LEC #  TOPICS  LECTURE NOTES 

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 
RiskInformed Operational Decision Management (RIODM): 1. Risk, Event Trees and Fault Trees (PDF) Structure Functions (PDF) Valve Test Example (PDF) 
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 

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 
Basic Probabilistic Concepts (PDF) Convergence of Binomial and Normal Distributions for Large Numbers of Trials (PDF) Convergence of Binomial and Poisson Distributions in Limiting Case of n Large, p<<1 (PDF) Plane Crash Example (PDF) 
V. Multivariate Distributions  
910 
V.1 Joint and Conditional Distribution Functions V.2 Moments V.3 The Multivariate Normal and Lognormal Distributions 

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 

VII. Statistical Methods  
1314 
VII.1 Student’s tdistribution VII.2 ChiSquared Distribution VII.3 Hypothesis Testing 

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 
Failure, Repair, Maintenance (PDF) Reliability and Availability (PDF) Operational Availability (PDF) 
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 
Bayes’ Theorem (PDF) Bayesian Inference (PDF) 
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 

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 
PRA: An Historical Perspective (PDF  1.8 MB) (Courtesy of Prof. George Apostolakis. Used with permission.) PRA Structure and Results (PDF  1.1 MB) Uncertainty (PDF) Types of Uncertainty (PDF) Common Cause Failures 1 (PDF) Common Cause Failures 2 (PDF) PRA in Managing Operations (PDF) Engineered Safety Features (PDF) Containment (PDF) 
Lecture Notes
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Fall
2005
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Lecture Notes