2021-2022 / MECA0010-1

Reliability and stochastic modeling of engineering systems


16h Th, 16h Pr, 28h Proj.

Number of credits

 Master of Science (MSc) in Aerospace Engineering5 crédits 
 Master of Science (MSc) in Biomedical Engineering5 crédits 
 Master of Science (MSc) in Mechanical Engineering (EMSHIP+, Erasmus Mundus)5 crédits 
 Master of Science (MSc) in Mechanical Engineering (EMSHIP+, Erasmus Mundus)5 crédits 
 Master of Science (MSc) in Engineering Physics5 crédits 


Maarten Arnst

Language(s) of instruction

English language

Organisation and examination

Teaching in the first semester, review in January


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

Engineering structures and systems are rarely perfectly known, may present defects, and are often subjected to loadings that can be random or difficult to predict, thus making their design, fabrication, operation, reliability, maintenance, and simulation uncertain. This course aims at familiarizing the students with probabilistic methods that can be used to account for uncertainties in engineering analyses and to ascertain the accuracy of simulation predictions.
After a brief review of the basic concepts from the probability theory and from statistics, the course will be divided in three parts.  The first part is dedicated to stochastic modeling in the field of biomedical sciences and engineering, with a focus on jump Markov processes and their use in modeling infectious disease spread and epidemiology.  
The second part is dedicated to probabilistic methods for the quantification of uncertainties in engineering analysis. After presenting the most widespread and most used probabilistic methods (ISO98 Guide), attention will be turned towards more leading-edge probabilistic methods that are still the subject of ongoing scientific research (Monte Carlo methods, surrogate modeling, polynomial chaos methods, sensitivity analysis).
The third part is dedicated to the probabilistic analysis of the reliability and failures of engineering structures and systems. The main probabilistic method to be studied is the modeling of failure instances by means of Poisson stochastic processes. Attention will be turned towards the representation of running-in, useful-life, and aging phases (homogeneous and nonhomogeneous Poisson stochastic processes), the acquisition and exploitation of data about occurrence of failures in structures and systems in operation (statistical inferences, hypothesis tests), and the contribution of these to maintenance planning.

Learning outcomes of the learning unit

  • Understanding of the uncertainties that may affect the behavior, evolution, and simulation of structures and systems in mechanics and physics.
  • Ability to apply probabilistic methods for the quantification of uncertainties.
  • Ability to apply probabilistic methods for reliability analysis.
  • Ability to find and read papers from the scientific literature.
  • Ability to communicate effectively in written reports and oral presentations.

Prerequisite knowledge and skills

Students ideally have a background in probability theory (MATH0062 "Elements of probability calculus" or an equivalent course), statistics (MATH0487 "Elements of statistics" or an equivalent course), and stochastic processes (MATH0488 "Elements of stochastic processes" or an equivalent course). The required background material will be recalled in class as needed.

Planned learning activities and teaching methods

The course involves a series of lectures. In addition, students work on two projects. The first one revolves around reading two papers from the scientific literature.  The second one is a numerical project related to uncertainty quantification.  

Mode of delivery (face to face, distance learning, hybrid learning)

Distance learning.

Recommended or required readings

Each lecture is supported by slides prepared by the instructor. Papers from the historic and current international scientific literature complement the slides.

Assessment methods and criteria

Students are required to prepare two reports for their projects.  The final grade is a weighted average of the grades obtained for the reports, which takes into account their content, clarity, and neatness.

Work placement(s)

Organizational remarks

The course will be offered in the Fall semester.


Maarten ARNST : maarten.arnst@uliege.be