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 | Area Elective | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Natural & Applied Sciences Master's Degree |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture. |
| Course Lecturer(s) |
|
| 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;
|
| 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 | - |
Sources
| 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 | An ability to apply knowledge of mathematics, science, and engineering. | X | ||||
| 2 | An ability to design and conduct experiments, as well as to analyse and interpret data. | |||||
| 3 | An ability to design a system, component, or process to meet desired needs. | |||||
| 4 | An ability to function on multi-disciplinary domains. | |||||
| 5 | An ability to identify, formulate, and solve engineering problems. | X | ||||
| 6 | An understanding of professional and ethical responsibility. | |||||
| 7 | An ability to communicate effectively. | |||||
| 8 | Recognition of the need for, and an ability to engage in life-long learning. | |||||
| 9 | A knowledge of contemporary issues. | |||||
| 10 | An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice. | |||||
| 11 | Skills in project management and recognition of international standards and methodologies | |||||
| 12 | An ability to produce engineering products or prototypes that solve real-life problems. | |||||
| 13 | Skills that contribute to professional knowledge. | |||||
| 14 | An ability to make methodological scientific research. | |||||
| 15 | An ability to produce, report and present an original or known scientific body of knowledge. | |||||
| 16 | An ability to defend an originally produced idea. | |||||
ECTS/Workload Table
| 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 |
| Total Workload | 130 | ||