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 Natural & Applied Sciences Master's Degree
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 expand and get in-depth information with scientific researches in the field of mechanical engineering, evaluate information, review and implement.
2 Have comprehensive knowledge about current techniques and methods and their limitations in Mechanical engineering.
3 To complete and apply knowledge by using scientific methods using uncertain, limited or incomplete data; use information from different disciplines.
4 Being aware of the new and developing practices of Mechanical Engineering and being able to examine and learn when needed.
5 Ability to define and formulate problems related to Mechanical Engineering and develop methods for solving and apply innovative methods in solutions.
6 Ability to develop new and/or original ideas and methods; design complex systems or processes and develop innovative/alternative solutions in the designs.
7 Ability to design and apply theoretical, experimental and modeling based researches; analyze and solve complex problems encountered in this process.
8 Work effectively in disciplinary and multi-disciplinary teams, lead leadership in such teams and develop solution approaches in complex situations; work independently and take responsibility.
9 To establish oral and written communication by using a foreign language at least at the level of European Language Portfolio B2 General Level.
10 Ability to convey the process and results of their studies systematically and clearly in written and oral form in national and international environments.
11 To know the social, environmental, health, security, law dimensions, project management and business life applications of engineering applications and to be aware of the constraints of their engineering applications.
12 Ability to observe social, scientific and ethical values in the stages of data collection, interpretation and announcement and in all professional activities.

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