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Reliability of a network is of paramount importance, and the theory of reliability extends beyond just networks. Much of the mathematics was developed in industrial and systems engineering and can be ported over to the study of networks nicely. In this series, we’ll begin preparation for advanced networking-specific topics in reliability by covering several aspects of systems reliability engineering and the mathematics used to analyze coherent systems.

The webinar will cover these topics:

- Coherent Systems Analysis;
- Reliability Basics;
- Coherent Systems Analysis 2: Reliability Functions;
- Advanced Reliability Topics.

Each topic will be presented in a separate live session.

## Contents

### Coherent Systems Analysis

We’ll discuss how systems engineers set up a model to study coherent systems, the difference between a reliability graph (block diagram) and a physical layout, structure functions, structure importance, and cut- /path- sets, and how to use these in system design. You might want to watch the graph theory and network connectivity webinar first.

### Reliability Basics

This section will start with basic probability ideas that appear in literature and discussions of reliability. We’ll cover survival functions and their various representations, failure rates, time to failure, mean time to failure, mean residual life, mean time between failure, and some common probability distributions that appear in reliability analysis.

### Coherent Systems Analysis 2: Reliability Functions

After covering the basics of coherent system analysis and reliability, we're ready to combine aspects of the two to discuss system reliability functions, reliability importance, the relationship between system reliability and structure functions, various models (k of n, series, parallel), decomposition of complex systems, inclusion/exclusion principles, and fault tree analysis

### Advanced Reliability Topics

The previous three sections laid the foundation to get more specific in terms of applications to networking. Your networks are repairable systems, and studying these is a bit more advanced. We’ll foray into some basic stochastic processes called repair/renewal processes, the reliability of maintained systems, and mathematical notions of calculating availability.

## The Author

**Dr. Rachel Traylor** is a professional private-sector mathematician and the cofounder of the Math Citadel, a research and consulting firm specializing in mathematical consulting. She received her PhD in mathematics from the University of Texas at Arlington, a MS Statistics and BS Applied Mathematics from Georgia Tech. Her research interests include probability theory, reliability, and queuing theory; in particular, she’s been very interested in sequences of dependent random variables. She’s a former senior research scientist for Dell EMC, former university lecturer in mathematics and statistics (Foothill College, University of Texas at Arlington, Georgia Tech), and former DBA/Quality Analyst at Lockheed Martin. She has 6 pending patents and 9 academic publications in the fields of probability and reliability theory.

More about Rachel…