Probability And Its Applications To Reliability, Quality Control, And Risk Assessment

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. 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 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.