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.
| LEC # | TOPICS | READINGS |
|---|---|---|
| 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 |
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 |
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.