I. The Logic of Certainty

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

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

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

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

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

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

VII.1 Student’s t-distribution

VII.2 Chi-Squared Distribution

VII.3 Hypothesis Testing

Problem set 5 due
VIII. Elements of Statistics

VIII.1 Random Samples

VIII.2 Method of Moments

VIII.3 Method of Maximum Likelihood

VIII.4 Probability Plotting

IX. Applications to Reliability

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

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

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

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

Course Info

As Taught In
Fall 2005
Learning Resource Types
Problem Sets with Solutions
Exams with Solutions
Lecture Notes