What every engineer should know about decision making under uncertainty (2002)

WHAT EVERY
ENGINEER SHOULD
KNOW ABOUT

DECISION
MAKING UNDER
UNCERTAINTY
John X. Wang
Certified Six Sigma Master Black Belt
Certified Reliability Engineer
Ann Arbor, Michigan

Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.

M A R C E L

H
D E K K E R

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WHAT EVERY ENGINEER SHOULD KNOW
A Series
Founding Editor

William H. Middendorf
Department of Electrical and Computer Engineering
University of Cincinnati
Cincinnati, Ohio

1. What Every Engineer Should Know About Patents, William G. Konold,
Bruce Tittel, Donald F. Frei, and David S. Stallard

2. What Every Engineer Should Know About Product Liability, James F.
Thorpe and William H. Middendorf
3. What Every Engineer Should Know About Microcomputers: Hardware/Software Design, A Step-by-Step Example, William S. Bennett and
Carl F. Evert, Jr.
4. What Every Engineer Should Know About Economic Decision Analysis,
Dean S. Shupe
5. What Every Engineer Should Know About Human Resources Management, Desmond D. Martin and Richard L. Shell
6. What Every Engineer Should Know About Manufacturing Cost
Estimating, Eric M. Malstrom
7. What Every Engineer Should Know About Inventing, William H. Middendorf
8. What Every Engineer Should Know About Technology Transfer and
Innovation, Louis N. Mogavero and Robert S. Shane
9. What Every Engineer Should Know About Project Management, Arnold
M. Ruskin and W. Eugene Estes
10. What Every Engineer Should Know About Computer-Aided Design and
Computer-Aided Manufacturing: The CAD/CAM Revolution, John K.
Krouse
11. What Every Engineer Should Know About Robots, Maurice I. Zeldman
12. What Every Engineer Should Know About Microcomputer Systems
Design and Debugging, Bill Wray and Bill Crawford
13. What Every Engineer Should Know About Engineering Information
Resources, Margaret T. Schenk and James K. Webster
14. What Every Engineer Should Know About Microcomputer Program
Design, Keith R. Wehmeyer
15. What Every Engineer Should Know About Computer Modeling and
Simulation, Don M. Ingels
16. What Every Engineer Should Know About Engineering Workstations,
Justin E. Hartow III

Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.

17. What Every Engineer Should Know About Practical CAD/CAM Appli
cations, John Stark
18. What Every Engineer Should Know About Threaded Fasteners:
Materials and Design, Alexander Blake
19. What Every Engineer Should Know About Data Communications, Carl
Stephen Clifton
20. What Every Engineer Should Know About Material and Component
Failure, Failure Analysis, and Litigation, Lawrence E. Murr
21. What Every Engineer Should Know About Corrosion, Philip Schweitzer
22. What Every Engineer Should Know About Lasers, D. C. Winburn
23. What Every Engineer Should Know About Finite Element Analysis,
edited by John R. Brauer
24. What Every Engineer Should Know About Patents: Second Edition,
William G. Konold, Bruce Titiel, Donald F. Frei, and David S. Stallard
25. What Every Engineer Should Know About Electronic Communications
Systems, L. R. McKay
26. What Every Engineer Should Know About Quality Control, Thomas
Pyzdek
27. What Every Engineer Should Know About Microcomputers: Hardware/Software Design, A Step-by-Step Example. Second Edition, Revised and Expanded, William S. Bennett, Carl F. Evert, and Leslie C.
Lander
28. What Every Engineer Should Know About Ceramics, Solomon Musikant
29. What Every Engineer Should Know About Developing Plastics Products,
Bruce C. Wendle
30. What Every Engineer Should Know About Reliability and Risk Analysis,
M. Modarres
31. What Every Engineer Should Know About Finite Element Analysis:
Second Edition, Revised and Expanded, edited by John R. Brauer
32. What Every Engineer Should Know About Accounting and Finance, Jae

K. Shim and Norman Henteleff
33. What Every Engineer Should Know About Project Management: Second
Edition, Revised and Expanded, Arnold M. Ruskin and W. Eugene Estes
34. What Every Engineer Should Know About Concurrent Engineering,
Thomas A. Salomone
35. What Every Engineer Should Know About Ethics, Kenneth K.
Humphreys
36. What Every Engineer Should Know About Risk Engineering and
Managment, John X. Wang and Marvin L. Roush
37. What Every Engineer Should Know About Decision Making Under
Uncertainty, John X. Wang

ADDITIONAL VOLUMES IN PREPARATION

Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.


Preface
The Roman philosopher Seneca said "Nothing is certain except the
past." This statement seems very true for engineering, which faces
today's and tomorrow's challenges for technical product design, development, production, and services. Most engineering activities
involve decision making in terms of selecting the concept, configuration, materials, geometry, and conditions of operation. The information and data necessary for decision making are known with different degrees of confidence at different stages of design. For example, at the preliminary or conceptual design stage, very little information is known about the system. However, as we progress towards the final design, more and more data will be known about the
system and its behavior. Thus the ability to handle different types of
uncertainty in decision making becomes extremely important.
Volume 36 of the What Every Engineer Should Know... series
dealt primarily with decision making under risk. In risk engineering
and management, information may be unavailable, but a probabilistic description of the missing information is available. A technical
decision in such a case might be that a manufacturing engineer
knows the probability distribution of manufacturing process outputs,
and is trying to determine how to set an inspection policy. The design response might be to construct a stochastic program and find a

minimum cost solution for a known defect rate.
Decision making under uncertainty, by contrast, involves distributions that are unknown. This situation involves less knowledge
than decision making under risk. A situation that involves decision
making under uncertainty might be that a communications design

Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.


iv

Preface

engineer knows that transmission quality is a function of the antenna
design, the frequency, and the background radiation, but is unsure of
what the distribution of background radiation will be in the user environment. In this situation the design response might be to collect
field data in the user environment to characterize the radiation, so
that antenna design and frequency can be chosen.
Decision making also involves a still more profound lack of
knowledge, where the functional form is completely unknown, and
often the relevant input and output variables are unknown as well.
An example of this more profound uncertainty is that of a design
engineer who is considering building airplane wing panels out of
composite materials, but is uncertain of the ability of the new materials to withstand shock loads, and indeed which design variables
might affect shock loads. The engineering design response to this
situation might be to start an R&D project that will vary possible
input variables (panel thickness, bond angle, securement method,
loading, etc.), and determine which, if any, of these variables has a
significant effect on shock resistance.
Uncertainty is an important factor in engineering decisions.
This book introduces general techniques for thinking systematically

and quantitatively about uncertainty in engineering decision problems. Topics include: spreadsheet simulation models, sensitivity
analysis, probabilistic decision analysis models, value of information, forecasting, utility analysis including uncertainty, etc. The use
of spreadsheets is emphasized throughout the book.
In engineering many design problems, the component geometry (due to machine limitations and tolerances), material strength
(due to variations in manufacturing processes and chemical composition of materials) and loads (due to component wearout, imbalances and uncertain external effects) are to be treated as random
variables with known mean and variability characteristics. The resulting design procedure is known as reliability-based design. The
reliability-based design is recognized as a more rational procedure

Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.


Preface

v

compared to the traditional factor of safety-based design methods.
Chapter 1 presents an overview of the decision making under uncertainty using classical and contemporary engineering design examples.
In Chapter 2, we develop the first set of spreadsheet simulation
models illustrated in a Microsoft® Excel workbook to introduce
some basic ideas about simulation models in spreadsheets: the
RANDQ function as a Uniform random variable on 0 to 1, independence, conditional probability, conditional independence, and
the use of simulation tables and data tables in Excel. We see how to
build some conditional probabilities into a simulation model, and
how then to estimate other conditional probabilities from simulation
data.
Chapter 3 reviews basic ideas about continuous random variables using a second set of spreadsheet models. Topics: random
variables with Normal probability distributions (NORMINV,
NORMSDIST), making a probability density chart from an inverse
cumulative function, and Lognormal random variables (EXP, LN,
LNORMINV). To illustrate the application of these probability distributions, we work through the spreadsheet analyses of a case

study: decision analysis at a bioengineering firm.
In Chapter 4 we begin to study correlation in Excel using covariance and correlation functions. We use a spreadsheet model to
simulate Multivariate Normals and linear combinations of random
variables. The case study for a transportation network is used to illustrate the spreadsheet simulation models for correlation topics.
Chapter 5 shows how conditional expectations and conditional
cumulative distributions can be estimated in a simulation model.
Here we also consider the relationship between correlation models
and regression models. Statistical dependence and formulaic dependence, the law of expected posteriors, and regression models are
presented in this chapter.

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vi

Preface

In Chapter 6, we analyze decision variables and strategic use
of information to optimize engineering decisions. Here we enhance
our spreadsheet simulation models with the use of Excel Solver.
Also, we introduce risk aversion: utility functions and certainty
equivalents for a decision maker with constant risk tolerance.
Scheduling resources so that real-time requirements can be satisfied (and proved to be satisfied) is a key aspect of engineering decision making for project scheduling and resource allocation. Consider a project involving numerous tasks or activities. Each activity
requires resources (e.g., people, equipment) and time to complete.
The more resources allocated to any activity, the shorter the time
that may be needed to complete it. We address project scheduling
problems using Critical Path Methods (CPM) or probabilistic Program Evaluation and Review Techniques (PERT) in Chapter 7.
Process control describes numerous methods for monitoring
the quality of a production process. Once a process is under control
the question arises, "to what extent does the long-term performance

of the process comply with engineering requirements or managerial
goals?" For example, considering a piston ring production line, how
many of the piston rings that we are using fall within the design
specification limits? In more general terms, the question is, "how
capable is our process (or supplier) in terms of producing items
within the specification limits?" The procedures and indices described in Chapter 8 allow us to summarize the process capability in
terms of meaningful percentages and indices for engineering decision making.
Chapter 9 presents emerging decision-making paradigms including a balanced scorecard decision-making system. The balanced
scorecard is a new decision-making concept that could help managers at all levels monitor results in their key areas. The balanced
scorecard decision-making system is fundamentally different from
project management in several respects. The balanced scorecard decision-making process, derived from Deming's Total Quality Man-

Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.


Preface

vii

agement, is a continuous cyclical process, which also reflects the
nature of engineering decision-making process.
As Soren Aabye Kieregaard (1813-1855), a Danish writer and
thinker, said, "Life can only be understood backwards, but it must
be lived forwards." Decision making under uncertainty is an inherent part of an engineer's life, since the invention, design, development, manufacture, and service of engineering products require a
forward-looking attitude.
The author wishes to thank Professor Michael Panza of
Gannon University for his very helpful review insights.

JohnX. Wang

Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.


About the Author
JOHN X. WANG is a Six Sigma Quality Master Black Belt certified by
Visteon Corporation, Dearborn, Michigan. He is also a Six Sigma Quality
Black Belt certified by the General Electric Company. The coauthor of
What Every Engineer Should Know About Risk Engineering and Management (Marcel Dekker, Inc.) and author or coauthor of numerous professional papers on fault diagnosis, reliability engineering, and other topics,
Dr. Wang is a Certified Reliability Engineer under the American Society
for Quality, and a member of the Institute of Electrical and Electronics
Engineers and the American Society for Mechanical Engineers. He received the B.A. (1985) and M.S. (1987) degrees from Tsinghua University, Beijing, China, and the Ph.D. degree (1995) from the University of
Maryland, College Park.

Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.


Contents
PREFACE
CHAPTER 1 ENGINEERING: MAKING HARD DECISIONS
UNDER UNCERTAINTY
1.1
1.2
1.3
1.4
1.5
1.6
1.7

Case Study: Galileo's Cantilever Beam
Impact of Engineering Decision Making

Uncertainty and Risk Engineering
Decision Making and System Analysis
Engineering Decision Making in Six Steps
Customer-Focused Engineering Decision-Making System
Summary
References

CHAPTER 2 ENGINEERING JUDGMENT FOR DISCRETE
UNCERTAIN VARIABLES
2.1
2.2
2.3
2.4
2.5
2.6
2.7

Case Study: Production of Electronic Modules
How Would Engineers Flip Coins?
Synthesize Knowledge into a Simulation Model
Simulation for What-If Analysis
Simulating Conditional Independence
Production Quantity and Quality Measures
Summary
References

Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.


x

Contents

CHAPTER 3 DECISION ANALYSIS INVOLVING
CONTINUOUS UNCERTAIN VARIABLES
3.1
3.2
3.3
3.4
3.5
3.6
3.7

Case Study: A Bioengineering Firm
Normal Distributions
Lognormal Distributions
Selection Between Normal and Lognormal Distributions
Decision Tree Analysis
Capital Budgeting
Summary
References

4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8

Case Study: A Transportation Network
Covariance and Correlation
Linear Functions of Several Random Variables
Multivariate Normal Random Variables
Estimating Correlations from Data
Accuracy of Sample Estimates
Customer-Focused Engineering Decision Making
Summary
References

Chapter 5 PERFORMING ENGINEERING
PREDICTIONS
5.1 Case Study: A Construction Project
5.2 The Law of Expected Posteriors
5.3 Linear Regression Models
5.4 Regression Analysis and Least Squared Errors
5.5 The Theory o f Constraints
5.6 Summary
References

Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.


Contents

CHAPTER 6 ENGINEERING DECISION VARIABLES ANALYSIS AND OPTIMIZATION
6.1 Case Study: Production Planning of Snowboards
6.2 Method 1: Simulating Payoffs for Each Engineering
Strategy

6.3 Method 2: Simulating Payoffs from Alternative Strategies
Simultaneously
6.4 Method 3: Optimizing Engineering Decision Variables to
Maximize Payoff
6.5 Value of Information for Engineering Decisions
6.6 Decision Criteria: How to Value Engineering Alternatives
6.7 Evaluation of Cash Flow Information: Payback Method
6.8 The Time Value of Money
6.9 Evaluation of Cash Flow Information: Net Present Value
(NPV) Method
6.10 Evaluation of Cash Flow Information: Internal Rate of
Return (IRR) Method
6.11 Variable Cash Flow
6.12 Proj ect Ranking
6.13 Summary
References
CHAPTER 7 PROJECT SCHEDULING AND BUDGETING
UNDER UNCERTAINTY
7.1 Case Study: Expansion of a Fiber Optics Firm's Office
Space
7.2 Establish a Project Scheduling Network
7.3 Spreadsheet Strategies for Solving CPM Problems Using
Excel
7.4 Solving Critical Path Problems Using Excel Solver
7.5 Crashing CPM Networks Using Excel
7.6 Developing an Approximate PERT Solution in Excel
7.7 Developing a Complete PERT Solution in Excel

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xii

Contents

7.8 Probabilistic Solutions to Project Scheduling Simulation
Using Excel
7.9 Project Budgeting
7.10 Summary
References
CHAPTER 8 PROCESS CONTROL - DECISIONS BASED
ON CHARTS AND INDEXES
8.1
8.2
8.3
8.4
8.5
8.6
8.7

Processes and Process Variability
Statistical Process Control
Types of Out-of-Control Conditions
Sampling and Control Charts
Steps in Determining Process Capability
Capability Indexes
Continuous Quality Improvement vs. Business
Process Re-engineering

8.8 Six Sigma Quality
8.9 Summary
References

CHAPTER 9 ENGINEERING DECISION MAKING:
A NEW PARADIGM
9.1 Engineering Decision Making: Past, Present, and
Future
9.2 Engineering Decision-Making Tool Box
9.3 Balancing Technical Merits, Economy, and Delivery
9.4 Engineering Decision Making in a Corporate Setting
9.5 Summary
References
APPENDIX A ENGINEERING DECISION-MAKING
SOFTWARE EVALUATION CHECKLIST

Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.


Contents

APPENDIX B FOUR PRIMARY CONTINUOUS
DISTRIBUTIONS

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xiii


1

Engineering: Making Hard
Decisions Under Uncertainty
The goal of most engineering analysis is to provide
information or the basis for decision making.
Engineering decision making could range from
simply selecting the size of a column in a structure,
to selecting the site for a major dam, to deciding
whether a hybrid vehicle is a viable option for
transportation. However, uncertainties are invariably present in practically all facets of engineering
decision making. From this perspective, the
modeling and assessment of uncertainty is
unavoidable in any decision made during the
planning and design of an engineering system.

1.1 CASE STUDY: GALILEO'S CANTILEVER BEAM
Engineering design, analysis, modeling and testing are often built
upon assumptions, which can be traced back to engineering during
the Renaissance Age. The first proposition that Galileo set out to
establish concerns the nature of the resistance to fracture of the
weightless cantilever beam with a cantilever beam with a concentrated load at its end. In the Dialogues Concerning Two New Sci-

Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.


Chapter 1

ences, Galileo states his fundamental assumption about the behavior
of the cantilever beam of Figure 1.1 as follows:
It is clear that, if the cylinder breaks, fracture will occur at
the point B where the edge of the mortise acts as a fulcrum for the

lever BC, to which the force is applied; the thickness of the solid
BA is the other ann of the lever along which is located the resistance. This resistance opposes the separation of the part BD, lying
outside the wall, from that portion lying inside.

D

Figure 1.1 Galileo's loaded cantilever.
Here, Galileo sees the cantilever being pulled apart at section
AB uniformly across the section. Today's mechanical engineers can
easily recognize the following errors in the earliest cantilever beam
engineering model:
assuming a uniform tensile stress across the section AB

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Engineering: Making Hard Decisions Under Uncertainty

3

neglecting shear stress
A cantilever is a beam supported at one end and carrying a load
at the other end or distributed along the unsupported portion. The
upper half of the thickness of such a beam is subjected to tensile
stress, tending to elongate the fibers, the lower half to compressive
stress, tending to crush them. Cantilevers are employed extensively
in building construction and in machines. In a building, any beam
built into a wall and with the free end projecting forms a cantilever.
Longer cantilevers are incorporated in buildings when clear space is
required below, with the cantilevers carrying a gallery, roof, canopy,

runway for an overhead traveling crane, or part of a building above.
hi bridge building a cantilever construction is employed for
large spans in certain sites, especially for heavy loading; the classic
type is the Forth Bridge, Scotland, composed of three cantilevers
with two connecting suspended spans. Cantilever cranes are necessary when a considerable area has to be served, as in steel stockyards and shipbuilding berths. In the lighter types a central traveling
tower sustains the cantilever girders on either side. The big hammerhead cranes (up to 300-ton capacity) used in working on ships
that have proceeded from the yards to fitting-out basins have a fixed
tower and revolving pivot reaching down to rotate the cantilever in a
circle.
Beams that strengthen a structure are subject to stresses put
upon them by the weight of the structure and by external forces such
as wind. How does an engineer know that the beams will be able to
withstand such stresses? The answer to this question begins with the
linear analysis of static deflections of beams. Intuitively, the strength
of a beam is proportional to "the amount of force that may be placed
upon it before it begins to noticeably bend." The strategy is to
mathematically describe the quantities that affect the deformation of
a beam, and to relate these quantities through a differential equation
that describes the bending of a beam. These quantities are discussed
below.

Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.


Chapter 1

Material Properties
The amount by which a material stretches or compresses when subjected to a given force per unit area is measured by the modulus of
elasticity. For small loads, there is an approximately linear relationship between the force per area (called stress) and the elongation per
unit length (called strain) that the beam experiences. The slope of

this stress-strain relationship is the modulus of elasticity. In intuitive
terms, the larger the modulus of elasticity, the more rigid the material.
Load
When a force is applied to a beam, the force is called a load, since
the force is often the result of stacking or distributing some mass on
top of the beam and considering the resulting force due to gravity.
The shape of the mass distribution (or, more generally, the shape of
the load) is a key factor in determining how the beam will bend.
Cross section
The cross section of a beam is determined by taking an imaginary
cut through the beam perpendicular to the beam's bending axis. For
example, engineers sometimes use "I-beams" and "T-beams" which
have cross sections that look like the letters "I" and "T." The cross
section of a beam determines how a beam reacts to a load, and for
this module we will always assume that the beam is a so-called
prismatic beam with a uniform cross section. The important mathematical properties of a cross-section are its centroid and moment of
inertia.
Support
The way in which a beam is supported also affects the way the beam
bends. Mathematically, the method by which a beam is supported
determines the boundary conditions for the differential equation that
models the deflection of the beam.

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Engineering: Making Hard Decisions Under Uncertainty

5

Among the most crucial assumptions in the solution of any engineering problem is the assumption of how any particular mode of
failure will occur. As discussed before, a beam is said to be cantilevered when it projects outward, supported only at one end. A cantilever bridge is generally made with three spans, of which the outer
spans are both anchored down at the shore and cantilever out over
the channel to be crossed. The central span rests on the cantilevered
arms extending from the outer spans; it carries vertical loads like a
simply supported beam or a truss—that is, by tension forces in the
lower chords and compression in the upper chords. The cantilevers
carry their loads by tension in the upper chords and compression in
the lower ones. Inner towers carry those forces by compression to
the foundation, and outer towers carry the forces by tension to the
far foundations.
Like suspension bridges, steel cantilever bridges generally
carry heavy loads over water, so their construction begins with the
sinking of caissons and the erection of towers and anchorage. For
steel cantilever bridges, the steel frame is built out from the towers
toward the center and the abutments. When a shorter central span is
required, it is usually floated out and raised into place. The deck is
added last. The cantilever method for erecting prestressed concrete
bridges consists of building a concrete cantilever in short segments,
prestressing each succeeding segment onto the earlier ones. Each
new segment is supported by the previous segment while it is being
cast, thus avoiding the need for false work.
In Asia, wooden cantilever bridges were popular. The basic design used piles driven into the riverbed and old boats filled with
stones sunk between them to make cofferdam-like foundations.
When the highest of the stone-filled boats reached above the lowwater level, layers of logs were crisscrossed in such a way that, as
they rose in height, they jutted farther out toward the adjacent piers.
At the top, the Y-shaped, cantilevering piers were joined by long
tree trunks. By crisscrossing the logs, the builders allowed water to
pass through the piers, offering less resistance to floods than with a

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6

Chapter 1

solid design. In this respect, these designs presaged some of the advantages of the early iron bridges. In parts of China many bridges
had to stand in the spongy silt of river valleys. As these bridges were
subject to an unpredictable assortment of tension and compression,
the Chinese created a flexible masonry-arch bridge. Using thin,
curved slabs of stone, the bridges yielded to considerable deformation before failure.

Figure 1.2 A stone arch bridge.
Engineering builds upon assumptions, which are vulnerable to
uncertainties. Galileo's Dialogues Concerning Two New Sciences
includes what is considered the first attempt to provide an analytical
basis for the design of beams to carry designed loads. Galileo also
recognized the responsibility of designers in making things correctly
or incorrectly. Because Renaissance engineers did not fully understand the principles upon which they were building bridges, ships,
and other constructions, they committed the human errors that were
the ultimate causes of many design failures. However, Galileo set
out to lay the foundations for a new engineering science. This foun-

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Engineering: Making Hard Decisions Under Uncertainty

7

dation gives today's engineers the analytical tools to eliminate errors
from their conceptions and explorations.
1.2 IMPACT OF ENGINEERING DECISION MAKING
The Hyatt Regency Hotel was built in Kansas City, Missouri in
1978. A state-of-the-art facility, this hotel boasted a 40 story hotel
tower and conference facilities. These two components were connected by an open concept atrium. Within this atrium, three suspended walkways connected the hotel and conference facilities on
the second, third and fourth levels. Due to their suspension, these
walkways were referred to as "floating walkways" or "skyways."
The atrium boasted 17 000 square ft (1584 m2) and was 50 ft (15m)
high. It seemed unbelievable that such an architectural masterpiece
could be the involved in the United States' most devastating structural failure in terms of loss of life and injuries.
It was July 17, 1981 when the guests at the brand new Hyatt
Regency Hotel in Kansas City witnessed a catastrophe. Approximately 2000 people were gathered to watch a dance contest in the
hotel's state-of-the-art lobby. While the majority of the guests were
on the ground level, some were dancing on the floating walkways on
the second, third and fourth levels. At about 7:05 pm a loud crack
was heard as the second-and fourth-level walkways collapsed onto
the ground level. This disaster took the lives of 114 people and left
over 200 injured.
The failure of the Hyatt Regency walkway was caused by a
combination of a few things. The original construction consisted of
beams on the sides of the walkway which were hung from a box
beam. Three walkways were to exist, for the second, third and fourth
floor levels. In the design, the third floor would be constructed completely independent of the other two floor walkways. The second
floor would be held up by hanger rods that would be connected
through the fourth floor, to the roof framing. The hanger rods would
be threaded the entire way up in order to permit each floor to be held

Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.

8

Chapter 1

up by independent nuts. This original design was designed to withstand 90 kN of force for each hanger rod connection. Since the bolt
connection to the wide flange had virtually no moment, it was modeled as a hinge. The fixed end of the walkway was also modeled as a
hinge while the bearing end was modeled as a roller.

Figure 1.3 The original walkway design.
The new design, created in part to prevent the necessity of requiring the thread to be throughout the entire rod, consisted of one
hanger connection between the roof and the fourth floor and a sec-

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Engineering: Making Hard Decisions Under Uncertainty

9

ond between the second and the fourth floor. This revised design
consisted of the following:
one end of each support rod was attached to the atrium's
roof crossbeams;
the bottom end went through the box beam where a washer
and nut were threaded on;
the second rod was attached to the box beam 4" from the
first rod;
additional rods suspended down to support the second level

in a similar manner.
Due to the addition of another rod in the actual design, the load
on the nut connecting the fourth floor segment was increased. The
original load for each hanger rod was to be 90 kN, but with the design alteration the load was increased to 181 kN for the fourth floor
box beam. Since the box beams were longitudinally welded, as proposed in the original design, they could not hold the weight of the
two walkways. During the collapse, the box beam split and the support rod pulled through the box beam resulting in the fourth and
second level walkways falling to the ground level.
The collapse of the Kansas City Hyatt Regency walkway was a
great structural mishap which can be explained in terms of the
common results of most structural disasters. In general there exist
six main causes for most structural failures.
a lack of consideration for every force acting on particular
connections. This is especially prevalent in cases in which a
volume change will effect the forces;
abrupt geometry changes which result in high concentrations of stress on particular areas;
a failure to take motion and rotation into account in the design;

Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.