Do

wn

load

ed f

rom

in

form

s.o

rg b

y [

12

8.1

72

.48.1

70

] o

n 1

3 M

ay 2

01

6,

at 1

1:4

2 .

Fo

r per

sonal

use

only

, al

l ri

gh

ts r

eser

ved

.

Debonding

Loss of Tile

Debris

Damage

Reentry

Heating

Loss of

Additional

Tiles

Subsystem

Malfunction

Loss of

Shuttle

Inspection

Decisions

Maintenance

Decisions

Design

Decisions

In-flight Repair

Decisions

Flight

Decisions

Take-off

Decisions

Deep

Knowledge

Some

Knowledge

Outside

Expert’s Area

M. E. Pate-Cornell, L. M. Lakats, D. M. Murphy, D. M. Gaba (1997) Anesthesia Patient Risk: A Quantitative Approach to Organizational Factors and Risk Management Options. Risk Analysis 17(4): 511-523

Fatigue

Cognitive

Problems

Personality

Problems

Severe

Distraction

Drug

Abuse

Alcohol

Abuse

Neurological

Problems

Lack of

Training

Lack of

Supervision

Accident

Periodic

Simulator Test

Formal Retirement

Procedure

Periodic

Medical Exam

Strict Supervision

of Residents

Formal

Recertification

Simulator

Training - Resident

Simulator

Training - Expert

Random

Alcohol Testing

Random

Drug Testing

Work Schedule

Deep

Knowledge

Some

Knowledge

Outside

Expert’s Area

Incidents

Type of

Other

Vessel

Location

Current

Speed &

Direction

Proximity

To Shore

Human

Error

Nav. Aid

Failures

Propulsion

Failure

Steering

Failure

Maintenance

Practices

Engineering

Crew Training

Wind

Speed &

DirectionVessel Type

Drift

GroundingCollision

Powered

Grounding

Bridge Crew

Training

Bridge Crew

Experience

Accidents

Proximity

To Other

Vessel

Situational

Variables

Organizational

Variables

Deep

Knowledge

Some

Knowledge

Outside

Expert’s Area

S:DP4153DRiskProfileWhat-IfFV- VesselTimeExp.:5%ofBaseCaseVTE

23-24 22-23

21-22 20-21

19-20 18-19

17-18 16-17

15-16 14-15

13-14 12-13

11-12 10-11

9-10 8-9

7-8 6-7

5-6 4-5

3-4 2-3

1-2 0-1

R:KM3483DRiskProfileWhat-IfFV- VesselTimeExp.:7%ofBaseCaseVTE

23-24 22-23

21-22 20-21

19-20 18-19

17-18 16-17

15-16 14-15

13-14 12-13

11-12 10-11

9-10 8-9

7-8 6-7

5-6 4-5

3-4 2-3

1-2 0-1

Q:GW4873DRiskProfileWhat-IfFV- VesselTimeExp.:12%ofBaseCaseVTE

23-24 22-23

21-22 20-21

19-20 18-19

17-18 16-17

15-16 14-15

13-14 12-13

11-12 10-11

9-10 8-9

7-8 6-7

5-6 4-5

3-4 2-3

1-2 0-1

T:GW- KM- DP3DRiskProfileWhat-IfFV- VesselTimeExp.:24%ofBaseCaseVTE

23-24 22-23

21-22 20-21

19-20 18-19

17-18 16-17

15-16 14-15

13-14 12-13

11-12 10-11

9-10 8-9

7-8 6-7

5-6 4-5

3-4 2-3

1-2 0-1

E.g. Inadequate Skills,

Knowledge,Equipment,

Maintenance,Management

Stage 1Basic/Root

Causes

E.g. Human Error,

Equipment Failure,

Stage 2Immediate

Causes

E.g. Propulsion Failure,

Steering Failure,Hull Failure,

Nav. Aid. Failure,Human Error

Stage 3Incident

E.g. Collisions,

Groundings,Founderings,

Allisions,Fire/Explosion

Stage 4Accident

E.g. Oil Outflow,

Persons in Peril

Stage 5Consequence

E.g. Environmental

Damage,Loss of Life

Stage 6Impact

ORGANIZATIONAL FACTORSVessel type Flag/classification societyVessel age Management type/changesPilot/officers on bridge Vessel incident/accident historyIndividual/team training Safety management system

SITUATIONAL FACTORSType of waterway VisibilityTraffic situation WindTraffic density CurrentVisibility Time of day

Risk Reduction Interventions

E.g.

Inadequate Skills,

Knowledge,

Equipment,

Maintenance,

Management

E.g.

Human Error,

Equipment Failure,

E.g.

Propulsion Failure,

Steering Failure,

Hull Failure,

Nav. Aid. Failure,

Human Error

E.g.

Collisions,

Groundings,

Founderings,

Allisions,

Fire/Explosion

E.g.

Oil Outflow,

Persons in Peril

E.g.

Environmental

Damage,

Loss of Life

Stage 1

Basic/Root

Causes

Stage 2

Immediate

Causes

Stage 3

Incident

Stage 4

Accident

Stage 5

Consequence

Stage 6

Impact

E.g.

Emergency Repair or

Assist Tug,

Emergency Response

Coordination,

VTS Watch

Risk Reduction/

Prevention

4. Intervene to

Prevent Accident

if Incident Occurs

E.g.

Double Hull,

Double Bottom

Risk Reduction/

Prevention

5. Reduce

Consequence

(Oil Outflow)

if Accident Occurs

E.g.

Pollution

Response Vessel,

Oil Boom,

Pollution

Response

Coordination

Risk Reduction/

Prevention

6. Reduce Impact if

Oil Outflow Occurs

E.g.

ISM,

Training,

Better

Maintenance

Risk Reduction/

Prevention

1. Decrease

Frequency of

Root/Basic

Causes

E.g.

Inspection Program,

Double Engine,

Double Steering,

Redundant Nav Aids,

Work Hour Limits,

Drug/Alcohol Tests

Risk Reduction/

Prevention

2. Decrease

Frequency of

Immediate

Causes

3. Decrease

Exposure to

Hazardous

Situations

E.g.

Closure Conditions,

One-way Zone,

Traffic Sep. Scheme,

Traffic Management,

Nav. Aids for Poor

Visibility

Pate-Cornell, M. E. (1996) Uncertainties in Risk Analysis: Six Levels of Treatment.

Risk Analysis 54 95-111.

Correlations LawComputer

ScienceMedicine Library Science Business Admin.

With mean similarity rank

0.93 0.96 0.92 0.88 0.88

With base rate 0.33 -0.35 0.27 -0.03 0.62

32

Issaquah class ferry

On the Bremerton to Seattle route

Crossing situation within 15 minutes

Other vessel is a navy vessel

No other vessels around

Good visibility

Negligible wind

34

Issaquah class ferry on the Bremerton to Seattle route in a

crossing situation within 15 minutes, no other vessels around,

good visibility, negligible wind.

Other vessel is a navy vessel Other vessel is a product tanker

Example taken from the Washington State Ferries Risk Assessment

35

Issaquah Ferry Class -

SEA-BRE(A) Ferry Route -

Navy 1st Interacting Vessel Product Tanker

Crossing Traffic Scenario 1st Vessel -

< 1 mile Traffic Proximity 1st Vessel -

No Vessel 2nd Interacting Vessel -

No Vessel Traffic Scenario 2nd Vessel -

No Vessel Traffic Proximity 2nd Vessel -

> 0.5 Miles Visibility -

Along Ferry Wind Direction -

0 Wind Speed -

Likelihood of Collision -

9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9

36

0 0( | , , ) exp ,TP Event X p p X Model

0

0

( | , ) exp( )exp ( ) ,

( | , ) exp( )

TT

T

P Event R p RR L

P Event L p L

Compare left

and right

scenarios

ji

T

ijiji uXzy ,,, )ln( Regression

analysis

37

9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9Likelihood of Collision

, , ,ln( )i j i j i i jy z u

Expert errors are purely

disagreement about βi

38

Description Notation Values

Ferry route and class FR_FC 26

Type of 1st interacting vessel TT_1 13

Scenario of 1st interacting vessel TS_1 4

Proximity of 1st interacting vessel TP_1 Binary

Type of 2nd interacting vessel TT_2 5

Scenario of 2nd interacting vessel TS_2 4

Proximity of 2nd interacting vessel TP_2 Binary

Visibility VIS Binary

Wind direction WD Binary

Wind speed WS Continuous

-3

-2

-1

0

1

2

3

FR-FC TT_1 TS_1 TP_1 TT_2 TS_2 TP_2 VIS WD WS FR-FC

*TT_1

FR-FC

*TS_1

FR-FC

*VIS

TT_1

*TS_1

TT_

*VIS

TS_1

*VIS

Density o

f B

eta

Szwed et al.’s analysis with independence

Σ,0~

1

MVNormal

e

e

e

p

Winkler, R. L. (1981). Combining probability distributions from

dependent information sources. Management Science, 27, 479–

488.

41

2*2* 2/exp),;( Σ

1*

1

1

1 1

T

T

Σ

Σ

*2

1

1

1 1T

Σ

42

T

iX

T

ijiji Xyu ,,

Σ,0~

,

1,

MVNormal

u

u

u

pi

i

T

i

Each expert’s

assessment is

related to β by

the model

β is a model

parameter and

can’t be

observed

Each expert

assesses Θ

directly

Θ is a real

quantity and

could be

observed

1 12 1 1| , , exp exp 1 1

2 2

N TT TTp tr tr

Y X Σ Σ VΣ B X X B Σ

1

* * *1| , , exp .

2

T

p

Y X Σ

1

* 1

ˆ 1

1 1T

BΣ

Σ

1

* 11 1

T

T

X X

Σ

Σ

1

ˆ T T

B X X X Y

Merrick, J. R.W., van Dorp, J. R., & Singh, A. (2005b). Analysis of

correlated expert judgments from extended pairwise comparisons.

Decision Analysis, 2(1), 17–29.

44

1*

1

1

1 1

T

T

Σ

Σ

1

* 1

ˆ 1

1 1T

BΣ

Σ

1

* 11 1

T

T

X X

Σ

Σ

*2

1

1

1 1T

Σ

For β:

For Θ:

Slight difference removed if we define

the regression on the transpose

We followed Press’s convention

' 1 ' 'T Y X U

1T

Y X U

45

11,

11

1ˆ~,,|

1

111

1

111

Σ

XXAA

Σ

ΣBXXXXAΣXY

T

T

T

TTMVNormal

| , ~ ,Inv Wishart m N Σ Y X G V

Updating BXYBXYV ˆˆ T

mWishartInv ,~ G

11

,~|1

Σ

AΣ

TMVNormal

46

-300

-200

-100

0

100

200

300

FR-FC TT_1 TS_1 TP_1 TT_2 TS_2 TP_2 VIS WD WS FR-FC

*TT_1

FR-FC

*TS_1

FR-FC

*VIS

TT_1

*TS_1

TT_1

*VIS

TS_1

*VIS

De

nsity

of B

eta

Assume independence between the experts a priori

47

-3

-2

-1

0

1

2

3

FR-FC TT_1 TS_1 TP_1 TT_2 TS_2 TP_2 VIS WD WS FR-FC

*TT_1

FR-FC

*TS_1

FR-FC

*VIS

TT_1

*TS_1

TT_

*VIS

TS_1

*VIS

De

nsity

of B

eta

-3

-2

-1

0

1

2

3

FR-FC TT_1 TS_1 TP_1 TT_2 TS_2 TP_2 VIS WD WS FR-FC

*TT_1

FR-FC

*TS_1

FR-FC

*VIS

TT_1

*TS_1

TT_

*VIS

TS_1

*VIS

Density o

f B

eta

Our analysis with dependence

Szwed et al.’s analysis with independence

Doesn’t dependence

between

experts

increase

posterior

variance?

Dependent

Experts

Independent

Experts

48

1,1

0

1

-1 0 1

3,1

0

1

-1 0 1

3,3

0

1

-1 0 1

7,1

0

1

-1 0 1

7,3

0

1

-1 0 1

7,7

0

1

-1 0 1

4,1

0

1

-1 0 1

4,3

0

1

-1 0 1

4,7

0

1

-1 0 1

4,4

0

1

-1 0 1

2,1

0

1

-1 0 1

2,3

0

1

-1 0 1

2,7

0

1

-1 0 1

2,4

0

1

-1 0 1

2,2

0

1

-1 0 1

6,1

0

1

-1 0 1

6,3

0

1

-1 0 1

6,7

0

1

-1 0 1

6,4

0

1

-1 0 1

6,2

0

1

-1 0 1

6,6

0

1

-1 0 1

5,1

0

1

-1 0 1

5,3

0

1

-1 0 1

5,7

0

1

-1 0 1

5,4

0

1

-1 0 1

5,2

0

1

-1 0 1

5,6

0

1

-1 0 1

5,5

0

1

-1 0 1

8,1

0

1

-1 0 1

8,3

0

1

-0.9 0.1

8,7

0

1

-1 0 1

8,4

0

1

-1 0 1

8,2

0

1

-1 0 1

8,6

0

1

-1 0 1

8,5

0

1

-1 0 1

8,8

0

1

-1 0 1

Experts 1, 3 and 7 are correlated

Experts 2, 4 and 6 are correlated

Experts 5 and 8 are negatively or

uncorrelated with other experts

Remember we assumed

independence a priori,

but we learnt about Σ!

49

Comparing the

two scenarios

we pictured

earlier

90%

Credibility

Interval

Prior [1.88*10-35, 5.32*1034]

Dependent [4.38,5.84] ½ width = 0.73

Independent [4.43,7.04] ½ width = 1.3

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

Ratio of probabilities

Pro

ba

bilt

y d

en

sity

prior dependent experts independent experts

50