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.
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 
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 
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.