Download pdf - A Practical Approach to Quantitative Risk Assessment -- Lin

A Practical Approach to Quantitative

Risk Assessment

Xun Guo Lin & Richard Jarrett

Division of Mathematical and Information Sciences

Canberra & MelbourneRisk Conference, Wellington, 2009

Quantitative Risk Assessment 2

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


1989 Newcastle Earthquake

5.6 magnitude

13 deaths

160 injuries

1,000 homeless

A$4.4b loss


1999 Sydney Hail Storm

70,000 cars damaged

50 injuries

2,400 homes damages

A$2.2b loss


Total Natural Disaster Loss in Australia

(1967-1999) is A$37.8b (aggregated events A$10m)

Annual cost of

natural disasters:

A$1.14 billionor $85 / yperson

30%

26%

24%

13%7%

0%

FLOOD

SEVERE STORM

CYCLONE

EARTHQUAKEBUSHFIRE

LANDSLIDE

Australian Bureau of Transport Economics (2001)

A$284mil/year

A$266mil/year


Example of Terrorism Events


Examples of Maritime Threats to Australia

Illegal ArrivalsIllegal Spills


Contents

Framework of Quantitative Risk Assessment

Consequence Score

Likelihood Score

Risk Score & Risk Matrix Approach

Framework for Multiple Threats/Hazards


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!


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


Example of Consequence Scores

Consequence

Description

Consequence

in $

Consequence

Score

Insignificant $1,000,000 6

Minor $10,000,000 7

Moderate $100,000,000 8

Major $1 Billion 9

Catastrophic $10 Billion 10


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

Death, injury

or illness

Economic

/Business Environmental Symbolic External Reputational

9:

Major

Multiple

fatalities,

remains

collection

compromised

$3 million

$3 billion

Damage to a

conservation

value where

recovery > 10

years

Serious

damage to

a nationally

important

symbol

Suspended or

grave

damage to

bilateral

relations

Government

unable to

effectively

govern

10:

Catastrophic

Mass

fatalities,

remains

collection

compromised

$3 billion+

Irreversible loss

of a

conservation

value of a

bioregion

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

Economic

/Business Social

Environ

mental Symbolic External

Reputation

/Public

Image

Overall

Score

(Example 1) 6 9 6 6 6 6 6 9.0026

(Example 2) 6 9 6 9 9 6 6 9.4777

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


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


Example of Likelihood Scores

(based on annual rates)

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)

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


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)


Risk Matrix Approach

Likelihood

Consequences

IMPROBABLE

(-4)

REMOTE

(-3)

OCCASIONAL

(-2)

PROBABLE

(-1)

LIKELY

(0)

CATASTROPHIC

(10)

VERY

HIGH

MAJOR (9) HIGH

MODERATE (8) MEDIUM

MINOR (7) 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


Risk Matrix with Scoring Ranges

Consequence

Score

Likelihood Score

-4

[-4.5, -3.5)

-3

[-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!


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


Overall Consequence Score

Each identified risk gets scored 6-10 on each category and the scores are combined (how?)

Hazard

Death,

injury or

illness

Economic

/Business Social

Environ

mental Symbolic External

Reputation

/Public

Image

Overall

Score

(Example 1) 6 9 6 6 6 6 6 9.0026

(Example 2) 6 9 6 9 9 6 6 9.4777

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


Risk Matrix Approach

Likelihood

Consequences

IMPROBABLE

(-4)

REMOTE

(-3)

OCCASIONAL

(-2)

PROBABLE

(-1)

LIKELY

(0)

CATASTROPHIC

(10)

VERY

HIGH

MAJOR (9) HIGH

MODERATE (8) MEDIUM

MINOR (7) 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


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


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

Overall 7.66 0.57 8.23 $45,389,807 3.7162 $168,678,862