Course Objectives
After completing this course a student should:

Topics Covered
Modeling of uncertainty, sample paths, basic probability theory, random variables, joint distributions, expected values, conditional probability, limit distributions, discrete event simulation, generating random variates, arrival processes, the Poisson process, memory-less property, superposition and decomposition property, discrete time Markov chains, transient and steady-state analysis, exponential distribution, continuous time birth-death chains, queuing models, Little’s Law, Markovian queues, queuing approximations.

Class/Laboratory Schedule
This class meets three times a week for a fifty-minute lecture. There are approximately five homework assignments as well as short (5-10 minute) in-class assignments that are to be completed in small groups. Some homework assignments require use of computer software and there are two laboratory session to demonstrate the use of this software. A group project involves data gathering from a real-world system, formulating a model of the system, and analyzing its performance. Each group of 4-5 students gives two in-class presentations: a status report after the data gathering and partial modeling, and a final report presenting the conclusions and recommendations of the project. A written final report is also required.

Contribution to Professional Component
The students learn how to apply their knowledge in probability and statistics to analyze real-world engineering systems. For their project they will gather data from a real system that then needs to be interpreted and used to formulate a model of the system. The students will then apply the techniques from class to analyze the model in order to improve the design and/or operation of the system. The project, as well as many of the other assignments, will be performed in small groups, encouraging the students to develop their ability of work as part of a team. The students will also enhance their communication skills through oral presentations and a written report.

Relationship to Program Objectives
This course provides tools and experience for modeling of production and service systems as well as integration of processes. An important element of the course is for the students to gain an understanding of how to apply their knowledge of probability and statistics to analyze real-world systems. The students will also gather and analyze real-world data and use this to build a model of the real system. Students work extensively in teams, providing them with valuable experience in working in such environments, and present their results to the class, enhancing their communication skills.

Course Coordinator
Prepared by Sigurdur Olafsson, December 1999.