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
Major Area Courses X
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 Gains the ability to understand and apply knowledge in the fields of mathematics, science and basic sciences at the level of expertise.
2 Gains the ability to access wide and deep knowledge in the field of Engineering by doing scientific research with current techniques and methods, evaluate, interpret and implement the gained knowledge.
3 Being aware of the latest developments his/her field of study, defines problems, formulates and develops new and/or original ideas and methods in solutions.
4 Designs and applies theoretical, experimental, and model-based research, analyzes and interprets the results obtained at the level of expertise.
5 Gains the ability to use the applications, techniques, modern tools and equipment in his/her field of study at the level of expertise.
6 Designs, executes and finalizes an original work process independently.
7 Can work in interdisciplinary and interdisciplinary teams, lead teams, use the information of different disciplines together and develop solution approaches.
8 Pays regard to scientific, social and ethical values in all professional activities and acquires responsibility consciousness at the level of expertise.
9 Contributes to the literature by communicating the processes and results of his/her academic studies in written form or orally in national and international academic environments, communicates effectively with communities and scientific staff working in the field of specialization.
10 Gains the skill of lifelong learning at the level of expertise.
11 Communicates verbally and in written form using a foreign language at least at the European Language Portfolio B2 General Level.
12 Recognizes the social, environmental, health, safety, legal aspects of engineering applications, as well as project management and business life practices, being aware of the limitations they place on engineering applications.

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