Readings
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. HS., 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.
Course readings.

LEC #

TOPICS

READINGS

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

Ang and Tang: Chapters 1 and 2.
Rausand and Hoyland: Sections 3.93.11.

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

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

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


V. Multivariate Distributions

910

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

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

Ang and Tang: Chapter 4.

VII. Statistical Methods

1314

VII.1 Student's tdistribution
VII.2 ChiSquared 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 StressStrength Interference Theory
IX.4 Modeling of Loads and Strength
IX.5 ReliabilityBased 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): 121132.
Vatn, J., P. Hokstad, and L. Bodsberg. "An overall model for maintenance optimization." Reliability Engineering and System Safety 51 (1996): 241257.

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): 23102314.


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

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

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: McGrawHill, 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: McGrawHill, 1980. ISBN: 9780070331785.
Papoulis, Athanasios. Probability and Statistics. Englewood Cliffs, NJ: Prentice Hall, 1990. ISBN: 9780137116980.
Rao, Singiresu S. ReliabilityBased Design. New York, NY: McGrawHill, 1992. ISBN: 9780070511927.
