| 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 |
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| 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 |
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| 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 |
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Exam 1 |
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| 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 |
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| 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 |
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|
Exam 2 |
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| 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 |
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Final Exam |
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