# 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)
N/A
Course Language English N/A Natural & Applied Sciences Master's Degree Face To Face Lecture. 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. 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. 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 -

### Sources

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

### Evaluation System

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 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Ability to apply knowledge on Mathematics, Science and Engineering to advanced systems.
2 Implementing long-term research and development studies in major areas of Electrical and Electronics Engineering.
3 Ability to use modern engineering tools, techniques and facilities in design and other engineering applications.
4 Graduating researchers active on innovation and entrepreneurship.
5 Ability to report and present research results effectively.
6 Increasing the performance on accessing information resources and on following recent developments in science and technology.
7 An understanding of professional and ethical responsibility.
8 Increasing the performance on effective communications in both Turkish and English.
9 Increasing the performance on project management.
10 Ability to work successfully at project teams in interdisciplinary fields.

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 3 48
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 16 2 32
Presentation/Seminar Prepration
Project
Report
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