The (The (uncertainuncertain) flow of the ) flow of the presentationpresentation
PARTI I: The uncertainty of risk
� Problem Setting: RISK, QRA, PRA
� Uncertainty: types and sources
� Worries
� Frameworks of uncertainty/information/knowledge representation
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PART II: The risk of uncertainty
� Decision maker dreams and nightmares
The (The (riskyrisky) flow of the ) flow of the presentationpresentation
PART III: “Things I know”
� “Faithful” representation of information and introduction of knowledge
PART IV: Jingles
� Conclusions
� Advertisement
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� Advertisement
� Thanks
PART I: The uncertainty of risk
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Safety
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Hazard
barrier
The parmesan The parmesan cheesecheese modelmodel
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No Hazard
No
Redundancy Training Safety Reviews
Multiple Multiple barriersbarriers
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No Hazard
Hazard
RedundancyRedundancy exampleexample
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Geological Barrier
Technical BarriersEmbeddingStorage caskOver packsBackfill
Multiple Multiple barrierbarrier system system exampleexample
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Waste
Coated particle
Inner graphite zone
Fuel-free graphite zone
60 mm
0.5 mm
0.095 mm0.040 mm
0.035 mm0.040 mm
PyC PyCSiC buffer fuel
Multiple Multiple barrierbarrier system system exampleexample
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Graphite matrix Outer PyC SiC Inner PyC Kernel
Risk
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Not all risk mitigation strategies work...
Reality: an Reality: an exampleexample of a protection of a protection barrierbarrier
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Hazard
HumanErrors
ProceduralErrorsFaults in
Redundancies
The The swissswiss cheesecheese modelmodel
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Hazard
Safeguards
Environment
UNCERTAINTY
The concept of RiskThe concept of Risk
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People
UNCERTAINTY
1. What undesired conditions may occur? ? Accident, A
3. What is the likelihood (uncertainty) of occurren ce? Uncertainty, L( U)
Risk = (A, C, U)
Risk and Quantitative Risk Risk and Quantitative Risk AnalysisAnalysis (QRA)(QRA)
2. What damage do they cause? Consequence, C
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3. What is the likelihood (uncertainty) of occurren ce? Uncertainty, L( U)
Quantitative Risk Analysis Model =(a, c, l(u), K)
Alternative 1 Alternative 2
- Design configuration 1- Redundancy allocation 1- Evacuation plan 1
- Design configuration 2- Redundancy allocation 2- Evacuation plan 2
Risk and Quantitative Risk Risk and Quantitative Risk AnalysisAnalysis (QRA)(QRA)
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RISK 1 RISK 2
C: How many fatalities C1?
L: What is the likelihood of having C1 fatalities or more?
C: How many fatalities C2?
L: What is the likelihood of having C2 fatalities or more?
A
SYSTEMRISK
MODEL“ λ is between 10 -3 and 10 -2 [h -1]”
KN
OW
LED
GE
K
(UNCERTAIN)
Quantitative Risk Quantitative Risk AnalysisAnalysis
tX
tX
…
valve 1
valve 2
valve N
…
t1
t2
tNtX
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“ λ is between 10 and 10 [h ]”
“ λ is quite small”
KN
OW
LED
GE
K
REPRESENTATIONOF UNCERTAINTY
MUNCERTAINTYPROPAGATION
(UNCERTAIN)RISK MEASURES
(a,c,u,M,K)
SYSTEMRISK
MODEL
…0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
1
2
3
4
5
6
7
8
9
probability density function
Er
t
“ λ is UNIFORM
KN
OW
LED
GE
K
valve 1
valve 2
valve N
fT(t, λ)
(PROBABILISTIC)
Probabilistic Risk AnalysisProbabilistic Risk Analysis
fz (Z)
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“ λ is UNIFORMbetween 10 -3 and 10 -2 [h -1]”
“ λ is less than 10 -2 [h -1] with probability 0.9”
KN
OW
LED
GE
K
PROBABILISTICREPRESENTATIONOF UNCERTAINTY
(M=P)
UNCERTAINTYPROPAGATION
(PROBABILISTIC)RISK MEASURES
(a,c,u,P,K)
Uncertainty
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Uncertainty is not in the things but in our head: uncertainty is lack of knowledge
J. Bernoulli
20
Imprecise character of measurement or
conclusion
Imprecise or vague character of picture perception
Unforeseen character of results issued from action
or evolution
Uncertainty
Characteristic of who is uncertain
Being of someone who does not know what to decide
Uncertainty (in the dictionary)Uncertainty (in the dictionary)
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or evolution
Impossibility for person to foresee or to know in
advance his behavior or events by which he will be
concerned
[TLFi : Trésor de la Langue Française Informatisé]
Perturbing state of person waiting for the uncertain
events
Accent on the subjectAccent on the object
Adapted from S. Farnoud and S. Tillement, IFIS Toulouse 2010
21
Uncertainty
From latin certus
from latin certitudo
Uncertainty (in the epistemology)Uncertainty (in the epistemology)
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From the latin verb cernere
« discern, decide »
from latin cerno : from common indo-european (s)ker :
cutcut, which pairs it with the ancient greek krino : shear
Adapted from S. Farnoud and S. Tillement, IFIS Toulouse 2010
22 Modern era airmoderne
– Socrate, Platon, Carnéade
– Sophism
Renaissance
Middle Ages
2000
500
1500
Incoherence of philosophies of Ghazali, necessity to prove the validity of reason, independent from
reason.
Descartes, Pascal, Kant
Laplace, Carnap, Shackle, Gödel
De Finetti, Knight, Zadeh, …
Uncertainty (in the history)Uncertainty (in the history)
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Prehistory
– The development of Homo sapiens in an uncertain environment: predator, war ....
Chimpanzees still live in this environment [Philippe De Wilde 2010].
– Evolution has selected the anatomy of the brain that is optimized to some degree to
cope with uncertainty[Philippe De Wilde 2010].
– Sophism
– Skepticism
– 500 before J.C. Empédocle d'Agrigente (father of rhetoric), Gorgias
– Mathematics were used to create confidence [Philippe De Wilde 2010].
– Logic provides reasoning rules to reduce uncertainty.
– Religion provides a narrative to create confidence [Philippe De Wilde 2010].
– Mythe was the first attempt to reduce uncertainty [Gérald Bronner 1997].
-1000
0
- 500
Antiquity
-3000
Adapted from S. Farnoud and S. Tillement, IFIS Toulouse 2010
UncertaintyUncertainty in QRAin QRA
» reducible uncertainty» property of the analyst» lack of knowledge or
aleatory uncertainty
» irreducible uncertainty» property of the system» random
epistemic uncertainty
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23
Adapted from G. Apostolakis, Workshop LA 2010 and M. Beer, Seminar Paris 2012
» lack of knowledge or perception» random
fluctuations / variability/ stochasticity
UncertaintyUncertainty in QRAin QRA
» reducible uncertainty» property of the analyst» lack of knowledge or
aleatory uncertainty
» irreducible uncertainty» property of the system» random
epistemic uncertainty
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24
Adapted from G. Apostolakis, Workshop LA 2010 and M. Beer, Seminar Paris 2012
» lack of knowledge or perception» random
fluctuations / variability/ stochasticity
�Epistemic uncertainties are further categorized as being due to parameter values, modelassumptions, and incomplete analyses (“Known unknowns” – initiating events, failure modes or mechanisms are known but not included in the model; “Unknown unknowns” – phenomena or failure mechanisms are unknown)
UncertaintyUncertainty in QRAin QRA
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25
failure mechanisms are unknown)
Adapted from G. Apostolakis, Workshop LA 2010
p1
p
{S1, lS1, c1}
{S2, lS2, c2}
{S3, lS3, c3}
{S4, lS4, c4}
1 ‒ p1
1 – p2
p2
1 – p2ALEATORYALEATORY
Initiator Event (IE)
Event 1: Shut-down valve
Event 2: Emergency andevacuation procedure
(aleatory and epistemic) Uncertainty in QRA(aleatory and epistemic) Uncertainty in QRA
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p2{S4, lS4, c4}
EPISTEMICEPISTEMIC
Aleatory : variability , randomness (in occurrence of the events in thescenarios)Epistemic : lack of knowledge/information ( on the values of the parameters of the probability and consequence models)
p1
p
{S1, lS1, c1}
{S2, lS2, c2}
{S3, lS3, c3}
{S4, lS4, c4}
1 ‒ p1
1 – p2
p2
1 – p2ALEATORYALEATORY
Initiator Event (IE)
Event 1: Shut-down valve
Event 2: Emergency andevacuation procedure
((aleatoryaleatory and and epistemicepistemic) ) UncertaintyUncertainty in PRAin PRA
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p2{S4, lS4, c4}
EPISTEMICEPISTEMIC
Aleatory : STOCHASTIC MODELS
Epistemic : PROBABILITIES
Probability used for representing both randomness and incomplete
information/partial knowledge
28
Sufficiently informative (statistical) data : P=limiting relative frequency (chance); in practice, estimated value P*
tX
tX
tX
…
valve 1
valve 2
valve N
…
t1
t2
tN
Hardware failure occurrence times: Event 1 = failure of shut-down valve
Probablistic representation of Probablistic representation of epistemic uncertainty in PRAepistemic uncertainty in PRA
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Realizations of a random variable � Probability Density Function
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
1
2
3
4
5
6
7
8
9
probability density function
E
t
f*T(t, λ*)
P(A/K)
�Betting interpretation:
� The probability of the event A, P(A), equals the amount of money that the assigner would be willing to bet if he/she would receive a single unit of payment in the case that the
event A were to occur, and nothing otherwise.
Probablistic representation of Probablistic representation of epistemic uncertainty in PRAepistemic uncertainty in PRA
Scarce (possibly qualitative) data : P(A/K)=Subjective probability (knowledge-based probability)
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event A were to occur, and nothing otherwise.
�Comparison with a standard
� The assessor compares his/her uncertainty about the occurrence of the event A with e.g. drawing a favourable ball from an urn that contains P(A) · 100 % favourable
balls (Lindley, 2000).
Adapted from T. Aven, Workshop LA 2010
PRA
EpistemicEpistemic UncertaintyUncertainty
lK = (Statistical) Data
M = Frequentist Probability
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30
K = Beliefs
M = Subjective Probability
c
Worries
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In risk analysis assumptions are made that may be convenient but not really justified from the available information and knowledge:
� Distributions are stationary (unchanging in time)
� Variables, experts are independent of one another
� Uniform distributions model “complete” uncertainty
Worries: known unknownsWorries: known unknowns
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� Uniform distributions model “complete” uncertainty
Adapted from S. Ferson, Workshop LA 2010
Uniform Uniform Uniform Uniform
Worries: known unknownsWorries: known unknowns
Instability
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Prob
abil
ityde
nsit
y
Adapted from S. Ferson, Workshop LA 2010
UniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniform
The more (uncertain)
Prob
abil
ity d
ensi
ty
Worries: known unknownsWorries: known unknowns
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inputs, the more certainty in the output: Where does this surety/confidence come from?What justifies it?
Prob
abil
ity d
ensi
ty
Adapted from S. Ferson, Workshop LA 2010
Worries: unknown unknownsWorries: unknown unknowns
Elicited probabilities are impreciseuncertainties ”hidden” in K
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P(health problems | K) =0.01
SurprisesAdapted from T. Aven, Workshop LA 2010
Frameworks of uncertainty/information/knowledge
representation
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Uncertainty representationUncertainty representation
Tools for representing uncertainty
– Probability distributions : good for expressing
variability, but information-demanding and thus becomes paradoxical when information is incomplete (choice of a
single distribution not satisfactory)
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Adapted from D. Dubois, Workshop LA 2010
– Sets (numerical intervals): good for representing
incomplete information, but a very crude representation of uncertainty
Find representations that allow for both aspects ofuncertainty
Uncertainty representationUncertainty representation
Representations that allow for both aspects of uncertainty
� Frameworks capable of distinguishing between uncertainty due to variability from uncertainty due to lack of knowledge or
missing information� More informative than the sets of pure interval (or classical)
logic
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Adapted from D. Dubois, Workshop LA 2010
logic� Less demanding than single probability distributions� Explicitly allowing for missing information
Blend intervals and probability
Uncertainty representationUncertainty representation
Blending intervals and probability
� Sets of probabilities: imprecise probability theory ([P*(A), P*(A)])
� Random sets: Dempster-Shafer Theory ([Bel(A),Pl(A)])
� Fuzzy sets: numerical possibility theory ([Π(A,N(A)])
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Adapted from D. Dubois, Workshop LA 2010
Instead of a single degree of probability, each event A has a degree of belief (certainty) and a
degree of plausibility which “bound all probabilities”
Uncertainty representationUncertainty representation
Practical ways for representing probability sets
• Fuzzy (numerical) intervals (possibility theory)• Probability intervals (bounding the probabilities of
events)• Probability boxes (pairs of pdfs or cdfs)
• Generalized p-boxes (pairs of co-monotonic possibility
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Adapted from D. Dubois, Workshop LA 2010
• Generalized p-boxes (pairs of co-monotonic possibility distributions)
• Clouds (pairs of possibility distributions)
(Some are special random sets, others not)
Example: P-box
1
Interval bounds on a cdf
Uncertainty representationUncertainty representation
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01.0 2.0 3.00.0 X
cdf
Adapted from S. Ferson, Workshop LA 2010
Probability Bounds Framework: what it does
�Bridges qualitative information and quantitative data
�Distinguishes variability and incomplete knowledge
�When data are abundant, it is equivalent to probability theory
�When data are sparse, it yields both conservative and optimistic results
Uncertainty representationUncertainty representation
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optimistic results
� It enables representing the continuum of situations between these extremes
�Accounts for uncertainties of both kinds about
�Parameters
�Distribution shapes
�Dependencies among variables
�Structure of the model
Adapted from S. Ferson, Workshop LA 2010
EpistemicEpistemic UncertaintyUncertainty
lK = (Statistical) Data
M = Frequentist Probability
Bounded Probability Risk Analysis
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M = Imprecise ProbabilityRandom Sets (D-S Theory)Possibility theory
K = Beliefs
c
PART II: The risk of uncertainty
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Decision maker dreams…Decision maker dreams…
Probability Bounds: how to use the results
�When uncertainty makes no difference
bounding gives confidence in the reliability of the decision
Offshore
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Adapted from S. Ferson, Workshop LA 2010
cdf
Offshore plant 2
Offshore plant 1
Probability Bounds: how to use the results
�When uncertainty swamps the decision
use results to identify issues to further investigate
…and nightmares…and nightmares
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Adapted from S. Ferson, Workshop LA 2010
cdf
Offshore plant 1
Offshore plant 2
Can uncertainty swamp the decision?
�Yes, if large
�Too wide bounds: need to get more information and knowledge in the analysis
…and nightmares…and nightmares
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� If not possible … do not force unjustifiable behavior into the analysis
results should not mislead decisions
Adapted from S. Ferson, Workshop LA 2010
PART III: “Things I Know”
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THINGS
Things I know: InformationThings I know: Information--based boundsbased bounds
cdf
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Do not add knowledge that is not included in the available
information
cdf
ThingsThings I know: (expert) I know: (expert) knowledgeknowledge--basedbased boundsbounds
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Do add expert knowledge when reliable
cdf
ThingsThings I know: (expert) I know: (expert) knowledgeknowledge--basedbased boundsbounds
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Do add expert knowledge when reliable
PART IV: Jingles
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Concluding remarks
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Probability Bounds Framework
�Combines interval and probability methods, generalizing them: analyst can relax (towards interval analysis) or tighten (towards probability analysis) his/her assumptions, depending on what the information and knowledge on the problem justifies
Concluding remarksConcluding remarks
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information and knowledge on the problem justifies
�Allows distinguishing variability (modeled as randomness, by methods of probability theory) from imprecise information/knowledge (modeled as ignorance, by bounding methods such as interval analysis)
Adapted from S. Ferson, Workshop LA 2010
Theoretical issues
� Operational definitions (betting-like, standard comparison-like) of uncertainty representation, according to given behavioral rationality
�Dependence and independence (objective and epistemic) of information and (expert)
Concluding remarksConcluding remarks
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epistemic) of information and (expert) knowledge sources
� Information and knowkedge fusion
�Mathematical operations for uncertainty calculus (e.g. Dempster rule of combination)
Adapted from D. Dubois, Workshop LA 2010
Practical issues
�Constructing bounding (imprecise) probabilities, from data (statistics with interval data) from experts (elicitation of upper/lower bounds for faithful representaton of incomplete information/knowledge)
�Uncertainty propagation (computational
ConcludingConcluding remarksremarks
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�Uncertainty propagation (computational challenges of blending Monte Carlo simulation with interval mathematics)
�Representation of results with meaningful summary measures
�Updating with additional evidence
�Accounting for dependeces in information sources, when fusing them
Adapted from D. Dubois, Workshop LA 2010
Updating…
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cum
ulat
ive
prob
abili
ty, F
P (
B1)
Basic Event B1 (Case B)
0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pos
sibi
lity
valu
e, πP
(B
2)
Basic Event B2 (Case B)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pos
sibi
lity
valu
e, πP
(B
3)
Basic Event B3 (Case B)
0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability of Basic Event B4, P(B4)
Cum
ulat
ive
prob
abili
ty, F
P (
B4)
Basic Event B4 (Case B)
Upper CDF
Lower CDF
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pos
sibi
lity
valu
e, πP
(B
5)
Basic Event B5 (Case B)
0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability of Basic Event B6, P(B
6)
Cum
ulat
ive
prob
abili
ty, F
P (
B6)
Basic Event B6 (Case B)
Epistemically-uncertain Basic Event (BE) probabilities
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0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140
Probability of Basic Event B1, P(B1)
Probability of Basic Event B2, P(B2)
0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140
0.1
Probability of Basic Event B3, P(B3)
Probability of Basic Event B4, P(B4)
0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140
0.1
Probability of Basic Event B5, P(B5)
6 6
P(B5)
Pos
sibi
lity
valu
e3 additional tests: 2 failures, 1 success
priorposterior
1
Dependences…
0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability of Basic Event B1, P(B1)
Cum
ulat
ive
prob
abili
ty, F
P (
B1)
Basic Event B1 (Case B)
0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability of Basic Event B2, P(B2)
Pos
sibi
lity
valu
e, πP
(B
2)
Basic Event B2 (Case B)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pos
sibi
lity
valu
e, πP
(B
3)
Basic Event B3 (Case B)
0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability of Basic Event B4, P(B4)
Cum
ulat
ive
prob
abili
ty, F
P (
B4)
Basic Event B4 (Case B)
Upper CDFLower CDF
0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pos
sibi
lity
valu
e, πP
(B
5)
Basic Event B5 (Case B)
0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability of Basic Event B6, P(B
6)
Cu
mu
lativ
e p
roba
bilit
y, F
P (
B6)
Basic Event B6 (Case B)
“ Epistemic” dependence between BE probabilities
Epistemically-uncertain Basic Event (BE) probabilities
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0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140
Probability of Basic Event B3, P(B3)
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014Probability of Basic Event B5, P(B5)
“ Objective” dependence between BEs
10-4
10-3
10-2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
P(X)
Cum
ulat
ive
prob
abili
ty
10-4
10-3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
P(X)
Cum
ulat
ive
prob
abili
ty
…and nightmares…and nightmares
PERFECT STORMS
the killing in Norway on 22 July 2011, when a man placed a car-bomb outside the government
office and massacred a number of people on the island of Utøya
outside Oslo.
the eruption of the Icelandic volcano, which
paralyzed the air traffic over the Atlantic and western Europe
for a while in 2010
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the Fukushima Daiichi nuclear disaster in Japan in March 2011
the financial crisis that started in 2008
the failure of the BP DeepwaterHorizon platform
9/11 attacks on the US
…and …and nightmaresnightmares
BLACK SWANS
the killing in Norway on 22 July 2011, when a man placed a car-bomb outside the government
office and massacred a number of people on the island of Utøya
outside Oslo.
the eruption of the Icelandic volcano, which
paralyzed the air traffic over the Atlantic and western Europe
for a while in 2010
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Introduction to exploration activities 60Agip KCO
Piping and long distance pipelines60
the Fukushima Daiichi nuclear disaster in Japan in March 2011
the financial crisis that started in 2008
the failure of the BP DeepwaterHorizon platform
9/11 attacks on the United States
The Decision Making process
� QRA results are one input to a subjective decision-making process
� Analytical results are debated and stakeholder values are included, within a deliberative process of decision-making
� Coherently with safety concepts such as defense-in-depth, multiple barriers and design basis accidents,
Concluding remarksConcluding remarks
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depth, multiple barriers and design basis accidents, conservatism in the decisions is added where appropriate (to protect from the known and unknown unknowns)
Adapted from G. Apostolakis, Workshop LA 2010 and ANS DC 2012
Decision-Making ProcessUse a disciplined process to achieve the risk manag ement goal:
Identify issueIdentify Options
Analyze
DeliberateImplementDecision
Monitor
The one million euros question
€ € € € € €
“OK, these approaches are interesting, but does all of this actually make any practical difference in
real-world decisions?”
€ € € € € €
Concluding remarksConcluding remarks
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(€ Are probability bounds/imprecise probabilities a more proper starting point than pure probability theory for robust and confident
decision making, faithful to information and knowledge?€)
(€ How to do it in practice? information before knowledge for faithfulness to information and unbiased exploitation of knowledge–bounds “as large as justified by information” + expert knowledge (without forcing) to see the effects in a “sensitivity analysis- like
process?€)
The one billion euros questionConcluding remarksConcluding remarks
lK = (Statistical) Data
M = Frequentist Probability
Signals
Precursors
Near
PERFECT STORMS
€ € € € € € € € €
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c
M = ?
K = Beliefs
Signals Near misses
BLACK SWANS
Design Basis Accidents
Defense in depth
EpistemicEpistemic UncertaintyUncertainty
lK = (Statistical) Data
M = Frequentist Probability
Signals
Precursors
Near
PERFECT STORMS
The one billion euros question
€ € € € € € € € €
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c
M = ?
K = Beliefs
Signals Near misses
BLACK SWANS
Design Basis Accidents
Defense in depth
Final Final remarksremarks
l
Precursors
Near
PERFECT STORMS
There are known knowns
But there are also unknownunknowns – the ones we don't
One should expect that the expectedcan be prevented, but theunexpected should have beenexpected
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c
SignalsNear
misses
BLACK SWANSWe also know there are knownunknowns; that is to say we knowthere are some things we do notknow.
unknowns – the ones we don'tknow we don't know.
Knowing ignorance is strength,ignoring knowledge is sickness
Knowing ignorance is strength, ignoring knowledge is sickness
Final Final remarksremarks
There are known knowns; there are things we know we know.We also know there are known unknowns; that is to say weknow there are some things we do not know. But there arealso unknown unknowns – the ones we don't know we don'tknow.
One should expect that the expected can be prevented, butthe unexpected should have been expected
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Knowing ignorance is strength, ignoring knowledge is sickness
PRA is a mature methodology, but there isstill quite some work to be done in order torender our systems safer.
BACK UP SLIDESBACK UP SLIDES
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Lao Tsu, 600 BC
RISK MODEL (based on knowledge K)
Model inputVariables of interest
Measure of Uncertainty
Measure of uncertainty
Uncertainty propagation
Quantitative Risk AnalysisQuantitative Risk Analysis
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G(x)Model input
Xof interest
Z
UncertaintyM
uncertaintyM
Sensitivity analysis and importance ranking
Adapted from T. Aven, Workshop LA 2010
�Model = representation of reality uncertainty
�Risk = (A,C,U)�Risk description=(A,C,U,M,K)
Quantitative Risk AnalysisQuantitative Risk Analysis
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�Risk description=(A,C,U,M,K)�Model error Z-G(X)≠0
Adapted from T. Aven, Workshop LA 2010
�The mathematical theories for characterizing situations under uncertainty have been
�Set theory
�Probability Theory
�Since the mid 1960s, a number of generalizations of these classical theories became available for formalizing the various classical set theory and
Uncertainty in theoryUncertainty in theory
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72
formalizing the various classical set theory and probability theory
�The introduction of a number of alternative representations of uncertainty has sparked a lively discussion on their characteristics and usefulness
Adapted from G. Apostolakis, Workshop LA 2010
In practice: uncertainty and imprecision
separate treatment of uncertainty and imprecision
•
generalized models combining probabilistics and set theory
information defies a pure probabilistic modeling
» interval probabilities» p-boxes» random sets
Probability sets
••
Uncertainty representationUncertainty representation
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common basic feature:
set of plausible probabilistic models over a range of imprecision
» random sets» fuzzy random variables / fuzzy probabilities» evidence theory / Dempster-Shafer theory
bounds on probabilities for events of interest
(set of models which agree with the observations)
Adapted from M. Beer, Seminar Paris 2012
…and …and nightmaresnightmares
the killing in Norway on 22 July 2011, when a man placed a car-bomb outside the government
office and massacred a number of people on the island of Utøya
outside Oslo.
the eruption of the Icelandic volcano, which
paralyzed the air traffic over the Atlantic and western Europe
for a while in 2010
74Agip KCO
Introduction to exploration activities 74Agip KCO
Piping and long distance pipelines74
the Fukushima Daiichi nuclear disaster in Japan in March 2011
the financial crisis that started in 2008
the failure of the BP DeepwaterHorizon platform
9/11 attacks on the United States