WI4052 Risk Analysis
General Objectives
This course is given for students of Applied Mathematics and other Engineering
specializations. It requires at least a basic knowledge of probability and statistics.
Lectures are based on the book by Bedford and Cooke “Probabilistic Risk AnalysisFoundations and Methods”
The material covers risk modelling, life distributions, event trees, fault trees, reliability
diagrams, reliability data bases, dependence modelling, software reliability, decisionmaking under risk. Students must be able to justify the use of probabilistic methods in
risk analysis and apply techniques like fault trees, binary decision diagrams and Bayesian
belief nets. They should know how to estimate parameters of models for dependent
failure rates. Moreover they should be able to perform competing risks analysis for
simple reliability data sets. Students should understand basic techniques of
incorporating expert knowledge into risk models.
Specific Objectives
Introduction & Uncertainty
- An opening discussion on uncertainty, its role in risk analysis and its interpretations.
Formulates a clear, consistent and workable framework for working with
uncertainty and its description in terms of probability theory. This should help the
students to familiarize with the existing knowledge in the field of risk analysis and
its applications (see exit qualification (e.q.) 1).
Probability & Univariate random variables
- A review of basic knowledge about probabilities and statistics Multivariate random
variables & Stochastic processes
- Generalisation to more dimensions and sequences of random events/variables
occurring through time. Applications of homogeneous and non- homogenous
Poisson processes are presented and discussed. Challenges when dealing with real
applications are investigated (e.q.3).
Bayesian and classical estimations &Testing
- The general problem of statistical inference is presented and discussed. Given
observations about a random phenomenon one can make inference about the
probability distribution describing it. Hypothesis testing is touched upon. Should
improve the student’s ability to develop and analyze mathematical models for
problems from other disciplines and assess their usefulness (e.q.3).
Fault trees & Binary decision diagrams & Dependent failures & Bayesian belief nets
- This chapter covers knowledge about probabilistic graphical models with different
levels of complexity. Assumptions of each model are presented and generalised in
order to be incorporated in more complex ones. Applications are basically defining
the need for different models. Challenges and limitations are discussed. This helps
the student to understand the needs related to developing models and the process
should give insights in a methodological approach to modeling (e.q. 2,4).
Expert Judgment
- When data is sparse or unavailable, the quantification of models relies on expert
opinion. Structured methods for expert elicitation exist and are discussed. The
foundations are principles of a structured method are discussed (e.q. 5).
Reliability data bases
- Presents mathematical tools for defining and analysing populations from which
reliability data is to be gathered
Software reliability
- This last part discusses problems associated with judging the quality and
reliability of software.
The course as a whole tries to familiarise the student with the existing knowledge in the
field of risk analysis and its applications. Having a deep insight in the existing methods
and the needs of real life applications will help students in their ability to extend and
develop models (e.q. 1,2).
The connection of this subject with other disciplines is a constant throughout the course
since the risk models serve as tools in real life applications (e.q. 3).
Individual study and research into the existing literature is essential in dealing with the
problems raised during lectures and in the homeworks that they have to hand in every
other week. Team work is encouraged for solving the problems in the homeworks (e.q.
5,6).
Specificatietabel1 (ook wel ‘toetsmatrijs’) voor [Risk Analysis]
Een specificatietabel is een matrix met enerzijds te toetsen onderwerpen en anderzijds het cognitieve
niveau van de toetsvragen. De specificatietabel weerspiegelt de doelen van het vak.
Het gebruik van de specificatietabel is noodzakelijk om de toets zo representatief mogelijk te laten zijn. In
de cellen komt te staan hoeveel vragen gewijd gaan worden aan een bepaald onderwerp, gegeven een
bepaald niveau. Als u van mening bent dat een bepaald onderwerp erg belangrijk is, dan maakt u daar
relatief veel vragen over.
Bij gelijkblijvende leerdoelen en inhoud over de jaren heen mag de specificatietabel niet wijzigen. Dit
zorgt voor een onderlinge vergelijkbaarheid van de toetsen.
Vak: Risk Analysis
Vakcode: wi4052
Leerstof /
niveau
Feitenkennis
(leerstof kunnen
reproduceren)
Inzicht
(leerstof
kunnen
uitleggen in
eigen
woorden)
Toepassing
(leerstof kunnen
gebruiken in
vergelijkbare
situatie)
Probleem
oplossing
(analyseren
en oplossen
van nieuwe
vraag)
Totaal
Introduction &
Uncertainty
0
5
0
0
5
Probability
0 (they should
know these)
0
5
5
10
Univariate
random
variables
0(they should
know these)
0
5
5
10
Bayesian and
classical
estimations
&Testing
5
10
0
5
20
Fault trees
0
5
0
5
10
Binary decision
diagrams
0
5
0
0
5
Dependent
failures
0
5
0
5
10
1
Berkel, H.van: (1999) Zicht op toetsen, toetsconstructie in het hoger onderwijs. Van Gorcum, Assen p.7882.
Bayesian belief
nets
0
5
0
5
10
Expert
Judgment
0
5
0
5
10
Reliability data
bases
Software
reliability
0
5
0
0
5
0
5
0
0
5
Totaal
5
50
10
35
100
Invulinstructie: Keuze tussen cijfers en percentages:
Cijfers: U geeft 1 (beetje belangrijk), 2 (gemiddeld belangrijk) en 3 (zeer belangrijk) per onderwerp en
(eventueel meerdere) niveau. Bij een 3 stelt u drie keer zoveel vragen over dit onderwerp op het
aangegeven niveau.
Percentages: U verdeelt percentages over de onderwerpen en niveaus. Als u zich strikt houdt aan de
percentages kan het lastig worden deze om te zetten in (hele) aantallen vragen.