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.
|I. The Logic of Certainty|
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.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|
III.1 Discrete and Continuous Random Variables
III.2 Cumulative Distribution Functions
III.3 Probability Mass and Density Functions
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.
|IV. Useful Probability Distributions|
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|
V.1 Joint and Conditional Distribution Functions
V.3 The Multivariate Normal and Lognormal Distributions
|Ang and Tang: Section 3.3.
Rausand and Hoyland: Chapter 7.
|VI. Functions of Random Variables|
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|
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|
VIII.1 Random Samples
VIII.2 Method of Moments
VIII.3 Method of Maximum Likelihood
VIII.4 Probability Plotting
|IX. Applications to Reliability|
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|
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.
|XI. Monte Carlo Simulation|
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|
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.|
In addition to the course textbooks, the following books may be useful.