| Course Name | Probabilistic Systems Analysis |
| Code | Semester | Theory (hour/week) | Application/Lab (hour/week) | Local Credits | ECTS |
|---|---|---|---|---|---|
| IE 502 | Fall | 3 | 0 | 3 | 7.5 |
| Prerequisites | None | |||||
| Course Language | English | |||||
| Course Type | Required | |||||
| Course Level | Second Cycle | |||||
| Mode of Delivery | - | |||||
| Teaching Methods and Techniques of the Course | Problem SolvingLecturing / Presentation | |||||
| Course Coordinator | ||||||
| Course Lecturer(s) | ||||||
| Assistant(s) | - | |||||
| Course Objectives | Most problems encountered in scientific research requires acquaintance with stochastic models and the solution techniques used for these models. The stochastic versions of deterministic problems may also be defined and modelled. Using the models and techniques taught in this course, solution approaches will be sought to problems that are stochastic in nature or to the stochastic versions of deterministic problems. The student will gain the ability to build and analyze models. |
| Learning Outcomes | The students who succeeded in this course;
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| Course Description | The course involves defining and modelling a stochastic process and solving the problems related to the stochastic process being investigated. The underlying theory will be taught, followed by applications that illustrate the use of a stochastic process. |
| Related Sustainable Development Goals | |
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| Core Courses | |
| Major Area Courses | X | |
| Supportive Courses | ||
| Media and Managment Skills Courses | ||
| Transferable Skill Courses |
| Week | Subjects | Required Materials |
| 1 | Probability Models and Axioms; Conditioning and Bayes' Rule; Independence | Related chapter of course book |
| 2 | Counting; Discrete Random Variables; Probability Mass Functions; Expectations | Related chapter of course book |
| 3 | Joint PMFs; Multiple Discrete Random Variables | Related chapter of course book |
| 4 | Continuous Random Variables; Multiple Continuous Random Variables; Continuous Bayes' Rule | Related chapter of course book |
| 5 | Derived Distributions, Convolution; Covariance and Correlation | Related chapter of course book |
| 6 | MIDTERM | |
| 7 | Stochastic Processes: Bernoulli Process; Poisson Process - I | Related chapter of course book |
| 8 | Stochastic Processes: Poisson Process - II | Related chapter of course book |
| 9 | Stochastic Processes: Poisson Process – III | Related chapter of course book |
| 10 | Markov Chains – I & II | Related chapter of course book |
| 11 | Markov Chains – I & II | |
| 12 | Markov Chains – III | Related chapter of course book |
| 13 | Markov Chains – IV | Related chapter of course book |
| 14 | Project Presentations | Related chapter of course book |
| 15 | Review of the semester | Related chapter of course book |
| 16 | Final Exam |
| Course Notes/Textbooks | Ross, Sheldon. Introduction to Probability Models, 11th edition, Academic Press, 2014. ISBN: 978-0124079489 Bertsekas, Dimitri, and John Tsitsiklis. Introduction to Probability. 2nd ed. Athena, Scientific, 2008. ISBN: 9781886529236. Taylor, Howard M. and Karlin, Samuel. An Introduction to Stochastic Modeling, 3rd Edition, Academic Press, 1998, ISBN: 978-0-12-684887-8. |
| Suggested Readings/Materials | Sheldon Ross, Stochastic Processes, 2nd edition, Wiley, 1995. ISBN: 978-0471120629 |
| Semester Activities | Number | Weigthing |
| Participation | 1 | 10 |
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments | 1 | 20 |
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exam | ||
| Midterm | 1 | 35 |
| Final Exam | 35 | |
| Total |
| Weighting of Semester Activities on the Final Grade | 3 | 65 |
| Weighting of End-of-Semester Activities on the Final Grade | 1 | 35 |
| Total |
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Course Hours (Including exam week: 16 x total hours) | 16 | 3 | 48 |
| Laboratory / Application Hours (Including exam week: 16 x total hours) | 16 | ||
| Study Hours Out of Class | 16 | 5 | 80 |
| Field Work | |||
| Quizzes / Studio Critiques | |||
| Portfolio | |||
| Homework / Assignments | 3 | 15 | |
| Presentation / Jury | |||
| Project | |||
| Seminar / Workshop | |||
| Oral Exam | |||
| Midterms | 1 | 25 | |
| Final Exams | 28 | ||
| Total | 198 |
| # | Program Competencies/Outcomes | * Contribution Level | ||||
1 | 2 | 3 | 4 | 5 | ||
| 1 | To have an appropriate knowledge of methodological and practical elements of the basic sciences and to be able to apply this knowledge in order to describe engineering-related problems in the context of industrial systems. | X | ||||
| 2 | To be able to identify, formulate and solve Industrial Engineering-related problems by using state-of-the-art methods, techniques and equipment. | X | ||||
| 3 | To be able to use techniques and tools for analyzing and designing industrial systems with a commitment to quality. | X | ||||
| 4 | To be able to conduct basic research and write and publish articles in related conferences and journals. | X | ||||
| 5 | To be able to carry out tests to measure the performance of industrial systems, analyze and interpret the subsequent results. | X | ||||
| 6 | To be able to manage decision-making processes in industrial systems. | X | ||||
| 7 | To have an aptitude for life-long learning; to be aware of new and upcoming applications in the field and to be able to learn them whenever necessary. | X | ||||
| 8 | To have the scientific and ethical values within the society in the collection, interpretation, dissemination, containment and use of the necessary technologies related to Industrial Engineering. | X | ||||
| 9 | To be able to design and implement studies based on theory, experiments and modeling; to be able to analyze and resolve the complex problems that arise in this process; to be able to prepare an original thesis that comply with Industrial Engineering criteria. | X | ||||
| 10 | To be able to follow information about Industrial Engineering in a foreign language; to be able to present the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form. | X | ||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
