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Advanced Course on Key Elements of Risk Quantification and PSA
• • • • • Next Event:  NINE Headquarters, LUCCA (Italy), 27 September - 01 October 2021
• Early Registration deadline: 06 August, 2021

### MMARS - Advanced Course on Key Elements of Risk Quantification and PSA

Day 1
•    Boolean Algebra, Probability Theory, Random Variables
o    Basic rules and properties of Boolean algebra. Laws of absorption and idempotency
and why are they important for PSA. De Morgan’s theorem.
Definition of probability. Probability of logical sum of mutually exclusive events.
Probability of logical sum of any events. Probabilities of logical product and logical
sum of independent events. Conditional probability and event sequences.
(Why are these things important in PSA or quantitative risk assessment in general?)
Random variables, distinctive and continuous. Probability distributions. Cumulative
functions and density functions. How we determine or “judge out” a probability distribution.
•    Definition of “Risk” for an Engineer and Its Role in Considerations of Safety
o    “Risk curve” in the probability-consequence space. Frequency (probability)
of exceedance versus frequency (probability) of occurrence. Theoretical definition of risk.
(Why is risk in the PSA guidebooks presented by “complementary cumulative distribution
function”?) Presentation of “risk curve” in practice: risk matrix. Simplification by means of
representatives or substitutes for consequences (e.g. “reactor core damage”, “large (early)
releases"…). Margin assessment and risk assessment. What is the real meaning of
“combined" use of deterministic and probabilistic safety analyses”?

Day 2
•    Definition of “Risk” for an Engineer and Its Role in Considerations of Safety (continued)
o    Risk modeling: logic risk equation and quantitative (numeric) risk equation. Methods and
approaches. FMEA, HAZOP and similar techniques for risk evaluation. Event trees (ETs)
and fault trees as tools to develop the risk equation. Elements of ETs and FTs. “Basic events”.
Structure function.
•    Basics of Reliability Engineering As Used in PSA
o    Basic differential reliability equations. “Repair-to-failure” cycle. “Failure-to-repair” cycle.
Combined cycle. Basic terms: failure (repair) density function, failure (repair) rate,
and others. (What does it really mean “reliability” and what really is “availability”?)
Types of equipment (“components”) modeled in PSA. Repairable versus non-repairable.
Standby versus normally operating. Failure-on demand versus time-related failure.
Reliability models for “basic events” representing failures of systems, structures and
components (SSC) in PSA model. (Failure during mission time. Standby, periodically tested
component. Frequency-type basic events associated with initiators.) Parameters required
to quantify the reliability models (basic events) in PSA.

Day 3
•    Common Cause Failure (CCF) Modeling in PSA
o    Independent versus dependent failure events. Unconditional versus conditional failure
probability. Importance of CCF modeling in PSA model fault trees. CCF group. Basic CCF
failure probability model. Beta Factor Model. Multiple Greek Letters (MGL) Model. Alpha
Factors Model. Estimators for MGL and alpha factors. Availability of CCF data. Mapping
(“specialization”) of CCF events from source to target systems or plants. MGL vs. Alpha
Factors: which one is “better” to use in a PSA?
•    Data Analysis in PSA
o    Point estimate. Likelihood function. Maximum likelihood estimator (MLE). Estimate with
quantitative characterization of uncertainty. Two basic concepts: confidence intervals and
uncertainty distributions. Bayesian inference based on prior (“generic”) knowledge and
observed evidence (“plant-specific”. Basic terms: Prior distribution. Likelihood function.
Posterior distribution. Bayesian inference as applied to the two most basic reliability
parameters in a PSA: probability of failure on demand and failure rate (Prior distributions
usually found in the “generic” databases; Establishing of likelihood functions; Posterior
distributions: numerical integration or analytical calculation.) Estimating or assessing
other parameters for PSA model: Initiator frequencies. Unavailability due to test or
maintenance (TM). Others. How to estimate failure rate or failure probability in the case
of zero failures? How to establish uncertainty distribution for other types of parameters?

Day 4
•    Human Reliability Analysis (HRA)
o    Main types of human errors: pre-initiator errors, initiator-inducing errors and post-initiator
errors. Identification of human interfaces, characterization of human failure events (HFE),
definition of success criteria and other relevant shaping factors. Overview of techniques
for the assessment of human error probabilities (HEP) which are nowadays used in PSAs,
including: THERP, ASEP, SLIM, ATHEANA, SPAR-H and others. Dependency among human
failure events. Unconditional and conditional HEPs. Incorporation of HFEs into the PSA model.
Screening. Quantification.
•    Risk Quantification
o    “Risk” as a frequency (probability, likelihood) of the top event considered by the PSA.
What is a “minimal cutset”? PSA-model integration principles: “master FT” versus
combining system-level MCSs. Quantification of top-event based on the generated “list” of
MCSs. (“Inclusion-exclusion principle” and its approximations. What is “Mincut Upper Bound”
(MCUB) approximation?) Issues with “success events”. Propagation of parameter uncertainty.
Moment propagation. “Monte Carlo” sampling. Uncertainty distribution for top event
probability (frequency). Mean of the distribution versus point estimate.

Day 5
•    Special Topics 1: Probability of Phenomena and Other Probabilities Needed for PSA and
Quantitative Risk Assessments
o    Concept of “Accident Progression Event Tree” (APET) or event tree for phenomena
and how it compares to event trees for safety functions.
Structural failure probability. Consideration of stress versus strength (load versus capacity).
Convolution of stress and strength distributions. Other similar concepts. Time required
versus time needed. Probability of recovering power or other supporting functions or
systems (“recovery probability”). Containment fragility. Establishing probability distribution
based on the results of deterministic analyses or some other concepts.
•    Special Topics 2: Quantification of Risk from External Hazards with Focus on Seismic Events
o    Characterization of seismic hazard for seismic PSA. Seismic hazard frequency curve.
Seismic fragility curves. Convolution of seismic hazard with seismic fragility. Quantitative
screening of SSCs based on low seismic risk. Seismically-induced failures, random failures
and their combinations. Seismic risk quantification.