why risk models should be parameterised william marsh, [email protected] risk assessment and...
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Why Risk Models Should be Parameterised
William Marsh, [email protected]
Risk Assessment and Decision Analysis Research Group
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Acknowledgements
• Joint work with
George Bearfield
Rail Safety and Standards Board (RSSB), London
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Aims
• Introduce idea of a ‘parameterised risk model’
• Explain how a Bayesian Network is used to represent a parameterised risk model
• Argue that a parameterised risk model is– Clearer– More useful
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Outline
• Background– Risk analysis using fault and event trees– Bayesian networks
• An example parameterised risk model
• Using parameterised risk model
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Fault and Event Trees• Quantitive Risk Analysis
AND
OR
AND
Base event
Hazardous event
no 95%
yes 5%
no 80%
yes 20% yes 5%
no 95%
yes 5%
no 95%
no 75%
yes 25%
Outcome
Events
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RSSB’s Safety Risk Model
• 110 hazardous events– Fault and event
trees– Data from past
incidents
• UK rail network– Average
• Used to monitor risk for rail users and workers
• Informs safety decision making
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Bayesian Networks
• Uncertainvariables
• Probabilistic dependencies
)().|()().|( APABPBPBAP
Bayes’ Theorem
Fall
Incline Speed
YesNo
80%20%
MildNormalSevere
70% 20%10%
Conditional Probability Table
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Bayesian Networks
• Uncertainvariables
• Probabilistic dependencies
• Efficient inference algorithms
Bayes’ Theorem
Fall
Incline Speed
YesNo
60%40%
MildNormalSevere
0% 0%100%
)().|()().|( APABPBPBAP
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Example Parameterised Risk Model
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Falls on Stairs
• Falls on stairs common accident
• 500 falls on stairs / year (2001)
• Influenced by – stair design & maintenance– the users’ age, gender,
physical fitness and behaviour
• Injuries– Non fatal: bruises, bone
fractures and sprains …– Fatal injuries: fractures to
the skull, trunk, lower limbs
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Lose Footing
GATE 2
OR
GATE 3
AND
GATE 4
ANDMisstep
TripHazard Inattention Imbalance Slip
Fault TreeFailures Description
TripHazard Condition or design of stair covering creates a trip hazard
InAttention Lack of attention to possible trip hazard
Imbalance Imbalance causes sliding force between foot and step
Slip Lack of friction causes foot to slip Misstep Foot not placed correctly on stair
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Events and Outcomes
LoseFooting
Holds Falls Break
sideways
drops
forward
backwardyes
no
yes
no
holds
Vertical
Forward-short
Forward-long
Backward-short
Backward-long
Startled
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Events and Outcomes
LoseFooting
Holds Falls Break
sideways
drops
forward
backwardyes
no
yes
no
holds
Vertical
Forward-short
Forward-long
Backward-short
Backward-long
Startled
Events States Description Lose initiating Holds Holds, drops,
sideways. The person catches the railing, fall forwards or backward, or overbalances sideways into the stairwell.
Falls Forward, backward
Person falls forwards or backwards
Breaks Yes, no Person breaks their fall at a landing
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Can the Model be Generalised?
• Logic of accidents same (nearly) but numbers vary with design
• Reuse logic
• Estimating probabilities once only
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Factors – Risk Model Parameters
• Factors with discrete values
Factor Description Values Age Age of the person. young / old Design An open staircase has not sidewall. A straight
staircase is a single flight, not broken by landings. open / straight / landings
Length The length of the stairs, as determined by the number of steps.
short / long
Pitch The pitch of the staircase. gentle / steep Surface The material exposed on the floor. wooden / concrete /
carpeted Speed The speed with which the person descends the
stairs (before falling). normal / fast
Usage Are the stairs used by a single person at a time (‘single’) or many people or a rush of people?
single / many / rush
Visibility How easy it is to see the steps. Visibility may be enhanced by contrasting colours of the edge of the steps.
enhanced / lighted / poor
Width The width of the steps (not the width of the tread).
wide / narrow
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Factors to Base Events
• Base event probabilities depend on factors
TripHazard Inattention Imbalance Slip
Misstep
Visibility Usage AgeSpeed SurfacePitch
Age Young Old Speed Normal Fast Normal Fast
Imbalance=True 0.001 0.002 0.003 0.005
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Factors to Events
• Probabilities of event branches depend on factors
• … also on earlier events
Lose Holds Falls Break
Width PitchDesignAge
Falls Backwards Forwards Design Open Straight Landings Open Straight Landings
Breaks=Yes 40% 50% 90% 50% 75% 95% Breaks=No 60% 50% 10% 50% 25% 5%
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Lose Footing
TripHazard Inattention
GATE 2
OR
Imbalance Slip
GATE 3
AND
GATE 4
ANDMisstep
Visibility Usage AgeSpeed SurfacePitch
FT Bayesian Network
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Event Tree Bayesian Network
Lose Holds Falls Break
yes
no
yes
no
Vertical
Forward-short
Forward-long
Backward-short
Backward-long
Startled
outcome
n1
n3
n2
Width PitchDesign
n0
Age
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Accident Injury Score (AIS)
• Harm from accident
Age
Outcome Length
AIS
Injury
1-2 Minor 3-4 Serious 5 Critical 6 Unsurvivable
Head/neck major Head/neck moderate Limb None
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Complete Bayesian Network
AgenaRisk see: http://www.agenarisk.com/
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Explicit Factors make Clearer Models
• Are there factors in the fault or event tree?LoseFooting
Holds Falls Break
sideways
drops
forward
backwardyes
no
yes
no
holds
Vertical
Forward-short
Forward-long
Backward-short
Backward-longStartled
Age
backwardno
Backward-short
Backward-long
forward yes
no
Forward-short
Forward-long
yes
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Using the Parameterised Model
• Reuse of the model
• Modelling multiple scenarios
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Using the Parameterised Model
• Observe (some) factors
Age Length SurfaceVisibility
Usage
Design
Width
Pitch
Speed
Prior probability distributio
nAge=Young 65% Age=Old 35%
Age Young Old Usage=Single 10% 80% Usage=Many 50% 20% Usage=Rush 40% 0%
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Using the Parameterised Model
• Suppose 3 stairs– Value of each observed factor
Design Length Pitch Surface Vis CS, Entrance Landing Short Gentle Carpeted Poor CS, Lecture Rooms Straight Long Steep Wooden Enhanced Eng, Bancroft Road Open Long Gentle Concrete Lighted
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Results – Outcome Outcome Probabilities
0 0.00001 0.00002 0.00003 0.00004 0.00005 0.00006
Vertical:
Forw ard-short:
Forw ard-long:
Backw ard-short:
Backw ard-long:
Startled:
Eng Bancroft Road
CS Lecture Rooms
CS Entrance
• Probability distribution– Outcome of a ‘stair descent’– Hidden ‘nothing happens’ outcome
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Results – Accident Injury Score
AIS
0.00E+00 1.00E-06 2.00E-06 3.00E-06 4.00E-06 5.00E-06 6.00E-06 7.00E-06 8.00E-06
1-2
3-4
5
6
AIS
Probability
Accidents Per Year
AIS CS Entrance
CS Lecture Rooms
Eng Bancroft Rd
1-2 0.153 0.518 4.864 3-4 0.016 0.066 0.920 5 0.006 0.029 0.397 6 0.001 0.003 0.096
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System Risk
• University has many stairs in different buildings
• How to assess the total risk?
• Solution 1 – Used parameterised model for each stairs– Aggregate results
• Solution 2– Model ‘scenario’ in the Bayesian Network– Scenario: each state has shared characteristics
e.g. geographical area
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Scenario
• Each value is a ‘scenario’ for which we wish to estimate risk
Age Length SurfaceVisibility
Usage
Design
Width
Pitch
Speed
Scenario Could be each staircase
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Imprecise Scenarios
• Imagine three departments– Factors do not have single value– Probability distribution over factor values
Age Design Length Pitch Maths Young: 80%
Old: 20% Landing: 80% Straight: 15% Open: 5%
Short: 50% Long: 50%
Gentle: 25% Steep: 75%
Law Young: 70% Old: 30%
Landing: 70% Straight: 30% Open: 0%
Short: 75% Long: 25%
Gentle: 75% Steep: 25%
Arts Young: 60% Old: 40%
Landing: 50% Straight: 50% Open: 0%
Short: 30% Long: 70%
Gentle: 50% Steep: 50%
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Exposure
• Some scenarios more common
• Distribution of ‘stair descents’
Scenario Maths Laws Arts Total
Daily descents 3000 1500 2000 6500
Proportion 46% 23% 31%
Lose Footing
OnStair
GATE 1
AND
GATE 2
OR
GATE 3 GATE 4Misstep
Scenario
Proportion of events in each
scenario
Departments
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Using the System Model• Use 1
– Select a scenario– … like the
parameterised model– Scaled by total system
events AIS
0.00E+00 2.00E-07 4.00E-07 6.00E-07 8.00E-07 1.00E-06 1.20E-06 1.40E-06
1-2
3-4
5
6
AIS
Probability
Arts
Law
Maths
Accidents per Year AIS
Maths Law Arts 1-2 2.722 0.859 1.559 3-4 0.332 0.096 0.187 5 0.129 0.037 0.078 6 0.019 0.004 0.009
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Using the System Model• Use 2
– Whole system risk, – … weighted by exposure for each scenario
0.00E+00 5.00E-07 1.00E-06 1.50E-06 2.00E-06 2.50E-06
1-2
3-4
5
6
AIS
Probability AIS Accidents/Year 1-2 5.141 3-4 0.615 5 0.244 6 0.032
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Parameterised Risk Models in Practice
Improving Safety Decision Making
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Better Safety Decision Making
• Safety benefits of improvements– Existing models only support system-wide
improvements
• Detection of local excess risk– E.g. poor maintenance in one area– Requires risk distribution (not average)– … variations in equipment type and condition– … procedural and staffing variations
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Risk Profile: Sector and Network
0% 5% 10% 15% 20% 25% 30% 35%
A01
A02
A03
A04
A05
A07
A08
A09
A10
A11
A12
A13
A14
A15
A16
A17
A18
A19
A21
A22
A23
A24
A25
A26
A27
A28
A01 Collision between trains
A04 Train collision with vehicle at level crossing
A12 Accident at platform/train interface
A14 Accident involving trespass or surfing
A17 Assault
A22 Slips, trips and falls on railway infrastructure
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D e ra ilm e n t c o n ta in m e n t M a in ta in c le a ra n c e s c a rria g e s fa lld e ra ils to c e s s /a d ja c s e c o n d a ry c o llis io nh it lin e s id e s tru c S tru c tu re C o lla p s es trik e tu n n e l p o rta l
S tru c tu re C 1
S tru c tu re C 2F a ll 1
F a ll 2S trik e 1
S trik e 2c e s s 1
c le a ra n c e
c o n ta in m e n t
c o n ta in m e n t fitte d
n u m b e r o f tra c k s L in e s id e O b je c t D e n s ity L in e s id e O b je c t T y p e
tra ffic d e n s ity
tra in s p e e d
tra c k c u rv a tu re
tra c k fa u lt ty p e
ro llin g s to c k fa u lt ty p e
ro llin g s to c k fa u lt s e v e rity
tra c k fa u lt s e v e rity
tra c k ty p e
e ffe c tiv e n e s s o f in fra s tru tu re m a in t
tra c k in s p e c tio n in te rv a ls
E ffe c tiv e n e s s o f r.s to c k m a in te n a n
R o llin g s to c k in s p e c tio n in te rv a l
g 1 - d e ra ilm e n t o c c u rs
g 2 - o v e rs p e e d d e ra ilm e n t
g 1 3 - S & C d e ra ilm e n t
g 2 1 - o b s tru c tio n d e ra ilm e n t
g 3 - tra c k fa u lt d e ra ilm e n t
e 1 - tra in o v e rs p e e d lim it
e 2 - d e ra ilm e n t o c c u rs (O S )
e 3 - tra c k fa u lt o c c u rs g 5 - tra in e x p o s e d to tra c k fa u lt e 4 - d e ra ilm e n t o c c u rs (T F )
g 6 -tra c k fa u lt n o t d e te c te d g 7 - tf d e te c te d & n o t c o n tro lle d
e 6 - tra c k fix a n d T S R re q u ire d e 7 - T S R w o rk s , tra c k fix fa ilse 8 - T S R fa ils , tra c k fix w o rk s
e 1 3 - S & C fa u lt o c c u rs
g 1 5 - S & C fa u lt n o t d e te c te d
e 1 4 - d e ra ilm e n t o c c u rs (S & C )
g 1 7 - R S F d e ra ilm e n t
e 1 7 - R S fa u lt o c c u rs
g 1 8 - R S fa u lt n o t a d d re s s e d e 1 8 - d e ra ilm e n t o c c u rs (R S )
g 1 9 - R S fa u lt n o t d e te c te d g 2 0 - R S fa u lt a llo w e d to re m a in
e 2 0 - R S F n o t fix e d e 2 1 - tra in s ta y s in s e rv ic e
e 2 2 - o b s tru c tio n o c c u rs
e 2 3 - o b s tru c tio n n o t d e te c te d
e 2 4 - d e ra ilm e n t o c c u rs
S & C fa u lt s e v e rity
ty p e o f o b s tru c tio n
lo c a tio n o f tra c k
d riv e r p e rfo rm a n c e
e 9 - T S R o n ly re q u ire d
e 5 - tra c k fa u lt d e te c te dg 8 - tra c k fa u lt n o t c o n tro lle d
g 9 -2 c o n tro ls re q u ire d - tra c k fix fag 1 0 -2 c o n tro ls re q u ire d - T S R n o t a
g 11 - T S R re q u ire d a n d n o t a p p lie d g 1 2 - lin e b lo c k re q u ire d a n d n o t a
e 1 0 - T S R n o t a p p lie d e 11 - lin e b lo c k o n ly re q u ire d e 1 2 - lin e b lo c k n o t a p p lie d
g 1 4 - tra in e x p o s e d to S & C fa u lt
e 1 5 - S & C fa u lt d e te c te d
g 1 6 - tf d e te c te d & n o t c o n tro lle d
e 1 6 - S & C fa u lt n o t c o n tro lle d
e 1 9 - R S F d e te c te d
a c c id e n t o u tc o m e
d riv e r fa ils to s lo w tra in
Derailment
Event tree
FactorsFault treeInvestigation found the cause to be:
‘the poor condition of points 2182A at the time of the incident, and that this resulted from inappropriate adjustment and from insufficient maintenance ….’
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Summary
• Parameterised ET + FT – Using Bayesian Networks– Factors made explicit– Clearer and more compact
• Reuse of risk model
• Risk profiles– Guide changes to reduce risk– Challenge of including more causes
Thank You