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 | Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area. | X | ||||
| 2 | Has the ability to obtain, to evaluate, to interpret and to apply information by doing scientific research. | X | ||||
| 3 | Can apply gained knowledge and problem solving abilities in inter-disciplinary research. | X | ||||
| 4 | Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary. | X | ||||
| 5 | Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study. | X | ||||
| 6 | Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework. | X | ||||
| 7 | Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility. | X | ||||
| 8 | Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge. | X | ||||
| 11 | Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | X | ||||
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 | ||