LEC #  TOPICS  KEY DATES 

I. The Logic of Certainty  
12 
I.1 Events and Boolean Operations I.2 Event Sequence Identification (Failure Modes and Effects Analysis; Hazard and Operability Analysis; Fault Tree Analysis; Event Tree Analysis) I.3 Coherent Structure Functions I.4 Minimal Cut (Path) Sets 

II. Probability  
34 
II.1 Definitions and Interpretations (Axiomatic; Subjectivistic; Frequentistic) II.2 Basic Rules II.3 Theorem of Total Probability II.4 Bayes’ Theorem 
Problem set 1 due 
III. Random Variables and Distribution Functions  
56 
III.1 Discrete and Continuous Random Variables III.2 Cumulative Distribution Functions III.3 Probability Mass and Density Functions III.4 Moments III.5 Failure Models and Reliability III.6 Failure Rates 

IV. Useful Probability Distributions  
78 
IV.1 Bernoulli Trials and the Binomial Distribution IV.2 The Poisson Distribution IV.3 The Exponential Distribution IV.4 The Normal and Lognormal Distributions IV.5 The Concept of Correlation 
Problem set 2 due 
V. Multivariate Distributions  
910 
V.1 Joint and Conditional Distribution Functions V.2 Moments V.3 The Multivariate Normal and Lognormal Distributions 
Problem set 3 due 
Exam 1  
VI. Functions of Random Variables  
1112 
VI.1 Single Random Variable VI.2 Multiple Random Variables VI.3 Moments of Functions of Random Variables VI.4 Approximate Evaluation of the Mean and Variance of a Function VI.5 Analytical Results for the Normal and Lognormal Distributions 
Problem set 4 due 
VII. Statistical Methods  
1314 
VII.1 Student’s tdistribution VII.2 ChiSquared Distribution VII.3 Hypothesis Testing 
Problem set 5 due 
VIII. Elements of Statistics  
15 
VIII.1 Random Samples VIII.2 Method of Moments VIII.3 Method of Maximum Likelihood VIII.4 Probability Plotting 

IX. Applications to Reliability  
16 
IX.1 Simple Logical Configurations (Series; Parallel; Standby Redundancy) IX.2 Complex Systems IX.3 StressStrength Interference Theory IX.4 Modeling of Loads and Strength IX.5 ReliabilityBased Design IX.6 Elementary Markov Models 
Problem set 6 due 
X. Bayesian Statistics  
17 
X.1 Bayes’ Theorem and Inference X.2 Conjugate Families of Distributions X.3 Comparison with Frequentist Statistics X.4 Elicitation and Utilization of Expert Opinions 

Exam 2  
XI. Monte Carlo Simulation  
18 
XI.1 The Concept of Simulation XI.2 Generation of Random Numbers XI.3 Generation of Jointly Distributed Random Numbers XI.4 Latin Hypercube Sampling XI.5 Examples from Risk and Reliability Assessment 
Problem set 7 due 
XII. Probabilistic Risk Assessment of Complex Systems  
1923 
XII.1 Risk Curves and Accident Scenario Identification XII.2 EventTree and FaultTree Analysis XII.3 Unavailability Theory of Repairable and Periodically Tested Systems XII.4 Dependent (CommonCause) Failures XII.5 Human Reliability Models XII.6 Component Importance XII.7 Examples from Risk Assessments for Nuclear Reactors, Chemical Process Systems, and Waste Repositories 
Problem set 8 due Problem set 9 due Problem set 10 due 
Final Exam 
Calendar
Course Info
Instructor
Departments
As Taught In
Fall
2005
Level
Learning Resource Types
assignment_turned_in
Problem Sets with Solutions
grading
Exams with Solutions
notes
Lecture Notes