Reliability Theory: Networking through a Systems Analysis Lens

Overall rating: 4.93 Instructor: 4.82 Materials: 4.97 more …

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;
  • Special Topics in Reliability;
  • Monte Carlo Simulation.

Each topic will be presented in a separate live session.


This webinar is part of Networking Fundamentals roadmap and accessible with standard subscription

Access content


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.

Special Topics in Reliability

This webinar will continue the overview of concepts in reliability theory that are relevant to network engineers. We will look at different network failure criteria we can impose on a network, such as all-terminal, k-component, and others. Next, we’ll examine static vs. dynamic reliability, though the main focus of these two lectures will be on static reliability. We’ll again review determination of system reliability in the “brute force” ways using state enumeration and path/cut sets. Next, we’ll discuss different kinds of reliability importance measures and how to use them. Then we shall spend a bit of time discussing multistate network reliability, a useful but less commonly applied set of ideas. Finally, with the remaining time, we’ll work our way through lots of practical examples to cement these ideas.

The webinar is a very high-level overview of topics and is intended to provide an introductory exposure rather than provide a detailed roadmap of the use of each of these topics. Resources will be provided for more in-depth reading and study.

Monte Carlo Simulation

This webinar will hone in on one particular method of estimating the reliability of complex networks — Monte Carlo simulation. The necessary statistical background will be provided to understand what Monte Carlo simulation is and does in general, as well as pros, cons, and limitations. We’ll then turn to one particular method of estimating network reliability via Monte Carlo simulation, and, time permitting, the estimation of component importance measures discussed in the previous lecture.

The Author

Rachel TraylorRachel Traylor is a mathematician whose favorite coworkers are engineers. Her research interests span pure and applied mathematics, but mainly focus on probability theory and its applications to reliability and queueing. She’s invested in closing the disconnect between academic mathematics and the practical world of engineering. She’s held private-sector research positions at Dell EMC, done time as a database administrator for Lockheed Martin Aeronautics, and been an adjunct professor/lecturer at several colleges and universities across the US (Georgia Tech, the University of Texas at Arlington, Marquette University, and Foothill College).

More about Rachel…

Happy Campers

About the webinar

Valuable for the reason Rachel pointed out -- some vendors make reliability claims that when read critically are more or less senseless BS. Valuable because it helps pick through the claims.

Jim Warner
Accessible explanation of a tough but very useful subject. Looking forward to the next session!
I feel these webinars on fundamentals are great for all levels of engineer whether the material is new or as a refresher. I am very happy that these are being offered!
Wonderful webinar by Rachel Traylor!

The (mathematical) content is presented in a clear and approachable manner. I immediately saw how to apply it to actual network design problems.

I really hope for a follow-on webinar diving deeper into the material.
Erik Auerswald
I was a great pleasure to learn and think about the theoretic basement as day to day work is mostly based on best practices, trail and error, and lack of classical scientific methods. Thanks.
Andre Paul

About the materials

Practice is essential to learning most subjects. Have you considered putting together some examples specific to our subject matter and posting them after the webinar? I think this could help solidify the material and make us aware of any gaps we need to follow up on.
I would really appreciate more content of the same kind. I greatly enjoyed all the webinars by Rachel Traylor. :-)
Erik Auerswald