ECTS - Probabilistic Methods in Engineering

Probabilistic Methods in Engineering (MDES618) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Probabilistic Methods in Engineering MDES618 3 0 0 3 5
Pre-requisite Course(s)
Course Language English
Course Type N/A
Course Level Ph.D.
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives The aim of the course is to study basic methods of probability theory and mathematical statistics and to demonstrate the possible applications. Examples related to service systems, reliability, algorithms, and other subjects are given throughout the course. The course is constructed for students of engineering departments, using mathematics for its applications.
Course Learning Outcomes The students who succeeded in this course;
  • Find reliability functions and mean times to failure for systems of different types. Understand the notion of stochastic process and analyze different types of stochastic processes. Understand basic facts concerning Markov chains. Know special probability distributions such as Poisson, exponential, Erlang. Apply the methods of statistical inference.
Course Content Basic notions of probability theory, reliability theory, notion of a stochastic process, Poisson processes, Markov chains, statistical inference.

Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Sample space, random events, probability. Conditional probability. Independence. Ch.1.1-1.10
2 Random variables and probability distributions. Random vectors. Ch. 2.3, 2.4, 3.1, 3.6
3 Reliability theory. Finding reliabilities of different systems. Redundancy. Ch. 3.6-3.7
4 Failure rate and hazard function. IFR/DFR distributions. Ch. 3.3
5 Definition and examples of stochastic processes, their types. Ch. 6.1, 6.2
6 The Poisson process and its generalizations Ch. 6.5, 6.4
7 Random incidence. Midterm I Ch. 6.7
8 Markov chains: Markov property, transition probabilities, transition graph. Chapman-Kolmogorov equations. Ch. 7.1, 7.2
9 Classification of states and limiting probabilities. Regular chains and equilibrium. Ch. 7.3
10 Absorbing Markov chains. Fundamental matrix. Ch. 7.9
11 Random samples. Estimators, their characteristics. Ch. 10.1-10.2
12 Point and interval estimation. Midterm II Ch.10.2.3
13 Hypothesis testing. The null and alternative hypotheses, type I and type II errors. One-sided and two-sided tests. Tests on the population mean. Ch. 10.3.1
14 Tests on the population variance. Goodness-of-fit tests Ch.10.3.3, 10.3.4
15 Overall review -
16 Final exam -


Course Book 1. K. S. Trivedi, Probability and Statistics with Reliability, Queueing, and Computer Science Applications, 2nd Edition, Wiley, 2002.
Other Sources 2. Sheldon Ross, Introduction to Probability Models. Academic Press, 1994
3. T. Aven, U. Jensen, Stochastic models in reliability, Springer, 1999

Evaluation System

Requirements Number Percentage of Grade
Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics 2 20
Homework Assignments - -
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 40
Final Exam/Final Jury 1 40
Toplam 5 100
Percentage of Semester Work 60
Percentage of Final Work 40
Total 100

Course Category

Core Courses X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Ability to carry out advanced research activities, both individual and as a member of a team X
2 Ability to evaluate research topics and comment with scientific reasoning X
3 Ability to initiate and create new methodologies, implement them on novel research areas and topics X
4 Ability to produce experimental and/or analytical data in systematic manner, discuss and evaluate data to lead scintific conclusions X
5 Ability to apply scientific philosophy on analysis, modelling and design of engineering systems X
6 Ability to synthesis available knowledge on his/her domain to initiate, to carry, complete and present novel research at international level X
7 Contribute scientific and technological advancements on engineering domain of his/her interest area X
8 Contribute industrial and scientific advancements to improve the society through research activities X

ECTS/Workload Table

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 3 48
Special Course Internship
Field Work
Study Hours Out of Class 16 2 32
Presentation/Seminar Prepration
Homework Assignments 2 12 24
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 8 16
Prepration of Final Exams/Final Jury 1 10 10
Total Workload 130