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

Lecture Notes

LEC #	TOPICS	LECTURE NOTES
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	Risk-Informed Operational Decision Management (RIODM): 1. Risk, Event Trees and Fault Trees (PDF) 2. Reliability and Availability (PDF) Structure Functions (PDF) Valve Test Example (PDF)
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
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	Basic Probabilistic Concepts (PDF) Convergence of Binomial and Normal Distributions for Large Numbers of Trials (PDF) Convergence of Binomial and Poisson Distributions in Limiting Case of n Large, p<<1 (PDF) Plane Crash Example (PDF)
V. Multivariate Distributions
9-10	V.1 Joint and Conditional Distribution Functions V.2 Moments V.3 The Multivariate Normal and Lognormal Distributions
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
VII. Statistical Methods
13-14	VII.1 Student’s t-distribution VII.2 Chi-Squared Distribution VII.3 Hypothesis Testing
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	Failure, Repair, Maintenance (PDF) Reliability and Availability (PDF) Operational Availability (PDF)
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	Bayes’ Theorem (PDF) Bayesian Inference (PDF)
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	PRA: An Historical Perspective (PDF - 1.8 MB) (Courtesy of Prof. George Apostolakis. Used with permission.) PRA Structure and Results (PDF - 1.1 MB) Uncertainty (PDF) Types of Uncertainty (PDF) Common Cause Failures 1 (PDF) Common Cause Failures 2 (PDF) PRA in Managing Operations (PDF) Engineered Safety Features (PDF) Containment (PDF)