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Probability And Its Applications To Reliability, Quality Control, And Risk Assessment >> Content Detail



Study Materials



Readings

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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


Amazon logo 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.

Amazon logo 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 #TOPICSREADINGS
I. The Logic of Certainty
1-2I.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
3-4II.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
5-6III.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.

Amazon logo 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
7-8IV.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
9-10V.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
11-12VI.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
13-14VII.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
15VIII.1 Random Samples

VIII.2 Method of Moments

VIII.3 Method of Maximum Likelihood

VIII.4 Probability Plotting
IX. Applications to Reliability
16IX.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
17X.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
18XI.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
19-23XII.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.

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

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

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

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

Amazon logo 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.

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

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


 








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