Students are assigned readings from the textbooks for each class lecture topic, as listed in the following table. Additional reference books are also listed after the table.

## Textbooks

Ang, A. H-S., and W. H. Tang. Probability Concepts in Engineering Planning and Design, vol. 1, Basic Principles. New York, NY: John Wiley & Sons, 1975. ISBN: 9780471032007.

Rausand, M., and A. Hoyland. System Reliability Theory: Models, Statistical Methods, and Applications. 2nd ed. New York, NY: John Wiley & Sons, 2003. ISBN: 9780471471332.

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

Ang and Tang: Chapters 1 and 2.

Rausand and Hoyland: Sections 3.9-3.11.

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

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

Ang and Tang: Sections 3.1 and 3.2.

Rausand and Hoyland: Chapters 2, 4 and 6.

Henley, E. J., and H. Kumamoto. "Risk Study Comparison." Table 1.4 in Probabilistic Risk Assessment. Piscataway, NJ: IEEE Press, 1991, pp. I.6. ISBN: 9780879422905.

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

V. Multivariate Distributions
9-10

V.1 Joint and Conditional Distribution Functions

V.2 Moments

V.3 The Multivariate Normal and Lognormal Distributions

Ang and Tang: Section 3.3.

Rausand and Hoyland: Chapter 7.

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

Ang and Tang: Chapter 4.
VII. Statistical Methods
13-14

VII.1 Student's t-distribution

VII.2 Chi-Squared Distribution

VII.3 Hypothesis Testing

Ang and Tang: Chapters 5 and 6.

Rausand and Hoyland: Chapters 11 and 14.

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

Ang and Tang: Chapter 9.

Rausand and Hoyland: Chapters 8 and 9.

Rausand, Marvin. "Reliability centered maintenance." Reliability Engineering and System Safety 60 (1998): 121-132.

Vatn, J., P. Hokstad, and L. Bodsberg. "An overall model for maintenance optimization." Reliability Engineering and System Safety 51 (1996): 241-257.

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

Ang and Tang: Chapter 8.

Rausand and Hoyland: Chapter 13.

Huelsenbeck, J. P., et al. "Bayesian Inference of Phylogeny and Its Impact on Evolutionary Biology." Science 294, no. 5550 (December 14, 2001): 2310-2314.

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

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

Rausand and Hoyland: Chapters 5 and 10.
Final Exam

## Reference Books

In addition to the course textbooks, the following books may be useful.

Benjamin, Jack R., and C. Allin Cornell. Probability, Statistics, and Decision for Civil Engineers. 2nd ed. New York, NY: McGraw-Hill, 1963. ISBN: 9780070045583.

Center for Chemical Process Safety. Guidelines for Chemical Process Quantitative Risk Analysis. New York, NY: The American Institute of Chemical Engineers, 1989. ISBN: 9780816904020 .

DelMar, Donald, and George W. Sheldon. Introduction to Quality Control. St. Paul, MN: West Publishing Co., 1988. ISBN: 9780314684592.

Henley, Ernest J., and Hiromitsu Kumamoto. Probabilistic Risk Assessment: Reliability Engineering, Design, and Analysis. New York, NY: IEEE Press, 1991. ISBN: 9780879422905.

Juran, Joseph M., and Frank M. Gryna. Quality Planning and Analysis: From Product Development Through Use. 2nd ed. New York, NY: McGraw-Hill, 1980. ISBN: 9780070331785.

Papoulis, Athanasios. Probability and Statistics. Englewood Cliffs, NJ: Prentice Hall, 1990. ISBN: 9780137116980.

Rao, Singiresu S. Reliability-Based Design. New York, NY: McGraw-Hill, 1992. ISBN: 9780070511927.