Toward Considering Risk Attitudes in Engineering Organizations Using Utility Theory

Proceedings of the ASME 2012 International Design Engineering Technical Conferences &Computers and Information in Engineering Conference

IDETC/CIE 2012August 12-15, 2012, Chicago, IL, USA

DETC2012/DTM-70399

TOWARD CONSIDERING RISK ATTITUDES IN ENGINEERING ORGANIZATIONSUSING UTILITY THEORY

Douglas Van Bossuyt∗

Complex Engineered Systems

Design Laboratory

School of Mechanical, Industrial,

and Manufacturing Engineering

Oregon State University

Corvallis, OR 97331

Email: [email protected]

Chris Hoyle

Complex Engineered Systems

Design Laboratory




Corvallis, OR 97331

[email protected]

Irem Y. TumerComplex Engineered Systems

Design Laboratory




Corvallis, OR 97331

[email protected]

Andy DongDesign Lab

Faculty of Architecture,

Design, and Planning

University of Sydney

Sydney, NSW, 2006, Australia

[email protected]

Toni DoolenSchool of Mechanical, Industrial,



Corvallis, OR 97331

[email protected]

Richard Malak

Design Systems Laboratory

Department of Mechanical Engineering

Texas A&M University

College Station, Texas 77843

[email protected]

ABSTRACT

Design projects within large engineering organizations in-

volve numerous uncertainties that can lead to unacceptably high

levels of risk. Practicing designers recognize the existence of risk

and commonly are aware of events that raise risk levels. How-

ever, a disconnect exists between past project performance and

current project execution that limits decision-making. This dis-

connect is primarily due to a lack of quantitative models that

can be used for rational decision-making. Methods and tools

used to make decisions in risk-informed design generally use an

expected value approach. Research in the psychology domain

has shown that decision-makers and stakeholders have domain-

specific risk attitudes that often have variations between individ-

uals and between companies. Risk methods used in engineer-

ing such as Failure Modes and Effects Analysis (FMEA), Fault

∗Address all correspondence to this author.

Tree Analysis (FTA), and others are often ill-equipped to help

stakeholders make decisions based upon risk-tolerant or risk-

averse decision-making conditions. This paper focuses on the

specific issue of helping stakeholders make decisions under risk-

tolerant or risk-averse decision-making conditions and presents

a novel method of translating engineering risk data from the do-

main of expected value into a domain corrected for risk attitude.

This is done by using risk utility functions derived from the

Engineering-Domain-Specific Risk-Taking (E-DOSPERT) test.

This method allows decisions to be made based upon data that is

risk attitude corrected. Further, the method uses an aspirational

measure of risk attitude as opposed to existing lottery methods

of generating utility functions that are based upon past perfor-

mance. An illustrative test case using a simplified space mis-

sion designed in a collaborative design center environment is in-

cluded. The method is shown to change risk-informed decisions

1 Copyright © 2012 by ASME

in certain situations where a risk-tolerant or risk-averse decision-

maker would likely choose differently than the dictates of the

expected value approach.

INTRODUCTION

Risk is found throughout the complex system design pro-

cess, and recognizing and reacting to design project risk is a

key challenge within large engineering organizations. Practic-

ing designers recognize the existence of risk and commonly are

aware of events that raise risk levels. However, a disconnect ex-

ists between past project performance and current project execu-

tion that limits decision-making. Although designers may recall

a few cases from personal experience and be aware of anecdo-

tal evidence, rarely do they have access to a quantitative and

empirically-based model of how risk-mitigating actions impact

project outcomes. Further, when designing novel or innovative

products, the designer often aspires to create something that has

not been done before. The ability to quantitatively take aspi-

rational risk attitude into consideration in decision-making does

not exist. However, dealing with design risk in industrial orga-

nizations is a largely qualitative and informal endeavor. This

assessment was confirmed in interviews with leaders, project

managers, and designers in engineering organizations. Although

project leaders tend to have a qualitative understanding of the

events that lead to design risk and of the mitigating actions they

can take, they lack an empirically-based and quantitative ap-

proach to making informed design project decisions. Project

leaders might make decisions based on past experiences or anec-

dotal evidence provided by others, but the exchange of such in-

formation remains ad-hoc and rarely, if ever, is quantitative.

Engineering methods such as FTA, FMEA, and others are

commonly used to identify risks and aid in the risk-informed

decision-making process. In addition, there are many methods

that have been proposed in the engineering design research com-

munity to account for risk during the early stages of conceptual

design. Some pertinent examples are Functional Failure Identifi-

cation Propagation (FFIP) [1], Risk in Early Design (RED) [2],

Function Failure Design Method (FFDM) [3], and FMEA [4]

among others. Such methods are designed to guide decision-

makers away from more risky options and toward the least risky

options which results in the mitigation of large risks and the

creation of risk-averse or fault-tolerant designs. This approach

works well for industries, such as nuclear power and aerospace,

that are traditionally risk-averse. However, some industries and

companies thrive on risk taking. For instance, many of the most

successful Internet companies such as Google and Facebook, and

design innovation companies such as IDEO have become so suc-

cessful because they have sought out risks that traditional risk-

averse companies have not been willing to take. There is no cor-

rect level of risk that can be applied to all industries and compa-

nies.

This paper focuses on this aspect of quantifying risk in en-

gineering organizations. However, none of available risk assess-

ment methods have the ability to account for risk attitudes of

individual decision-makers or enterprises. The methods such

as FTA and FMEA, and tools such as trade studies commonly

deployed in industrial settings, view risk as an expected value

choice. For example, if an engineer must make a decision be-

tween one risk that has a 1% chance of occurrence and has a

consequential cost of $10,000 and another risk that has a chance

of 0.1% of occurrence and a consequential cost of $100,000, en-

gineering risk methods would indicate that both risks are equal

with regards to expected value. Therefore, either can be cho-

sen with the same expected value outcome. However, this ig-

nores individual and company risk preferences. Research over

the past two decades has produced the well-respected Domain-

Specific Risk-Taking (DOSPERT) test which enables the deter-

mination of risk attitude in several different content domains of

daily life [5]. Recent advances in the psychology of engineering

risk attitude have created the E-DOSPERT test that attempts to

categorize and determine engineering-specific risk domains [6].

This research seeks to create a link between the E-DOSPERT’s

engineering risk attitude information and traditional widely used

engineering risk methods to allow for individual and enterprise

risk attitudes to be expressed during the risk decision-making

process.

CONTRIBUTIONS

This paper specifically presents a novel method of account-

ing for aspirational risk attitude in risk-informed design. A single

criterion decision based design approach is adapted from risk at-

titude utility functions to bring engineering risk data from the

expected value domain into a risk attitude corrected domain that

is created to be appropriate to the individual stakeholder or en-

terprise. Rather than traditional lottery methods found in risk

utility function generation, the risk attitude utility functions are

developed via E-DOSPERT test results. Using risk attitude as

a lens stakeholders and decision-makers can make quantitative

risk decisions that would have been traditionally justified by “gut

feeling.” This paper draws an important distinction between ap-

propriate uses of E-DOSPERT-derived risk utility functions and

lottery-derived risk utility functions. While lottery methods are

suitable for later stages of the complex conceptual system design

process and beyond into physical design, the authors advocate

for using E-DOSPERT-derived risk utility functions in the early

phases of complex conceptual system design where aspiring to

create a new design can take precedence over developing a de-

sign based upon past performance.

This method will be useful for risk-averse enterprises and

decision-makers by highlighting higher certainty risks. A risk-

averse stakeholder generally favors high over low certainty op-

tions. Similarly, decision-makers who are and decision-makers

in industries where the corporate culture is risk-tolerant will find


that this method identifies large risks that can drive potential in-

novation and profit. For these reason, this paper develops a novel

way to account for risk attitude in risk-informed design. As such,

the method introduced in this paper will get us one step closer to

handling risk in large engineering organizations.

BACKGROUND

Assessing and Judging Risk

Risk plays an integral role in engineering organizations, yet

is handled differently depending on the type of business. For ex-

ample, highly innovative design firms embrace risk as an essen-

tial ingredient in their success. On the other hand, some entire

industries such as aerospace and nuclear power, are very risk-

averse. Research in risk trading in engineering design shows that

different engineers have different opinions of what makes an ac-

ceptable risk [7], and indicates that there is no single correct level

of acceptable risk for all situations or all people.

In psychology, risk is classically defined as the parameter

that differentiates between different individuals’ utility functions

[8]. The utility function of individuals is often expressed as a

quadratic, logarithmic, or exponential function [9]. This classic

Expected Utility (EU) approach to risk theorizes that an individ-

ual can be modeled choosing between risky options as the func-

tion of the return of the options, the probability of the options oc-

curring, and the risk aversion of the individual [10]. Within the

EU framework and other related methods [11], the shape of an

individual’s utility function denotes the individual’s risk attitude

as either risk-averse (i.e., someone who does not like to take risks

and desires certainty of outcome), risk neutral (i.e., someone who

takes necessary short-term risks to deliver long-term outcomes),

or risk-tolerant (i.e., someone who is comfortable with handling

larger risks, as defined by probability of the risk being realized,

if necessary and accepts more uncertainty in outcomes) behav-

ior [12, 13].

The theory of risk attitudes in the context of EU has encoun-

tered issues of inconsistent risk profiles across risk domains and

cross-method utility instability [14–17]. Different risk-averse or

risk-tolerant classifications often result when different methods

are used to measure people’s utility [14]. Further, individuals

are not consistent across different risk domains. While a person

might be risk-averse making financial decisions, they could be

risk-seeking in social situations [17].

Other methods have been developed within psychology to

make up for the shortcomings of the EU framework. For in-

stance, the risk-return framework of risky choice models people’s

preference for risky options based upon a trade-off between the

Expected Value (EV) and the riskiness of the choice [18]. This

is analogous to the way most engineering risk methods differen-

tiate between risk choices. Psychology extends this to treat per-

ceived risk as a variable that differentiates individuals based upon

content and context interpretations. The framework allows peo-

ple to have different risk preferences in different pre-determined

domains [5] and accounts for desiring risk in some areas while

preferring caution in others by the concept of perceived risk at-

titude. Variances in perceived risk attitude are viewed to be the

result of differences in perception of risks and benefits between

a decision-maker and an outside observer. For instance, in the

management field, managers have less optimistic perceptions of

risk than entrepreneurs [19]. The risk-return framework shows

that a person’s perception of risk affects the choices that person

will make.

In order to assess risk perceptions and attitudes within dif-

ferent domains, the DOSPERT test and related scale were cre-

ated [5]. Six independent domains were identified including the

ethical, investment, gambling, health/safety, recreational, and so-

cial domains within which the majority of day-to-day activities

can be categorized. The DOSPERT test is seeing widespread

adoption in psychology. Recently, the E-DOSPERT test [6] was

proposed as a method to determine engineering-specific risk at-

titudes as defined by four engineering risk domains including

risk identification, analysis, evaluation, and treatment [20]. The

E-DOSPERT scale has been shown to reliably measure general

engineering risk aversion and risk seeking attitudes. It can also

measure risk seeking and risk aversion attitudes in the risk iden-

tification and risk treatment domains. The 25 question version

of the E-DOSPERT test takes approximately 10 minutes to com-

plete.

Trading During Design

Trade studies are often used in creating conceptual com-

plex system designs. Trade studies can be used to create many

potential designs quickly through automated software packages

such as ModelCenter (http://www.phoenix-int.com) or Advanced

Trade Space Visualization (ATSV) [21] as part of ModelCenter.

Trade studies are also used by teams of people to conduct man-

ual trade study sessions [22]. Automated trade studies can also

be performed by computers using conditions and bounds set by

users. Many thousands of conceptual designs can be quickly cre-

ated with an automated trade study. Manual trade studies are con-

ducted by groups of system experts where only one or a handful

of conceptual designs will result.

The primary goal in a design trade study is to maximize

system-level utility. In order to achieve maximum utility, trade-

offs are made between system design variables [23]. This can be

represented as max f (Ð⇀U ) where

Ð⇀U represents relevant system

utility metrics. Design stakeholders choose system utility met-

rics. In the case of trade studies with multiple stakeholders, the

most preferred design of one stakeholder will not be the same as

that of another. Little direction is given in the literature on how

to create appropriate utility functions and selection criteria for

different design situations.

Collaborative Design Centers (CDCs) often will perform

manual trade studies as part of the design process. The most

cited example of a CDC is Team X which is housed in the Project


Design Center (PDC) at Jet Propulsion Laboratory (JPL) and de-

velops conceptual spacecraft mission designs [22]. In such man-

ually conducted trade studies, subsystem experts often disagree

over which tradeable parameters are the most important [24–26].

A variety of methods are available to resolve design decision

conflicts in both automated and manual trade studies [27, 28].

However, these methods do not take into account individual or

enterprise-level risk attitudes.

Decision Making

Finally, the Decision-Based Design (DBD) framework was

developed in the research community to address the growing

recognition [29–32] that decision-making is a fundamental part

of the design process. A decision-theoretic methodology is uti-

lized to select preferred product design alternatives and set target

product performance levels. A single selection criterion, V, in

the DBD implementation represents economic benefit to the en-

terprise [32]. This approach avoids the difficulties of weighting

factors and multi-objective optimization. A utility function, U,

which expresses the value of a designed artifact to the enterprise

when considering the decision-maker’s risk attitude, is created as

a function of the selection criterion, V. A preferred concept and

attribute targets are selected through the maximization of enter-

prise utility.

In order to effectively use the single criterion approach to

DBD, the selected criterion must be able to capture all of the is-

sues involved in the engineering design such as system features,

costs, risks, physical restrictions, and regulatory requirements.

The single criterion should allow both the interests of the users

and producers of the system to be considered. In most industrial

cases, the most universal unit of exchange is money. Material,

energy, information, faults and time can all be assigned a mon-

etary value. This can be seen in many design decision-making

processes and is practiced widely in industry.

One use of single criterion DBD developed by Hoyle et al.

[33] employs profit as the criterion in a method to determine op-

timum system configuration for Integrated Systems Health Man-

agement (ISHM). The determination of system profit is made

from the product of system availability and revenue, minus the

summation of cost of system risks, and the cost of fault detection.

This method can determine optimal ISHM while also determin-

ing the optimum detection/false alarm threshold and inspection

interval. Using the method has been found to increase profit by

11%, decrease cost by a factor of 2.4, and increase inspection

intervals by a factor of 1.5 [33].

Utility Theory

One approach to analyzing choice outcomes from a non-

neutral expected value perspective is to use risk-based utility

theory [11]. The utility of a range of probabilistic outcomes

can be determined in order to aid decision-makers. This is

done by translating monetary outcomes to utilities. A risk-

tolerant decision-maker’s higher intrinsic value for riskier de-

cisions skews the utility of those decisions higher than a risk-

neutral or risk-averse decision maker’s utility of the same deci-

sions. Figure 1 shows that for a Normal distribution of outcomes,

a risk-tolerant person’s utility distribution will shift to be more

heavily skewed toward higher value outcomes. Utility distribu-

tions for risk-averse individuals will skew more heavily toward

lower value outcomes, as can be seen in Figure 2. The risk neu-

tral state, shown in Figure 3, does not weight outcomes in ei-

ther direction along the utility axis. As can be seen in Figures

1 through 3, different utilities are found based upon a decision-

maker’s risk attitude.

FIGURE 1.

Risk-Tolerant

Utility Function.

FIGURE 2.

Risk-Averse

Utility Function.

FIGURE 3.

Risk Neutral

Utility Function.

Currently accepted methods of developing utility risk func-

tions, such as those in Figures 1 through 3, often require a series

of lotteries to be conducted [11]. Several sets of paired choices

are presented sequentially to an individual. These are often pre-

sented as lotteries where a participant selects amongst paired

probabilistic alternatives. A utility function is then fitted to the

lottery results. In currently accepted methods of utility function

generation, the form utility function is found that is consistent

the decision maker’s lottery results. The scale of the value axis

of the utility function is set to the minimum and maximum limits

of the values used to conduct the lotteries.

Developing and conducting lotteries can be time-consuming

and not intuitive to end-users [34]. Also, the utility functions de-

rived from lotteries are only valid for the range of values used in

the lottery. Therefore, while useful in many areas, lottery-based

methods of utility risk function generation are not always useful.

Pennings and Smidts [34] investigated using psychometric risk

attitude test results to create risk functions for Dutch hog farm-

ers to predict individual farmer behavior in hog futures markets.

The results of the research found lotteries to be the most accurate

method of predicting behavior in the context of the hog futures

market. However, the hog farmers’ self-reported behavior pre-

dictions were most closely correlated with the psychometric risk

attitude test results. The farmers also indicated that the psycho-


metric risk attitude test was more understandable than the lottery

method.

In this paper, the authors postulate that, while lottery meth-

ods of utility risk function generation are satisfactory for many

DBD situations, they are not as useful for early-phase conceptual

design. Lottery-based risk functions are only valid over the range

of values used in the initial lotteries. In the case of early-phase

conceptual design, the range of values might not be fully known

or could change during the design process. Re-running lotteries

to create expanded risk functions thus would become burden-

some to the practitioner. Further, in cases where utility functions

are developed based upon client or customer risk attitudes, con-

ducting multiple lottery sessions is impractical. Finally, as hinted

at in Pennings and Smidts’ research [34], lotteries do not closely

match what individuals believe they will do. However, actions of

individuals more closely align to the predictions of lottery meth-

ods than to self-reported methods. This can be interpreted as a

disconnect between what individuals aspire to do and what they

actually do. Utility functions generated by alternative methods

could potentially provide new insights for practitioners that will

allow decisions to be made based upon aspirations rather than

upon past performance, as is the case with lotteries.

METHODOLOGY

The long-term goal of this research is to develop a quanti-

tative model derived from empirical project data to make design

project decisions. To achieve this, project decision preferences

must be determined and formalized in terms of a utility function.

For example, preferences associated with commercial products

may be to maximize profitability under a particular risk attitude.

Given this utility function, project leaders must observe the state

of their project as it unfolds, determine the most preferred risk-

mitigating action, and execute the chosen course of action. Be-

fore this goal can be achieved, however, the ability of the various

stakeholders in assessing and judging risk must be addressed.

Risk-informed design methods are used to make decisions

about risk in system design, with tools such as FMEA and FTA

commonly used to evaluate system safety and reduce the likeli-

hood of failure. Such methods take an expected value approach

toward all engineering risk domains. However, design stakehold-

ers often have domain-specific risk attitudes that are not risk neu-

tral. This paper proposes a novel method to determine the true

value of risk decisions using utility theory and the E-DOSPERT

risk attitude research in an aspirational context. The method pre-

sented in this paper translates data from engineering risk methods

such as FMEA or FTA into utility functions

The Risk Attitude Premise

Using the proposed approach, risk-informed design deci-

sions can be made under risk tolerant or risk averse risk attitudes

rather than the expected value approach. For example, the mutu-

ally exclusive, distinct risks in Equations 1 and 2 are equal in the

context of risk-informed design. The risks are defined as such

due to the negative expected value outcome and would be de-

fined as benefits if the expected value were positive. In Equation

1, a 1% chance exists that a risk costing $10,000 to return the

system to a nominal operating state will occur while in Equation

2, there is a 0.1% chance of realizing a risk that costs $100,000

in order to return the system to a nominal state. Equation 2 rep-

resents a case in which additional system complexity has been

added to the base design of Equation 1, which has lowered the

probability of losing system functionality but has increased the

repair cost in the event of a fault. Both risks have an expected

value of -$100. Therefore, a decision-maker using risk-informed

design would have no guidance if choosing between the two de-

signs. The designs are of equal value using the expected value

approach within risk-informed design.

R1 = 0.99(0)+0.01(−$10,000) = −$100 (1)

R2 = 0.999(0)+0.001(−$100,000) = −$100 (2)

Equations 1 and 2 are of the form Rn = B+Am+Am+1+ . . .+Am+x where B = probability of benefit × outcome of benefit and

Am+x = probability of riskm+x× outcome of riskm+x. The bene-

fit and risk probabilities all sum to 100%. This research is only

interested in risks and their costs. Therefore all benefits are con-

sidered to be identical between risk choices, i.e., the full system

benefit is realized when the system is not in a fault state and is

equal among all design variants. For the purposes of this paper,

the outcome of the benefit is taken to always be zero.

Risk-informed design instructs decision-makers that the

choice between the risk in Equation 1 and the risk in Equation 2

does not matter because both outcomes have the same expected

value. However, a risk-averse decision-maker will choose the de-

sign in Equation 2 in order to have more certainty about the like-

lihood of occurrence of the risk. A risk-tolerant decision-maker

is not as concerned with certainty and will choose the design in

Equation 1 due to the lower financial consequence. The example

in Equations 1 and 2 has a clear choice outcome for risk-averse

and risk-tolerant decision-makers. The design choice presented

in Equations 3 and 4 is less clear for decision-makers that are not

risk neutral. One cannot rationalize the choice of a design charac-

terized by Equation 3 using risk-informed design. However, the

risk-tolerant decision-maker might still choose the design with

a larger negative expected value because she is more concerned

with the lower financial consequence than the certainty of the

outcome.

R1 = 0.99(0)+0.01(−$15,000) = −$150 (3)

R2 = 0.999(0)+0.001(−$100,000) = −$100 (4)


The risk-tolerant decision-maker’s higher intrinsic value for

the riskier decision in this example can be examined through the

lens of utility theory. Figures 1, 2, and 3 demonstrate how risk at-

titude can affect the utility of a value distribution. Figure 1 shows

that for a Normal distribution of outcomes, a risk-tolerant per-

son’s utility distribution will shift to be more heavily skewed to-

ward higher value outcomes. Utility distributions for risk-averse

individuals will skew more heavily toward lower value outcomes,

as can be seen in Figure 2. The risk neutral state, shown in Figure

3, does not weight outcomes in either direction along the utility

axis.

Utility Risk Functions Derived from Risk Attitude Data

Utility functions derived from discrete outcome distributions

can also be affected by risk attitudes. The utility for a system

feature with two potential discrete outcomes takes the form of

Equation 5 where u(s) represents the system utility, p0 is the

probability of the first outcome, u(xH) is the utility of the first

outcome, (1− p0) is the probability of the second outcome, and

u(xL) is the utility of the second outcome.

u(s) = p0×u(xH)+(1− p0)×u(xL) (5)

A generic utility problem where risk is represented as a dol-

lar figure is shown in Equation 6.

u(s) = 0.4×u($900)+0.6×u($400) (6)

Figure 4, developed via a series of lotteries, where the min-

imum value is $250 and maximum is $1,050, provides a risk-

averse quadratic utility function. Determining the utility of each

potential outcome is demonstrated in Equation 7 where the utility

of $900 is found to be 0.91 via inspection of the utility function,

as shown in Figure 4, and the utility of $400 is found to be 0.35

from the risk utility function as demonstrated in Figure 4.

u(s) = 0.4×(0.91)+0.6×(0.35) = 0.57 (7)

These utilities are then multiplied by their respective prob-

abilities and summed together to find the overall system util-

ity, u(s) = 0.57, for this risk-averse decision-maker. Reversing

the procedure, a utility of 0.57 produces a risk-adjusted value

of u−1 = $540 while a neutral utility function results in a risk-

adjusted value of u−1 = $600. This clearly shows that using risk

attitude in a utility function results in a different valuation of the

system than would be found without using a risk attitude func-

tion.

As previously discussed, while risk utility functions gen-

erated using lottery methods are useful in many situations,

early-phase conceptual design can benefit from an alternative

method. The authors propose using risk functions generated

from E-DOSPERT test results. Based upon the findings of

FIGURE 4. Risk-Averse Quadratic Utility Function Developed Using

the Lottery Method. The value of the potential outcomes is translated

via the risk averse utility function to the utility domain. The two utilities

are then combined using Equation 5, and translated back through the

risk averse utility function to find the risk-adjusted value of $540. Using

the risk neutral utility function, a value of $600 is found.

Van Bossuyt et. al. [6], the 25 question E-DOSPERT test pro-

vides sufficient statistical reliability to determine general engi-

neering risk tolerance or risk aversion. The authors propose the

mean of one’s responses to the 25 question E-DOSPERT test is

an appropriate metric for use with utility function assessment.

E-DOSPERT makes use of a 1-5 Likert Scale with 1 correspond-

ing to “Very Unlikely” and 5 corresponding to “Very Likely.” A

score of 3 corresponds to the neutral answer of “Not Sure.” Us-

ing the 25 risk tolerant questions in the E-DOSPERT test, a mean

score of 3 indicates a neutral risk attitude, a mean score of 5 in-

dicates extreme risk tolerance, and a mean score of 1 indicates

an extremely averse risk attitude.

In this research, the authors suggest that an exponential

function is an appropriate utility function to use with psychomet-

ric risk scale test results. The function may be either of the mono-

tonically increasing or decreasing exponential type [35]. An ex-

ponential function was chosen over other potential functions be-

cause it is believed that practitioners will be either constantly

risk averse or constantly risk tolerant during the early phases of

conceptual system design. In one study where a risk survey was

compared to the lottery method, it was found that risk functions

generated by the lottery method were exponential in nature [34].

Further, there was reasonable correlation between the risk sur-

vey results and lottery method results. Risk survey results were

also found to more closely align with self-predicted future per-

formance than lottery methods that were found to more closely

align with past performance [34]. Research is ongoing in this

area to verify that this holds true for the E-DOSPERT.

The choice of an exponential function also allows the direct

use of E-DOSPERT test results in the creation of a risk func-


tion [9]. The monotonically decreasing exponential utility func-

tion presented by Kirkwood [35] and developed by Pfanzagl [36]

shown in Equation 8 is used throughout the rest of this paper.

U(V) represents utility of the potential value(s) of interest. VMax

is the maximum possible value. It should be noted that VMax

need not be the maximum value of the range of potential val-

ues of interest but can be a larger number than the maximum

potential value of interest. This property is useful in situations

where a larger maximum value is possible than the set of poten-

tial values currently being investigated or when multiple sets of

potential values, representing multiple sets of outcomes of a de-

cision choice, span different numerical ranges. Similarly, VMin

is the minimum possible value which need only be smaller than

or equal to the smallest potential value of interest. Note that

VMin can either be a positive or negative number. R is the risk

tolerance/aversion coefficient of the utility function. In order to

convert an E-DOSPERT mean score (EDSMean) to an R value,

Equation 9 was developed by the authors based upon the work

of Kirkwood [35], Howard [37], and McNamee and Celona [38].

In Equation 9, RSF is a scaling factor. Several different rules

of thumb based upon financial measures are available to deter-

mine RSF such as finding a sufficient RSF that R will be roughly

6% of net sales, a 100-150% of net income, and about 16

of eq-

uity [37]. These rules of thumb have been found useful in the oil

and chemical industries [37]. Additional suggestions are given

by Kirkwood [35] and McNamee and Celona [38]. It is impor-

tant that the practitioner select an RSF that is appropriate to their

industry, company, and the specific analysis being performed. It

is beyond the scope of this paper to provide strict guidance on do-

main and situation-appropriate RSF values. It is also beyond the

scope of this paper to judge if practitioner level of expertise can

influence the selection of appropriate rules of thumb. For the ex-

amples and illustrations presented in this paper, RSF = 60 will be

used to clearly demonstrate the novel method to determine true

value of risk decisions using utility theory and the E-DOSPERT

test.

U(V) =e−

VMax−V

R −1

e−VMax−VMin

R −1(8)

R =VMax−VMin

1000∗

RSF

EDSMean−3(9)

The inverse of Equation 8, shown in Equation 10, is used

to calculate the certainty equivalent. CE(V) represents the

risk-adjusted value of the potential values of interest, otherwise

known as the certainty equivalent. In the method presented in this

paper, CE(V) is presented as a cost. In the special case of an E-

DOSPERT test result where the test-taker is found to have a per-

fectly risk neutral risk attitude, Equations 11 and 12 are used to

generate the risk utility function and find the risk-adjusted value

FIGURE 5. Monotonically Decreasing Exponential Risk Util-

ity Functions Developed Using Equation 8 where EDSMean =

2.8,2.9,3.0,3.1,3.2, RSF = 60, VMax = 1000, and VMin = 0.

of the potential values. Examples of monotonically increasing

exponential utility functions can be found in Kirkwood [35].

Other risk utility functions of potential interest to the practi-

tioner are available in Keeney and Raiffa [9]. A series of risk

utility functions generated in MATLAB using Equation 8 from

E-DOSPERT mean scores of EDSMean = 2.8,2.9,3.0,3.1,3.2,

VMax = 1000, VMin = 0, and RSF = 60 is shown in Figure 5.

CE(V) = R∗ log(−U(V)∗(eVMax

R −eVMin

R )−eVMax

R ) (10)

U(V) =VMax−V

VMax−VMin

(11)

CE(V) =U(V)∗(VMin−VMax)+VMax (12)

Risk Metrics Generated by Risk Methods

In order for engineering risk methods to make use of risk

attitude utility functions, risk metrics generated by the various

engineering risk methods must be translated into an easily com-

parable unit of measure. The authors advocate using consequen-

tial cost as it is a convenient and easily understood unit of mea-

sure. Consequential cost in the context of this research can be

defined as either the cost associated with the realization of a risk,

for instance replacement of a failed part, or as the price to mit-

igate the risk to an acceptable level. The case study in this pa-

per uses the latter definition of consequential cost. Therefore,

in order to use this risk attitude utility method, both consequen-

tial cost and probability must be determinable for the risks iden-

tified by engineering risk methods. Standard engineering tools

used in the design process often contain the necessary risk infor-

mation, but require translation into the appropriate probability

and cost metrics. For example, translating risk information from

an FMEA into probability and consequential cost is relatively

straightforward. Probability can be derived from the occurrence

metric. The occurrence metric is a measure of the probability

of an averse event occurring. In the case of a purely linear oc-

currence metric scale, the percent chance of failure can be found


by multiplying occurrence, Occ, by an appropriate factor, Oc f .

When the occurrence scale is not linear, an appropriate function

can be used to translate the occurrence metric into a probability

value. In the case of a linear occurrence metric scale, Oc f should

be determined by dividing 100 by the result of subtracting the

low (OccMin) end of the occurrence metric scale from the high

(OccMax) of the scale, as shown in Equation 13. Probability, P0,

can then be determined by Equation 14 where P1→n represents

the complete set of probabilities under consideration.

Oc f =100

OccMax−OccMin

(13)

P0 = 1−

Occ∗Oc f

100

∑P1→n

(14)

Consequential cost, representing value, can be determined

in a variety of manners. The authors suggest that consequential

cost should be determined by the cost to return the system to a

nominal state if the risk occurs. In the event that consequential

cost cannot be directly determined, a summation of the severity

and detection metrics can be used as an analogue metric to con-

sequential cost.

Table 1 provides a simplified FMEA for a complex sys-

tem design with three identified risks and the consequential cost

of each risk. Decision-Maker A has been tasked with decid-

ing which risk is the most important to fix. Decision-Maker A

has a risk-averse attitude where EDSMean = 2.88. The general-

ized form of Equation 5 is used in this example by setting p0

equal to Equation 14 where OccMax = 10, OccMin = 0, Oc f = 0.1,

VMin = $250, VMax = $1,050, and RSF = 20. Using a risk-averse

utility function generated from Equation 8 and Equation 5 ,the

risk-averse Decision-Maker A discovers that the most desirable

certainty equivalent choice to mitigate is CE(R3) = $2.9184,

while CE(R1) = $0.8909 and CE(R2) = $1.1292. Therefore, the

risk-averse decision is to mitigate the R3 risk as it has the high-

est certainty equivalent value. Certainty equivalents with higher

value are more desirable to mitigate than certainty equivalents

with lower values [39].

TABLE 1. Simplified FMEA Example for Decision-Maker A.

Risk Func. Sev. Occ. Det. RPN Cons. Cost

R1 Funct 1 7 3 4 84 $450

R2 Funct 2 4 5 8 160 $300

R3 Funct 3 2 8 3 48 $650

This method can also be used to compare between differ-

ent designs. For instance, using Table 1 as Design 1 and Ta-

ble 2 as Design 2, a risk-tolerant person, Decision-Maker B,

with an E-DOSPERT mean score of EDSMean = 3.15 can de-

termine which design is more preferred. Using the monoton-

ically decreasing exponential risk function of Equation 8 with

VMax = $1,000, VMin = $0, OccMax = 10, OccMin = 0, Oc f = 0.1,

RSF = 60, XH = 0, and XL =V(Rn) the utilities of risks, probabili-

ties, system utilities, and risk-adjusted values are found as shown

in Table 3. Equation 15 is then used to find the overall certainty

equivalents (CE) of the two designs where CEn(Rn) is the risk-

adjusted value of the individual identified risk, Rn. Equation 15

is valid when the identified risks are independent from one an-

other. Equation 15 is used rather than Equation 10 because each

of the risks identified in the FMEA presented in Tables 1 and

2 is an independent risk. Applying Equations 8 and 15 shows

that the risk-tolerant Decision-Maker B with an EDSMean = 3.15

would choose Design 1 as it has the smallest certainty equiva-

lent. Decision-Maker C who has an expected value risk neutral

decision making criteria would find Design 1 to have CE = $8.05

and Design 2 to have CE = $5.50, and thus would choose Design

2 as it has a lower certainty equivalent than Design 1. The lower

certainty equivalent is chosen when comparing between designs

due to certainty equivalent representing the risk-adjusted cost of

mitigating the identified risks within the designs.

CE(RTotal) =CE1(R1)+ . . .+CEn(Rn) (15)

TABLE 2. Simplified FMEA for Design 2 for Decision-Maker B.


R1 Funct 1 5 4 4 80 $400

R2 Funct 2 6 5 7 210 $700

R3 Funct 3 3 2 3 18 $200

CASE STUDYTo implement and test the proposed approach, NASA was

selected as the engineering organization in this paper. Specifi-

cally, the SuperNova/Acceleration Probe (SNAP) mission trade

study [40] performed by Team X provides the bulk of the back-

ground information necessary for this case study. Additional ma-

terial comes from the Space Mission Analysis and Design book

by Wertz and Larson [41]. Costing and risk data are simulated

for illustrative purposes only and should not be used beyond this

case study.

The SNAP mission was intended to investigate the nature

and origin of “Dark Energy” acceleration and expansion of the

universe. The experiment was designed to precisely measure the

history of the universe’s expansion from the present day back

to approximately 10 billion years in the past. Plans called for a


TABLE 3. Utility of Risk, Probability, and Risk-Adjusted Value Data

for Design 1 and Design 2 Risks for Decision-Maker B.

Design 1

Risk u(XL) 1-P0 U(s) CE(Rn)

R110.0024 0.0030 0.9994 $2.49

R210.0045 0.0050 0.9995 $2.23

R310.0051 0.0080 0.9971 $12.84

Risk-Adjusted Value (CE(Rtotal)) Total: $17.56

Design 2


R110.0034 0.0040 0.9994 $2.74

R210.0029 0.0050 0.9979 $9.40

R310.0020 0.0019 0.9999 $0.52

Risk-Adjusted Value (CE(Rtotal)) Total: $12.66

satellite in a high earth orbit on a four year mission to study the

brightness of la type supernovae and the redshift of la type su-

pernova host galaxies [40]. A la type supernova is a subcategory

of supernova that is the result of a white dwarf star exploding.

Several risks were identified in the SNAP mission report.

This paper makes use of and expands upon potential risks in the

power and attitude control subsystems. Table 4 details several

risks that will be used in the remainder of this paper. The con-

sequential cost dollar amounts in this case study are the cost of

mitigating the risk to an acceptable level. However, consequen-

tial cost may also be defined as the cost of outcome of a risk if it

is realized.

During the course of the CDC trade study session, the risks

outlined in Table 4 were identified. Risks R1 and R2 are potential

threats to mission success. Risks R31−2and R4 are threats to the

level of science data that can be returned from the spacecraft but

will not end the mission completely. The R31and R32

risks iden-

tify the same risk and propose two different solutions. R32also

utilizes the same solution as R4.

In order for the SNAP mission proposal to be considered for

further development funding, it must meet a specific cost cap.

In this fictitious example, the mission proposal is $40M away

from reaching the cost cap. Not all of the identified risks can be

mitigated under this cost cap. Based upon the Risk Priority Num-

bers (RPNs) of the four identified risks, R2 should be addressed

first. This however would not leave enough funds to address R1,

the next largest risk. Additionally, the customer believes that

severity of R1 is overstated and wants to take a more risk-tolerant

stance on R1 while addressing some of the science data concerns

of R3 and R4 within the limited resources available.

To help make risk mitigation decisions, the customer was

given the E-DOSPERT test. The result, EDSMean = 3.17, was

used with the monotonically decreasing exponential risk utility

function in Equation 8 where VMax = $120M, VMin = $0, XH = 0,

XL =V(Rn), OccMax = 10, OccMin = 0, Oc f = 0.1, and RSF = 60.

The consequential cost was used as potential outcome values

while the occurrence values were used to determine probabil-

ity of occurrence. Table 5 shows the resulting probability, and

utility data. From this data, decision-makers can see that risks

R1 and R31are the most preferred risks to mitigate under a risk-

tolerant decision process based upon desiring to mitigate risks

with the highest CE(Rn), and will cost in total less than $40M

in consequential cost to mitigate. A risk-neutral approach would

have chosen to mitigate risks R1 and R2. The two most preferred

risks to mitigate also satisfy some of the questions surrounding

mission success and science data return.

TABLE 5. Probability and Risk Utility Data for Identified Risks in

the SNAP Mission. The Certainty Equivalent is Derived Using the Cus-

tomer’s EDSMean.


R1 0.0006 0.0001 1.0378 $0.1681M

R2 0.0018 0.0020 1.0379 $0.1182M

R310.0048 0.0050 1.0378 $0.1641M

R320.0042 0.0050 1.0372 $0.4040M

R4 0.0032 0.0040 1.0373 $0.3991M

After a mission has been conceptually developed within

Team X, it is often placed into competition with other competing

conceptual spacecraft mission designs for further funding. In this

case study, the SNAP mission was put into competition against

two other missions for funding after mitigating the risks iden-

tified above. Table 6 summarizes the relevant SNAP risk data

and risk data for the other competing mission concepts. It is as-

sumed that each mission has already mitigated as many risks as

was possible under the budget cap.

The decision-maker has decided to use a monotonically de-

creasing exponential risk utility function as shown in Equation 8

based upon the information presented in Section of this paper.

Other utility functions are available [9] if the practitioner wishes

to use a different function. The following parameters have

been set by the decision maker to be VMax = $60M, VMin = $0,

OccMax = 10, OccMin = 0, Oc f = 10, and RSF = 20. The decision-

maker’s E-DOSPERT test result is EDS = 3.10, making her risk-

tolerant. Equation 10 is used to determine the certainty equiva-


TABLE 4. Simplified Case Study FMEA of SNAP Power and Attitude Control Subsystems.

Risk Function Failure Mode Effects Sev. Occ. Det. RPN Recommended Ac-

tion

Cons. Cost

R1 Spacecraft

pointing

Excessive jitter Long exposure pho-

tos are blurry

7 1 4 112 Increase reaction

wheel size

$30M

R2 Energy

storage

Ni-H2 battery cell

fails

Degraded battery

performance, possi-

ble mission loss

9 2 7 126 Use redundant

batteries or replace

with Li-Ion battery

$20M

R31Data stor-

age

Insufficient stor-

age space

Loss of science data

if downlink missed

5 5 2 30 Add second solid

state recorder

$15M

R32“ “ “ “ “ “ “ Add ground station $23M

R4 Ground

station

Missed downlink Fail to receive data

due to rain

4 5 4 80 Add ground station $25M

TABLE 6. Simplified FMEA for the SNAP Mission and Other Com-

peting Missions.

SNAP Mission


R1SNAPFunct 1 3 4 4 112 $30M

R4SNAPFunct 4 2 5 4 80 $25M

Competing Mission A


R1AFunct 1 4 5 3 84 $25M

R2AFunct 2 3 2 8 48 $20M

R3AFunct 3 5 3 4 60 $35M

Competing Mission B


R1BFunct 1 6 1 4 72 $40M

R2BFunct 2 8 3 5 120 $30M

lent, CE, of each design. Table 7 shows the utility, probability,

certainty equivalent.

By using the risk attitude utility function method, the

decision-makers see that the SNAP mission is the most pre-

ferred design in the case of risk tolerance. In other words, the

risk-adjusted value (CE(Rtotal)) is lowest for the SNAP mis-

sion. Therefore, assuming all other mission selection criteria are

equal, the SNAP mission would be the preferred mission to re-

ceive continued funding. This selection would not have been

made under a risk neutral, expected value decision making pro-

TABLE 7. Utility and Probability Data for Design 1 and Design 2

Risks.

SNAP Mission


R1SNAP0.0018 0.0030 0.9988 0.1542M

R2SNAP0.0014 0.0020 0.0014 0.0780M

Risk-Adjusted Value (CE(Rtotal)) Total: $0.2322M

Competing Mission A


R1A0.0035 0.0050 0.9985 0.1945M

R2A0.0016 0.0020 0.9996 0.0568M

R3A0.0015 0.0030 0.9985 0.1984M


Competing Mission B


R1B0.0003 0.0001 0.9993 0.0837M

R2B0.0018 0.0030 0.9988 0.1542M


cess and instead would have chosen Competing Mission A due

to the lower certainty equivalent. In the case of a neutral risk

attitude, CE(SNAP) = $0.1400M, CE(MissionA) = $0.2700M,


and CE(MissionB) = $0.1300M. A similar process to this would

then be repeated at the next level of mission selection after fur-

ther mission concept development.

CONCLUSION AND FUTURE WORK

The longterm goal of this research is to gain new knowledge

that enables mathematically sound and empirically grounded de-

cision making about project risk in large engineering organiza-

tions. A new methodology was introduced in this paper for

utility-based decision making using empirically-derived risk data

based on stakeholders’ risk attitude. Stakeholders’ risk attitude

is determined from the E-DOSPERT test that provides an aspi-

rational assessment of risk attitude in the context of utility the-

ory. As seen in the case study, the risk attitude utility function

method allows engineering risk methods that are in the expected

value domain to be translated into an appropriate risk attitude do-

main for a specific enterprise or decision-maker. Viewing the risk

information through the lens of risk attitude provides a decision-

maker with a new, numerically based approach to select and jus-

tify selection of the most important risks to address under con-

strained resources. Rather than using “gut feeling” to try and

explain risk decisions, this method gives stakeholders a way to

rationalize their risk-informed decisions.

Further expansion of this methodology will examine the

benefit side of Equation 5, which can add an expected benefit

if the risk outcome is not realized. This area of research could

be especially fruitful for comparing multiple risks against one

another for risk-tolerant enterprises. Large risks can have asso-

ciated large benefits. This method does not currently account for

the potential large return for taking a large risk.

Testing of this method should be conducted to determine

user satisfaction levels between utility risk functions generated

with lottery methods and with E-DOSPERT test results. Choice

determinations made with the help of risk functions generated

from the E-DOSPERT test could be compared against choices

made by individual respondents on risk decisions where a risk-

averse person would decide differently than a risk-tolerant per-

son. This would verify that risk atitude affects engineering risk

decisions. The same population of respondents would also be

provided data from the risk attitude utility function method using

risk utility functions generated with lotteries to make risk deci-

sions. In future work, this method will be tested and verified at at

a major aerospace corporation with production-level design en-

gineers who work in or with a Team X-like setting. This will in-

clude further testing and exploration of the creation of the scaling

factor, RSF with the intent of developing rules of thumb specific

to the aerospace industry.

The method has been shown to change risk-informed de-

cisions in certain situations where a risk-averse or risk-tolerant

decision-maker would likely choose differently than the expected

value approach suggests. As the E-DOSPERT test is further re-

fined, the risk attitude utility function method will become more

and more useful. Extension of the method to look at the ben-

efit side of the risk utility equation will provide further benefit

to the practitioner. The risk attitude utility function method is a

promising area of further research and practical application.

ACKNOWLEDGMENT

This research was funded in part by the National Science

Foundation (project number CMMI 1030060). The opinions,

findings, conclusions, and recommendations expressed are those

of the authors and do not necessarily reflect the views of the

sponsors. Special thanks go to Jacob Postman and Zach Bailey

for their MATLAB assistance.

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