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

Calendar

LEC #	TOPICS	KEY DATES
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
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	Problem set 1 due
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
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	Problem set 2 due
V. Multivariate Distributions
9-10	V.1 Joint and Conditional Distribution Functions V.2 Moments V.3 The Multivariate Normal and Lognormal Distributions	Problem set 3 due
	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	Problem set 4 due
VII. Statistical Methods
13-14	VII.1 Student’s t-distribution VII.2 Chi-Squared Distribution VII.3 Hypothesis Testing	Problem set 5 due
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	Problem set 6 due
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
	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	Problem set 7 due
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	Problem set 8 due Problem set 9 due Problem set 10 due
	Final Exam