7m/s)
65 deaths 640 injuries
45,000 homeless A$4.2b loss Quantitative Risk Assessment
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1989 Newcastle Earthquake
5.6 magnitude 13 deaths
160 injuries 1,000 homeless
A$4.4b loss
Quantitative Risk Assessment
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1999 Sydney Hail Storm 70,000 cars damaged 50 injuries
2,400 homes damages A$2.2b loss
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Total Natural Disaster Loss in Australia (1967-1999) is A$37.8b (aggregated events ≥ A$10m) Australian Bureau of Transport Economics (2001) A$284mil/year SEVERE STORM 26%
Annual cost of natural disasters:
FLOOD 30%
A$266mil/year CYCLONE 24%
LANDSLIDE 0% 7%
BUSHFIRE
13%
EARTHQUAKE
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A$1.14 billion or $85 / y∙person
Example of Terrorism Events
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Examples of Maritime Threats to Australia
Illegal Arrivals
Quantitative Risk Assessment
Illegal Spills
7
Contents • Framework of Quantitative Risk Assessment • Consequence Score • Likelihood Score • Risk Score & Risk Matrix Approach
• Framework for Multiple Threats/Hazards
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Framework of Quantitative Risk Assessment Based on Australia & New Zealand Standard on Risk Management (AS/NZS 4360), we can define RISK = Expected Cost = Consequence Likelihood where: the unit of Risk is in $ per time unit (eg year)
Risk is respect to a particular threat or multiple threats with multiple consequences Development of a severity scoring system for consequence
and likelihood with each level of change represents a 10-fold increase/decrease in values Risk Score = Overall Consequence Score + Likelihood Score
Practical, Simple & Useful! Quantitative Risk Assessment
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Example of Consequence Categories • Death, injury or illness to humans
• Economic or business impact • Social impact
• Environmental impact • Symbolic effect • External relationships • Damage to business reputation and public image Quantitative Risk Assessment
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Example of Consequence Scores
Consequence Consequence Consequence Description in $ Score Insignificant
$1,000,000
6
Minor
$10,000,000
7
Moderate
$100,000,000
8
Major
$1 Billion
9
Catastrophic
$10 Billion
10
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Scoring Consequences • Seven categories of consequences, not all $-values! • Great care taken to “line up” descriptions of similar severity across categories • 1 unit corresponds (roughly) to 10-fold step in “cost” or impact • Examples for severity levels 9 and 10 with only six categories: Severity 9: Major
Death, injury or illness
Economic /Business
Multiple fatalities, remains collection compromised
Damage to a $3 million conservation – $3 billion value where recovery > 10 years
Mass 10: fatalities, Catastrophic remains collection compromised
$3 billion+
Quantitative Risk Assessment
Environmental Symbolic
Irreversible loss of a conservation value of a bioregion 12
External
Reputational
Serious damage to a nationally important symbol
Suspended or grave damage to bilateral relations
Government unable to effectively govern
Destruction of nationally important symbol
Open armed conflict, Military invasion
Fall of Government outside the Constitutional Process
Overall Consequence Score • Each identified “risk” gets scored 6-10 on each category and the scores are combined (how?)
Hazard
Death, injury or illness
Social
Environ mental
Symbolic
External
Reputation /Public Image
Economic /Business
(Example 1)
6
9
6
6
6
6
6
9.0026
(Example 2)
6
9
6
9
9
6
6
9.4777
Overall Score
• Do this by summing 10x, and then taking logs! Log10(106+109+106+106+106+106+106) = Log10(1,006,000,000) = 9.0026
• Very different from the averaging, which is 6.43 for Ex 1 • Similar to taking “maximum”, but gives larger value if there is more than one „9‟ Quantitative Risk Assessment
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Overall Consequence Score Overall Cost
Consequence ($) = 10 Overall Consequence Score In Ex 1, 109.0026 = $1,006,004,677 In Ex 2, 109.4777 = $3,004,000,496
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Example of Likelihood Scores (based on annual rates) Likelihood
Description
Likelihood Score
Occasional
1 event in 100 years
-2
Probable
1 event in 10 years
-1
Possible
1 event in 3 years
-0.5
Likely
1 event per year
0
Very likely
3 events per year
0.5
Highly likely
10 events per year
1
Almost certain
30 events per year
1.5
• Again, one step change in score will have a 10-fold increase/decrease in the probability of occurrence • The formula to convert the Likelihood Score to probability is Rate of occurrence per year = 10Likelihood Score • eg, a Likelihood Score of -2 will have probability 10-2 = 1/100 = 0.01 (frequency per year) Quantitative Risk Assessment
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Risk Scores and Risk Levels Risk Score = Overall Consequence Score + Likelihood Score In Ex 1, Overall Consequence Score = 9.0026 Likelihood Score = -2 Risk Score = 7.0026 Risk = Expected cost = 107.0026 =$10,060,047 We can also define Risk Levels, eg Negligible (1.00 to 2.00) Low (2.00 to 4.00) Moderate (4.00 to 6.00) High (6.00 to 8.00) Very High (8.00 to 11) Quantitative Risk Assessment
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Risk Matrix Approach Likelihood Consequences
IMPROBABLE (-4)
REMOTE (-3)
OCCASIONAL (-2)
PROBABLE (-1)
LIKELY (0)
CATASTROPHIC (10)
VERY HIGH
MAJOR (9)
HIGH
MODERATE (8) MINOR (7)
MEDIUM LOW
Risk Level
Risk Management Action Required
Very High
Unacceptable (reduce risk through countermeasures)
High
Undesirable (management decision required)
Medium
Acceptable with review by management
Low
Acceptable without review 17
Quantitative Risk Assessment
Risk Matrix with Scoring Ranges Likelihood Score Consequence -4 -3 Score [-4.5, -3.5) [-3.5, -2.5)
-2 [-2.5, -1.5)
-1 [-1.5, -0.5)
0 [-0.5, 0.5)
10 [9.5, 10.5)
6 [5, 7)
7 [6, 8)
8 [7, 9)
9 [8, 10)
10 [9, 11)
9 [8.5, 9.5)
5 [4, 6)
6 [5, 7)
7 [6, 8)
8 [7, 9)
9 [8, 10)
8 [7.5, 8.5)
4 [3, 5)
5 [4, 6)
6 [5, 7)
7 [6, 8)
8 [7, 9)
7 [6.5, 7.5)
3 [2, 4)
4 [3, 5)
5 [4, 6)
6 [5, 7)
7 [6, 8)
6 [5.5, 6.5)
2 [1, 3)
3 [2, 4)
4 [3, 5)
5 [4, 6)
6 [5, 7)
Though 10-fold increase/decrease in score but no “gaps” Practical, Simple & Useful! Quantitative Risk Assessment
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Issues Related to Risk Management • Need to have defined actions at each level of Risk • Calibrate carefully to get appropriate level of response
• Risk is assessed relative to “current mitigation activities” • “Quantitative” does not mean “accurate” – be aware of (and allow for) the uncertainties in estimates of risk
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Overall Consequence Score • Each identified “risk” gets scored 6-10 on each category and the scores are combined (how?)
Hazard
Death, injury or illness
Social
Environ mental
Symbolic
External
Reputation /Public Image
Economic /Business
(Example 1)
6
9
6
6
6
6
6
9.0026
(Example 2)
6
9
6
9
9
6
6
9.4777
Overall Score
• Do this by summing 10x, and then taking logs! Log10(106+109+106+106+106+106+106) = Log10(1,006,000,000) = 9.0026
• Very different from the averaging, which is 6.43 for Ex 1 • Similar to taking “maximum”, but gives larger value if there is more than one „9‟ Quantitative Risk Assessment
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Risk Matrix Approach Likelihood Consequences
IMPROBABLE (-4)
REMOTE (-3)
OCCASIONAL (-2)
PROBABLE (-1)
LIKELY (0)
CATASTROPHIC (10)
VERY HIGH
MAJOR (9)
HIGH
MODERATE (8) MINOR (7)
MEDIUM LOW
Risk Level
Risk Management Action Required
Very High
Unacceptable (reduce risk through countermeasures)
High
Undesirable (management decision required)
Medium
Acceptable with review by management
Low
Acceptable without review 21
Quantitative Risk Assessment
Framework for Multiple Threats/Hazards • Assuming independent between threats
• Formulas to combine threats in a region or a threat in multi-regions • Risk Score = log(10Risk Score1+10Risk Score2) • Likelihood Score = log(10Likelihood Score1 +10Likelihood Score2) • Cons Score = Risk Score - Likelihood Score
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Numerical Example of Aggregating Multiple Threats or Hazards in Multiple Regions Region
Hazards
Cons Score
Lik Score
Risk Score
Cost / event
Rate
Exp Cost
1
1
7.0
0.0
7.0
$10,000,000
1.0000
$10,000,000
1
2
8.8
-1.0
7.8
$630,957,344
0.1000
$63,095,734
1
3
7.7
0.0
7.7
$50,118,723
1.0000
$50,118,723
1
4
7.9
-1.0
6.9
$79,432,823
0.1000
$7,943,282
2
1
7.3
0.0
7.3
$19,952,623
1.0000
$19,952,623
2
2
7.5
-0.5
7.0
$31,622,777
0.3162
$10,000,000
2
3
7.1
-1.0
6.1
$12,589,254
0.1000
$1,258,925
2
4
7.8
-1.0
6.8
$63,095,734
0.1000
$6,309,573
Summaries
1
all
7.8
0.3
8.1
$59,617,155
2.2000
$131,157,740
2
all
7.4
0.2
7.6
$24,746,363
1.5162
$37,521,122
all
1
7.2
0.3
7.5
$14,976,312
2.0000
$29,952,623
all
2
8.2
-0.4
7.9
$175,614,749
0.4162
$73,095,734
all
3
7.7
0.0
7.7
$46,706,953
1.1000
$51,377,649
all
4
7.9
-0.7
7.2
$71,264,279
0.2000
$14,252,856
7.66
0.57
8.23
$45,389,807
3.7162
$168,678,862
Overall
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