GRADUATE SCHOOL

M.SC. In Industrial Engineering (With Thesis)

IE 502 | Course Introduction and Application Information

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 Solving
Lecture / 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;
  • Discuss a scientific paper that involves stochastic models
  • Model any process that evolves over time.
  • Make scientific predictions about the future of a process using the models and techniques of stochastic processes.
  • Compare and contrast the models and techniques used in stochastic processes with those of other industrial engineering/operations research tools.
  • Classify the stochastic processes models.
  • Derive the equations of stochastic models, follow the proofs of theorems, and prove the validity of a solution.
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.

 



Course Category

Core Courses
Major Area Courses
X
Supportive Courses
Media and Management Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Probability concept, Conditional Probability, and Bayes Theorem
2 Random variable, Expectation, and Variance
3 Basic univariate discrete probability distributions
4 Basic univariate continous probability distributions
5 Two-dimensional joint discrete and continuous distributions, Covariance, Correlation and Introduction to Random processes
6 Two-dimensional joint discrete and continuous distributions, Covariance, Correlation and Introduction to Random processes (Cont’d)
7 Midterm Exam
8 Discrete-time Markov chains: Definitions, Modeling and the Chapman-Kolmogorov equation
9 Discrete-time Markov chains: State classification and First step analysis
10 Discrete-time Markov chains: Absorbing chains and Long-run analysis
11 Poisson Processes: Definition and Properties
12 Poisson Processes: Non-homogeneous and Compound Poisson processes
13 Continuous time Markov chains: Concepts and Birth-death processes
14 Continuous time Markov chains: Transition probability function and calculation of transition probabilities
15 Review of the Semester  
16 Final Exam

 

Course Notes/Textbooks

[1] Ross, Sheldon. Introduction to Probability Models, 11th edition, Academic Press, 2014. ISBN: 978-0124079489

[2] Taylor, Howard M. and Karlin, Samuel. An Introduction to Stochastic Modeling, 3rd Edition, Academic Press, 1998, ISBN: 978-0-12-684887-8.

[3] Frederick S. Hillier, Gerald J. Lieberman, Introduction to Operations Research, 10th Edition, 2010 Mc GrawHill, ISBN: 9780071267670

Suggested Readings/Materials

[4] Bertsekas, Dimitri, and John Tsitsiklis. Introduction to Probability. 2nd ed. Athena, Scientific, 2008. ISBN: 9781886529236.

[5] Sheldon Ross, Stochastic Processes, 2nd edition, Wiley, 1995. ISBN: 978-0471120629

 

EVALUATION SYSTEM

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 Exams
Midterm
1
35
Final Exam
1
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

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Theoretical Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: '.16.' x total hours)
16
0
Study Hours Out of Class
16
5
80
Field Work
0
Quizzes / Studio Critiques
0
Portfolio
0
Homework / Assignments
3
15
45
Presentation / Jury
0
Project
0
Seminar / Workshop
0
Oral Exam
0
Midterms
1
24
24
Final Exam
1
28
28
    Total
225

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
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

 


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