| LEC # | TOPICS | KEY DATES |
|---|---|---|
| I. The Logic of Certainty | ||
| 1-2 |
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 | ||
| 3-4 |
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 | ||
| 5-6 |
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 | ||
| 7-8 |
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 | ||
| 9-10 |
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 | ||
| 11-12 |
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 | ||
| 13-14 |
VII.1 Student's t-distribution VII.2 Chi-Squared 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 Stress-Strength Interference Theory IX.4 Modeling of Loads and Strength IX.5 Reliability-Based 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 | ||
| 19-23 |
XII.1 Risk Curves and Accident Scenario Identification XII.2 Event-Tree and Fault-Tree Analysis XII.3 Unavailability Theory of Repairable and Periodically Tested Systems XII.4 Dependent (Common-Cause) 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 | ||