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 | Ph.D. |
| 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 | Is independently able to build a problem in the area of study, solve the problem by developing solution techniques and assess the solutions. | X | ||||
| 2 | Is capable of creating a groundwork in the fundamental branches of mathematics as well as in his/her research area | X | ||||
| 3 | follows the latest national and international literature in Mathematics and in his/her area of research; and uses them in his/her related studies | X | ||||
| 4 | observes and adopts the scientific ethical values in his/her professional and social life | X | ||||
| 5 | presents in Turkish and English in academic/scientific events the results of his/her research or the latest studies and findings on a special topic and participates in discussions | X | ||||
| 6 | Develops skills to work independently or as a member of a team | X | ||||
| 7 | Develops competences in the areas of creative and critical thinking, problem solving and producing original studies. Follows recent scientific studies, is capable of making an analysis, synthesis and assessment of the knowledge acquired | X | ||||
| 8 | Is open to lifelong improvement of his/her acquired knowledge, skills and competences. | X | ||||
| 9 | Is able to apply the acquired knowledge and problem-solving skills to interdisciplinary studies, proposes different solution methods to problems in terms of mathematical models and from a mathematical point of view | X | ||||
| 10 | Uses the mathematical based softwares, informatics and communication technologies for scientific purposes | 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 | ||