IE 502 | Course Introduction and Application Information - M.SC. In Industrial Engineering (With Thesis)

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
National Occupation Classification	-
Course Coordinator	Dr. Öğr. Üyesi Oktay KARABAĞ
Course Lecturer(s)	Dr. Öğr. Üyesi Oktay KARABAĞ
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

Week	Subjects	Related Preparation	Learning Outcome
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, 11^th 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, 10^th 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, 2^nd 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 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

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

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	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	-

IE 502 | Course Introduction and Application Information

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

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ECTS / WORKLOAD TABLE

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