University of Vermont

Structural Monitoring Diagnostics and Prognostics Lab

K-12 Education

CE 395-Reliability of Engineering Systems

3 credits

Safe and reliable performance of engineering systems under a variety of uncertain and extreme working conditions is of enormous importance to society, especially considering the consequences associated with such failures. Nuclear power plants, bridges, aircrafts, power grids and computer networks, just to name a few, are examples of such systems. Many of these systems operate interdependently, cut across disciplinary boundaries and require advanced computational methods to evaluate their performance. As engineers we are interested not only in computing their response under assumed conditions, but more importantly, in modeling and quantifying the uncertainty associated with their performance. Our final goal is to use scientifically based predictions to make informed decisions related to design and operational safety.

The two main themes of the course will be: 1) Uncertainty modeling and quantification associated with computer-based simulations of engineering systems, and 2) Reliability of existing systems based on performance monitoring and damage models (Bayesian approach).


Probabilistic Risk Assessment of Engineering Systems. M.G. Stewart and R.E. Melchers. Chapman and Hall, 1997

Reliability and Risk – A Bayesian Perspective.i> N. Singpurwalla. John Wiley and Sons, 2006

Methods of Structural Safety.i H.O. Madsen, S. Krenk and N.C. Lind. Dover, 2006

Structural Reliability Analysis and Prediction, 2nd Edition by R. Melchers. John Wiley and Sons, 1999

Probability and Random Processes for Electrical Engineers 2nd Edition by A. Leon- Garcia. Addison-Wesley, 1994

Stochastic Systems. M. Grigoriu. Springer-Verlag, 2012 Random Fields. E. Vanmarke. MIT Press, 1983

Prerequisites by topic:

≥ STAT-151 (or equivalent)


Dr. Eric M. Hernandez Office: 217 Votey Hall


1. Review fundamental theory of probability – emphasis on measure theory
2. Provide tools for modeling and simulating random variables and random processes
3. Provide numerical methods for modeling and propagating uncertainties in engineering systems.
4. Provide methods to compute the reliability of engineering systems and components
5. State-of-the-art methods to update system reliability based on operational data


  • Introductory discussion: Systems, models, uncertainty, failure and risk
  • Foundations of probability theory-emphasis on measure theory
  • Random variables
  • Functions of random variables
  • Random processes
  • Random fields
  • Component reliability analysis
  • System reliability analysis
  • Second moment methods
  • Stochastic simulation methods
  • Analysis of failure data
  • Bayesian reliability analysis based on operational data

Computer Usage:



Assignments 20%
Final Research Project 30%
Midterm 25%
Final 25%

UVM POLICIES – Read Carefully

Student Learning Accommodations:

In keeping with University policy, any student with a documented disability interested in utilizing accommodations should contact ACCESS, the office of Disability Services on campus. ACCESS works with students to create reasonable and appropriate accommodations via an accommodation letter to their professors as early as possible each semester. Contact ACCESS: A170 Living/Learning Center; 802-656-7753;; UVM’s policy on disability certification and student support: Learn More

Religious Holidays:

Students have the right to practice the religion of their choice. If you need to miss class to observe a religious holiday, please submit the dates of your absence to me in writing by the end of the second full week of classes. You will be permitted to make up work within a mutually agreed-upon time.

Academic Integrity:

The policy addresses plagiarism, fabrication, collusion, and cheating. Learn More

Grade Appeals:

If you would like to contest a grade, please follow the procedures outlined in this policy: Learn More


For information on grading and GPA calculation, go to Learn More and click on Policies for an A-Z listing.

Code of Student Rights and Responsibilities:

Learn More

FERPA Rights Disclosure:

The purpose of this policy is to communicate the rights of students regarding access to, and privacy of their student educational records as provided for in the Family Educational Rights and Privacy Act (FERPA) of 1974. Learn More

Final exam policy:

The University final exam policy outlines expectations during final exams and explains timing and process of examination period. Learn More

Last modified February 01 2018 11:24 AM