Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Optional Tutorials: 1 session / week, 1 hour / session

General Information

ERBA (ESD.72) emphasizes three methodologies - reliability and probabilistic risk assessment (RPRA), decision analysis (DA), and cost-benefit analysis (CBA). All of these pertain to decision making in the presence of significant uncertainty. In ERBA, the issues of interest are: The risks associated with large engineering projects such as nuclear power reactors, the International Space Station, and critical infrastructures; the development of new products; the design of processes and operations with environmental externalities; and infrastructure renewal projects.

As part of RPRA, we will review elementary probability theory and statistics. This review will be helpful not only for this course but also other courses in the SDM (System Design and Management) program, such as 15.761, Operations Management, and ESD.33J, Systems Engineering.

ERBA presents and interprets some of the many frameworks helpful for balancing risks and benefits in these situations that typically involve human safety, potential environmental effects, and large financial and technological uncertainties. Although ERBA is applications-oriented, we want to help you develop a critical understanding of the assumptions, consequences, and practical limitations of the tools we present. We also provide perspective on the use of formal analysis in public decisions. Most students in ERBA are taking it to obtain some knowledge and experience on important topics that are not otherwise part of their academic programs.


There is no textbook for this course. The ESD.72J course reader, an adaptation of the study manual for the 1978 MIT Video Lecture Course "Decision Analysis" by Alvin Drake & Ralph Keeney, will be photocopied and available for the DA unit.

Some references that may be useful as background material are:


Buy at Amazon Hoyland, Arnljot, and Rausand, Marvin. System Reliability Theory. Hoboken, NJ: Wiley-Interscience, 1994. ISBN: 9780471471332.


Buy at Amazon Clemen, Robert T. Making Hard Decisions. 2nd ed. Boston, MA: Duxbury Press, 1997. ISBN: 9780534260347.


Buy at Amazon Thuesen, G. J., and Fabrycky, W. J. Engineering Economy. 9th ed. Englewood Cliff, NJ: Prentice-Hall, Inc., 2000. ISBN: 9780130281289.

Probability and Statistics

A good introductory book to probability/statistics from an engineering perspective is:

Buy at Amazon Ang, Alfredo H.-S., and Tang, W. H. Probability Concepts in Engineering Planning and Design, Basic Principles. Vol. 1. New York, NY: Wiley, 1975. ISBN: 9780471032007.


Each week, there will be an entirely optional tutorial session. These sessions are primarily for the benefit of the SDM students and will be conducted by the TAs and/or Prof. Apostolakis, who will discuss example problems and answer questions.

Assignments And Procedures

For ESD.72, there will be several problem sets (which will count for about 25% of the course's grade) and three quizzes (total of about 75% of the grade). There is no final examination. If you first make an effort to think things through for yourself, the TAs or the instructor responsible for the problem set will be glad to help you with homework before it is due. To help you understand what we expect of you, we shall also distribute examples of quizzes and solutions from previous semesters before each quiz.


Problem sets 25%
Three quizzes 75%


Part 1: Reliability and probabilistic risk assessment (RPRA)


RPRA1: The logic of certainty

2 RPRA 2: Elements of probability theory
3 RPRA 3: Probability distributions
4 RPRA 3: Probability distributions (cont.)
5 RPRA 4: Availability
6 RPRA 5: Data and epistemic uncertainties; statistics
7 RPRA 6: Probabilistic risk assessment
8 RPRA 6: Probabilistic risk assessment (cont.)
9 RPRA 7: Risk management
10 Guest lecture
11 Guest lecture
12 RPRA quiz
Part II: Decision analysis (DA)
13 DA 1: The multistage decision model
14 DA 2: The value of perfect information
15 DA 3: The axioms of rational behavior

DA 4: Introduction to utility

DA 5: Risk aversion

17 DA 6: Multiattribute utility theory
18 DA7: Decision analysis and risk management
19 Guest lecture
20 DA quiz
Part III: Cost-benefit analysis (CBA)
21 CBA 1: Background and fundamental premises
22 CBA 2: The time value of money
23 CBA 3: Bases for comparison of alternatives
24 CBA 4: Including uncertainty
25 CBA 5: Evaluating public activities
26 Guest lecture
27 CBA quiz