Teaching PRA and conducting
PRA research at universities
George Apostolakis
Head, Nuclear Risk Research Center
apostola@mit.edu
Presented at theSymposium on Risk Integrated Engineering
University of Tokyo
January 21, 201911

PRA Methodology•What universities can teach
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ProbabilityStatistics
PRA structure and models
PRA calculations
Risk management process and safety goals

What they cannot teachAccident sequence development

2

Probability and Statistics••••

U.S. nuclear and mechanical engineers do not, ingeneral, have a background in probability andstatistics
An introductory PRA course must cover theessentials of probability and statistics
Doing so limits the time for teaching PRA methods
Topics specific to PRA•

Bayesian methods
Aleatory and epistemic uncertainties
However, there is only one kind of uncertainty
Importance measure

Practitioners are uncomfortable defending their
judgment (as opposed to classical statistics)
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The Model of the “World”
 Deterministic, e.g., a mechanistic computercode Probabilistic (Aleatory) model,e.g., R(t/λ) = exp(- λt) Both deterministic and aleatory models of theworld have assumptions and parameters.
 How confident are we about the validity ofthese assumptions and the numerical valuesof the parameters?
2015

4

Epistemic Model• Uncertainties in assumptions are not handled
routinely. If necessary, sensitivity studies areperformed.
• Parameter uncertainties are reflected on appropriate
1000
epistemic distributions.
π(λ) 800600• For the failure rate:

400
2000.0005 0.001 0.0015 0.002 0.0025 0.003• π(λ)dλ = Pr(the failure rate has a value in dλ about λ)
2015

5λ

WASH-1400 Failure Rates

2015

6

Example of Bayesian updating ofepistemic distributions
Five components were tested for 100 hours
each and no failures were observed.
π ' (λ / E ) =L( E / λ )π (λ )∫ L( E / λ )π (λ )dλ

0.008
0.007

Posterior distribution

0.006
0.005
0.004

Probability

Prior distr.

0.003
0.002
0.001
0.000
1e-4

1e-3

1e-2λ20157

1e-1

Communication of Epistemic
Uncertainties

2015

8

Epistemic Correlation••

Consider two nominally identical isolation valves
They share the epistemic distribution of failure rate9Risk Curves
Propagating epistemic uncertainties through the PRA
models (usually via Monte Carlo simulation), we
produce the risk curves.

201510PRA Models••••••Event and fault trees
Human reliability
Reliability physics models
Common-cause failures
Examples from PRAs
External events

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PRA Methodological Research•
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Data specialization using Bayes theorem
Epistemic correlation of parameter distributions
Plant-to-plant variability
Fire methodology
Human Reliability Analysis
Uncertainties in phenomenological work
Model uncertainty
Safety goals
Risk management
Simulation methods
12Plant-to-Plant Variability•

Suppose the evidence from two plants is(1 fire in 8 years) and(0 fires in 6 years)•If we say that the evidence is (1 fire in 14 years), wewill be increasing the strength of the evidence
artificially resulting in a narrower distribution for thefire rate•

The evidence from the two plants must beprocessed separately so that the distribution will bebroader
2015

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Concluding Remarks•

Teaching a course in PRA is usually hampered by
the students’ lack of background in probability andstatistics•Most students have been exposed to classical(frequentist) statistics; they have difficulty
switching to Bayesian (subjectivist) statistics•A PRA course is necessarily limited to methodology•

Ideally, traditional engineering courses would
discuss uncertainties in their models.
201514