reading review

G. A. Hazelrigg^ National Science Foundation,

Arlington, VA

A Framework for Decision-Based Engineering Design Engineering design is increasingly recognized as a decision-making process. This recognition brings with it the richness of many well-developed theories and methods from economics, operations research, decision sciences, and other disciplines. Done correctly, it forces the process of engineering design into a total systems context, and demands that design decisions account for a product's total life cycle. It also provides a theory of design that is based on a rigorous set of axioms that underlie value theory. But the rigor of decision-based design also places stringent conditions on the process of engineering design that eliminate popular approaches such as Quality Function Deployment. This paper presents the underlying notions of decision- based design, points to some of the axioms that underlie the theory of decision-based design, and discusses the consequences of the theory on engineering education.

Introduction

Following the great scientific and engineering achievements of World War II, engineering education turned its focus from design to analysis, and engineering education institutions turned to the teaching of engineering as a process of applied science (Grayson, 1993; Hazelrigg, 1996a). In this model, engineering design is viewed as a problem-solving process: meet functional requirements subject to constraints at minimum cost, for exam- ple. This approach served the profession well through the era of the cold war, where markets tended to be highly concentrated and product specifications were provided by the customer, fre- quently the military. Producers for civilian consumer markets enjoyed the significant technological advances of the War com- bined with a general lack of competition resulting from the destruction of foreign productive capabilities.

As European and East Asian productive capacity recovered, however, American companies suddenly found their consumer markets diminishing. New approaches to engineering design were clearly called for. Recognition of this need was driven home by the Japanese adoption of Deming's principles of qual- ity control (Deming, 1986) and the growing U.S. demand for the resulting, higher quality products. The salt in this wound was provided by the U.S. industry's initial rejection of Deming's theories. Over the past decade, many new approaches to engi- neering design have been posited: Taguchi's theory of robust design (Taguchi, 1993), Quality Function Deployment (Akao, 1990; Wasserman, 1993, for example), design for manufacture (Boothroyd, 1987), design for assembly, design for the environ- ment, design for disposal, concurrent engineering, and Suh's axiomatic design (Sub, 1990) to name a few. Basically, these methods are ad hoc approaches that are not rooted in any funda- mental theory, nor do they provide a basis for engineering de- sign as a discipline. The possible exception here is Suh's attempt to root design in two axioms.

More recently, although the idea is certainly not new (Tribus, 1969; Sage, 1977; de Neufville, 1990; Hazelrigg, 1996a), de- sign has come to be thought of as a decision-making process. This notion is consistent with the definition of decision as (1) a choice from among a set (either closed or open) of options, (2) an irrevocable allocation of resources. It is also consistent with the Accreditation Board for Engineering and Technology's

' Tlie views expressed in tliis paper are strictly those of the author and do not necessarily reflect the views of the National Science Foundation or the Federal Government.

Contributed by the Design Theory and Methodology Committee for publication in the JOURNAL OF MECHANKAL DESIGN. Manuscript received Aug., 1995; revised Sept., 1998. Associate Technical Editor: D. L. Thurston.

definition of engineering design. The interesting thing about the view that engineering design is a decision-making process is that it opens the door to the application of the results of some 250 years of research on decision making. Not only are these results directly applicable to engineering design, they lead to new capabilities and unique results. For example, all the ap- proaches to engineering design noted above require as a starting point the functional specification of a product. But, where does this specification come from? None of the above methods pro- vide mathematically consistent and logically correct insights on the optimal specification of a product, nor do they enable an engineer to address the inevitable tradeoff between product cost and product performance. It is these deficiencies of current engi- neering design methods, coupled with the promise of decision- based design, that is the impetus for this work.

The Nature of Engineering Design In reductio ad absurdum, engineering design involves only

two steps: (1) determine all possible design options and (2) choose the best one. Simple as this may sound, engineering design is anything but simple for the reason that both steps are extremely difficult or impossible to perform for all but the most simple of products. Some of the difficulties encountered are the following:

• For most products, the range of possible design options is virtually limitless. Each possible design is defined by the specification of a configuration and dimensions placed on the configuration. Each dimension typically offers an infinity of design options, and there may be tens to mil- lions of dimensions needed to fully describe a particular configuration. But, in addition, the range of possible con- figurations may also be extraordinarily large. It is not uncommon for it to be impossible merely to construct an exhaustive taxonomy of design configuration options, each of which encompasses an infinity of possible design dimensions.

• It is not possible to know exactly how a particular design will perform until it is built. But the product cannot Ije built until the design is selected. Thus, design is always a matter of decision making under conditions of uncer- tainty and risk.^ Engineers frequently use models to assist in predicting the behavior of a design. But models, which

^ The words uncertainly and risk are used here in the classical decision theory sense. Uncertainty pertains to an inability to measure cuirent states or predict future events with precision. Risk is the variability of the payoff or outcome of a decision resulting from uncertainty.

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are abstractions of reality, are never precise and never predict the future with certainty. What is more, the models cannot be fully validated until after the design has been decided upon and the product built.

• In order to compare and rank order design options, it is necessary to have a valid measure of value. This is consis- tent with the notion of optimization in which the purpose of the value or objective function is to rank order all feasible choices of the control variables. It is not a trivial task to identify a valid value measure, particularly one that is valid under conditions of uncertainty and risk.

• The dimensionality of a typical design is so large that, even given an exhaustive list of design options, perfect models to describe the behavior of every option, and a valid value measure, it is computationally infeasible to search all possible options for the best one, even using state-of-the-art search techniques.

Because of these difficulties and peculiarities of engineering design, design can never be reduced to a prescriptive procedure exclusive of human input. Human input will always be needed for the following:

• Determination of which relationships to include in analyti- cal models and which can be left out,

• Assessment of probabilities (or their equivalent) describ- ing random events, namely the inputs to the models,

• Determination of an appropriate value measure, and • Judgement on which options to include in consideration

of alternative designs, and which to neglect.

Modem engineers work together in teams, often at remote locations, and often transferring design specifications and data across the Internet. The current approach to engineering design does not provide a basis for information exchange and design decision making based on information.^ As a result, the ap- proach that is used is based substantially on the imposition and management of constraints, with considerable resulting loss of value. Decision-based design seeks to base engineering design decisions on information obtained from a variety of sources, going well beyond the engineering disciplines. Substantial bene- fits can be gained through the rationality of the proposed ap- proach and its effective generation and use of information.

F u n d a m e n t a l s of Decision Analysis

The literature on decision making under uncertainty and risk extends back at least 250 years (Bernoulli, 1738), and modem books on the subject continue to be written (Clemen, 1991). The discipline of decision analysis, which has emerged from this literature, develops a normative approach in which decision making has three main elements: identification of options, deter- mination of expectations on each option (which are normally probabilistic), and an expression of values. The resulting deci- sion rule is: the preferred decision is the option whose expecta- tion has the highest value. Classical decision theory applies to the case where a known set of options has been defined. This, however, does not preclude the addition of new options to a previously defined set prior to the making of a decision. I believe that all formal design methods treat only known option sets. Therefore, this is not a restriction in excess of current practice.

An expectation comprises the range of possible outcomes of a decision paired with their probabilities of occurrence. Deter- mination of expectations on each option is the realm of model- ing. I contend that, for every decision we consciously make, we assess expectations on that set of options from which we

make our choice."* For example, each time we cross the street, we consider the options go and wait. We collect data by looking at the traffic, and we make an assessment of our chances of getting safely across. We go when we assess that our chance of survival is sufficiently high. We wait otherwise.^

As noted, expectations are practically always probabilistic. This is, fundamentally, because expectations relate to the future, and it is very difficult to predict the future with precision and certainty. For example, consider a bet on a coin flip. The out- comes of the bet are win and lose. The expectation is: win $x with probability pwin. lose $y with probability piose = 1 - Pwin- Note that heads and tails are not outcomes of concern to the decision maker; rather they are the form in which the bet is made. Engineers frequently get caught up in the physical aspect of a system and its physical performance measures. Usually, however, the performance metric of interest to the decision maker is a win-or-lose metric: How much money will I make if I choose this system design?

Classical decision theory (Luce and Raiffa, 1957) separates expectations and values. Expectations comprise that which can be expected from a particular decision; values relate to what people want. A common mistake is to think of these as the same thing. For example, a design goal may be to maximize some measure of performance, say / . / then is the expectation of what the system will be able to achieve if it is built. It is almost never the case that there is a one-to-one correspondence between the measure J and its value. More will be said of value soon.

Poor engineering decisions can result for several reasons: failure to define and include in the option set good options, failure to determine expectations accurately or appropriately, and failure to determine and use a proper value measure.

Fundamentals of Value Theory

Engineers are trained problem solvers. But, there is an im- portant difference between problems and decisions, and I think that this difference is worthy of emphasis. Decisions, as defined above, comprise resource allocations. Problems, in the sense of textbook problems, do not involve resources. A problem in the physical sciences can be defined as a question posed in the forms: (1) given the state of a system at one point in time, determine the state of the system at another point in time; (2) given elements of the state of a system at a point in time, determine other elements of its state at the same time; or (3) determine the logical conclusions that can be drawn from a set of data. Examples are respectively: given the initial position and velocity of a particle, determine its trajectory; given the specifications of a beam and its loading, determine the stresses in the beam; given a list of numbers, determine their sum. In each case, the problem has an answer that depends only on the statement of the problem, the data or boundary conditions, laws of nature and axioms of mathematics.

Decisions, however, involve options, expectations, and val- ues. And, whereas problems are solved in the absence of options and values, decisions cannot be made without their consider- ation (Carroll, 1865). Specifically, the scientific process seeks to eliminate human values from problem solving. Decision mak- ing cannot be done in the absence of human values. This is a black-and-white difference between problem solving and deci- sion making as they are defined here. All values are an expres- sion of human needs, wants, and desires. There is no known

' I use here a very specific definition of information. Information is the basis of decision malcing. In this definition, information does not exist in the absence of a decision, and it relates to the ability of the decision maker to take the choice that will indeed result in the most preferred outcome. This definition is in accord with the definition of information as used in game theory.

" Not everyone will agree. Some people, for example, contend that decisions are often made on the basis of if-then rules.

' An if-then rule would state, for example, if the nearest vehicle is more than X seconds from you, go. Otherwise, wait. I contend that, even here, uncertainty leads to a need for assessment of expectations. In some sense this is a recognition that every event is unique such that if-then rules are limited in their apphcation. In any case, it seems reasonable that engineering design should be a considered process, not simply governed by if-then rules.

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connection between the laws of nature and human values, and there are no physical laws that govern the determination of values.

The purpose of values in decision making is to rank order alternatives. As in the case of numerical optimization, it is convenient to make use of a numerical function to automate the process of rank ordering options for two reasons: (1) it is too cumbersome to make an ad hoc assessment of the relative merits of every design alternative versus every other design alternative, and (2) the comparison is generally too complex to make accurately and consistently without the use of a mathemat- ical value model, particularly given the presence of uncertainty. The requirement of a value function to rank order all alternatives imposes stringent mathematical conditions on preferences.

Let us say that a decision maker is confronted with three options, call them A,B, and C, each of which has a correspond- ing and deterministically known outcome. The decision maker is asked to rank order his/her preferences with the result that A > B > C, where the symbol > means "is preferred t o . " This preference ordering infers the existence of a real scalar function u such that UA > Un > Uc. Economists call the function « utility.'' Now, note that a preference ordering of the form A > B > C > A would require u^ > Un > Uc > UA- But, since « is a real scalar, this is impossible.^ The preference ordering that causes this dilemma is said to be intransitive, and a person who has such a preference order is called irrational. An irratio- nal person would not make a decision that is compatible with his/her stated preferences. An irrational person would not make a good design engineer. If, on the other hand, for every prefer- ence ordering of the form A > B > C, the ordering A > C also applies, then the preference ordering is said to be transitive and the decision maker is said to be rational. But Arrow (1963) has shown that groups consisting only of rational individuals can have irrational preferences. Namely, Arrow's Impossibility Theorem states that a group consisting only of rational individu- als need not exhibit transitive preferences, and in general it will not. This is an extremely important result with very substantial consequences to engineering design (Hazelrigg, 1996b). As a consequence of Arrow's Impossibility Theorem, any method that requires the formulation of a group utility or purports to determine group preferences is likely to be fundamentally flawed. An example is Quality Function Deployment.**

In general, engineers tend to think of designs as a compromise between competing objectives. This is an inappropriate view for decision-based design. Rather, a design is a decision that seeks to maximize value, where value is always expressed as a real scalar. Frequently, engineers think of the objectives of a system as its measures of performance: speed, size, payload, range, etc. But value is most often not measured in terms of physical performance characteristics. Rather it is a measure of the win-lose outcome of a design, namely. How much money will I make if I choose this design? Sometimes additional out- come attributes must be included: safety, environmental con- cerns, company image, for example. In these cases, the utility function is said to be a multi-attribute function. But it is always a real scalar. There is an extensive mathematics, well docu- mented in the literature, of multi-attribute utility theory (Keeny, 1973, 1974 are classical papers, for example). It is imperative that this mathematics be adhered to lest the resulting utility functions will not yield appropriate preference orderings.

Outcome: status quo

' All objective functions used in optimization are utility functions, and their puipose is to rank order all permissible alternatives.

' In the case of such a preference ordering, it is mathematically impossible to construct an objective function and, thus, optimization is impossible.

* Weierstrass (Hildebrandt and Tromba, 1985) showed that, to correctly solve a problem, one must first prove that a solution exists. QFD seeks to solve for the preferences of the consumers. But it was not proven that such preferences exist and, indeed, Arrow proves that, in general, they do not. Thus, any mathematical approach to obtain such preferences that does not first impose conditions that guarantee that group customer preferences exist is mathematically incorrect. This is not to say that it is an approximation. It is simply incorrect.

Decision to enter the lottery or remain at the status quo

More desired outcome, ..4;

Random event

Less desired outcome,/4,

Fig. 1 A von Neumann-Morgenstern lottery

Outcomes of a design decision can never be determined with certainty. Therefore, the value measure used to rank order alter- natives must be valid under conditions of uncertainty and risk. The great mathematician John Von Neumann and economist Oskar Morgenstern determined such a measure. It is referred to as von Neumann-Morgenstern utility (vN-M utility). VN-M utility is based on the notion of a lottery, referred to as a von Neumann-Morgenstern lottery, as depicted in Fig. 1. In this example, there is a more desired outcome and a less desired outcome. Obviously, the utility of the more desired outcome would be higher than the utility of the less desired outcome. Von Neumann and Morgenstern reasoned that, if the probability of the more desired outcome occurring approaches unity, the utility of the lottery should approach the utility of the more desired outcome. Conversely, if that probability approached zero, the utility of the lottery should approach the utility of the less desired outcome. With this reasoning, they concluded that the utility of the lottery should lie between the utilities of the less and more desired outcomes. VN-M utility is built upon this notion and the following six axioms:

1. All outcomes of a vN-M lottery can be ordered in terms of the decision maker's preferences, and that ordering is transitive (remember, this condition is necessary in order that rational decision making be possible).

2. Any compound lottery, that is, any lottery that has as an outcome another lottery, can be reduced to a simple lot- tery that has among its outcomes all the outcomes of the compound lottery with the associated probabilities of their occurrence (this condition equivalences compound and simple lotteries).

3. If the outcomes of a lottery. A,, A2,. . . , A ,̂ are ordered from most desired to least desired, then there exists a number p , 0 < p < 1, such that one is indifferent between an outcome A,, 1 < i < r, and the lottery A1 with proba- bility p and A, with probability p - 1 (this assures the continuity of preferences between outcomes At and A^).

4. For any lottery such as that given in axiom 3, with p specified, there exists a certainty outcome S, that can be substituted for A,, and the preferences of the decision maker will remain unchanged (this axiom provides that any lottery can be reduced to an equivalent lottery that contains only the outcomes Ai and A^).

5. The decision maker's preferences and indifferences among lotteries is transitive (this assures that rational preferences exist among lotteries).

6. Given two lotteries, each with only two outcomes, and which differ only in terms of the probabilities of the outcomes (that is, they have identical outcomes), the lottery in which the probability of the more desired out- come is higher is the preferred lottery (this is a statement of preference).

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I contend that these axioms are fundamental to the engi- neering design process. I believe that, if they did not apply, rational design would be impossible, and there would be no purpose to the education of engineers. Given these axioms, a simple but profound result obtains. It is called the expected utility theorem: The utility of a lottery is the sum of the utilities of all possible outcomes of the lottery weighted by their proba- bilities of occurrence. This theorem provides a valid measure of utility under conditions of uncertainty and risk. However, a stronger statement can be made. Subject to the six axioms of vN-M utility, not only does the expected utility theorem provide a valid utility measure (that is, a valid measure for rank ordering design alternatives), it is the only valid measure. All other measures are wrong (or equivalent).'

The axioms of vN-M utility do not allow totally arbitrary selection of utility. Rather, they dictate that the utility functions themselves also must satisfy the vN-M axioms. In particular, utilities must lead to proper rank ordering of options in the case of vN-M lotteries (Hazelrigg, 1996a). Thus, in general, it is not the case that the measure of value itself, say profit, is a valid utility under conditions of uncertainty and risk.

The Time Value of Resources What would you prefer to receive as a gift, $1 million or $1

million? These may seem the same, but suppose the first gift is $1 million handed to you today in a brown paper bag, and the second is $1 million given to you at the rate of $1 per year for the next million years. Most people would strongly prefer the lump sum in a paper bag, even if the payment of $1 per year were adjusted for inflation. Thus, decision makers are, in gen- eral, not indifferent to otherwise equivalent resources obtained at different points in time. To equivalence resources spread over time, economists have developed an approach called dis- counting (Heal, 1973). The idea is that a dollar received a year from today is worth less than a dollar received today by some fraction. Say, for example, you would be indifferent to receiving $0.90 today or one dollar a year from today. Then it is said that your discount rate is 10 percent, (1 - 0.1) X $1.00 = $0.90. Heal shows that the discount rate must be constant over time in order to preserve consistency in decision making. The key point is, failure to account for the fact that resources are spent or received over time will result in comparative assessments of worth that do not correspond to stated preferences.

A stream of revenues or costs discounted to the present and summed is referred to as the present value of revenues or the present value of costs.

A Framework for Decision-Based Engineering Design The fundamental premise of decision-based design is that

engineering design is a decision-making process. Rational deci- sions follow the rule that the preferred decision is the option whose expectation has the highest value. The framework for decision-based engineering design implements this concept.

Most products and processes are designed in order to make money. Arguably, there are other reasons for doing engineering design, but they pale in comparison. For example, one could argue that a weapon of war is designed to accomplish a specified military objective. Still, the military does not do the engineering design. That job is contracted out to a company whose likely goal is making money. Thus, while I recognize the possibility of a multi-attribute utility, the framework that follows is based on the notion that the goal of a design is to make money, and more is better.'" And the focus of this framework is on consumer

products, that is, products that may be purchased and used by a plurality of consumers.

The framework of decision-based design is shown in Fig, 2. The purpose of this framework is to enable the assessment of a value for every design option so that options can be rationally compared and a preferred choice taken. The value assigned to each design alternative is a vN-M utility. The assessment framework then enables iteration on the design to seek better designs, that is, designs that have higher utility. Keep in mind that the goal used here is profit. Profit consists of revenues less costs, discounted to account for the fact that revenues are obtained and costs incurred over time. Revenues are comprised of quantities of things sold times their prices. Costs are com- prised of quantities of things bought times their prices. Typi- cally, manufactured products are sold; resources, labor, and capital goods are bought. The quantity of products sold depends upon the demand for the products, which is a function of the attributes of the product, price, and time. The attributes of a product are those things that determine the worth of the product in the eyes of the customers."

A design engineer has control over some things that affect the worth of a design. For example, the engineer can choose the system configuration and its dimensions and its process of manufacture. Sometimes the engineer can exhibit some control over the use of the product. For example, the engineer might specify that the oil in a particular vehicle should be changed every 7,000 miles. The engineer might also have some control over warranty policy, quality control, distribution and sales, and disposal of the product. The variables over which the engineer has control are referred to as the design variables. We can think of an ordered set of design variables as the design vector, x.

Other variables affect the cost and performance of a system and its demand, yet are such that the engineer has no control over them. Examples include the weather, the future cost of labor, the future cost of capital, cost and availability of re- sources, cost and availability of fuels, and disposable income of potential customers. These variables are referred to as exoge- nous variables. Exogenous variables are key in assessing the worth of a design, but they are random variables and can be estimated only as discrete or continuous distributions. We can think of an ordered set of exogenous variables as the vector y.

The variables x andy have no particular meaning to a product's customers. Customers tend to be interested in things referred to as the attributes of a product: speed, acceleration, styling, color, feel, quality or reliability, economy, etc. We refer to an ordered set of attributes as the vector a. x and y transform into a, with uncertainty, and demand, ^, is a function of a, time, t, and price, P. The present value of revenues is determined as the product of P and q properly discounted and integrated over time.

As formulated here, x and y also determine costs, with some uncertainty. The costs that must be included here are all those costs that could detract from revenues to result in net revenues or profits: the costs of research, design, design verification, manufacture, test and quality control, distribution and sales, maintenance and repair or warranty costs as appropriate, liabil- ity, product disposal, and perhaps others. All life cycle revenues and costs must be included in the analysis in order to properly determine net revenues. Because all revenues and all costs must be taken into account to properly determine the utility of a design alternative, the decision-based design framework forces the design process into a systems context.

A point often missed in engineering design is that price, P, is not fixed by some magic force. Rather, it is a variable that

' I would like to leave the possibility that an equivalent theorem appUes for the application of fuzzy logic to the determination of a value function, although this is not obviously the case. Another possibility lies in complexity theory, but this is as yet unproven.

'° Extensions of this framework to the case of a multi-attribute utility are straight forward.

" I t is important to distinguish between demand and preference. A group of customers will have a demand for a product, which is a function of its attributes. But, Arrow's theorem proves that, in general, a group of customers will not, as a group, exhibit transitive preferences over a set of product attributes. The reason that a mathematical demand function exists is because it contains absolutely no customer preference information that would enable transitive rank ordering of product preferences as a function of product attributes.

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Optimal design for comparison with

other configurations

System configuration

M •

' ' System design

X

/

Choose X to max u

r System

attributes a . 1 ,,

Cost of manufacture and other life cycle

costs C

, L

Exogenous variables

y

Demand

1 1

/

Choose P(0 to max u

, 1

Utility u

,>

Corporate preferences

Fig. 2 A framework for decision-based engineering design

is free to be chosen. In fact, P can be a function of time, and generally is. The question is, how to set P? The answer is that P should be set to maximize the value of the particular design, namely x, subject to the exogenous variables, y. Thus, the framework includes an optimization on P, the purpose of which is to maximize utility, «, with respect to P, given x &ndy.

The process outlined above provides a utility measure for a particular design. One could then compare alternative designs using this utility measure and, in fact, automate the process of seeking better designs via an optimization scheme. Alternative system configurations can be compared only when each config- uration under comparison has been optimized with respect to its particular design parameters.

Implications of Decision-Based Design on Engineering Education

The adoption of decision-based design would have several sig- nificant impacts on engineering education. Indeed, decision-based design is the seed that glues together the heretofore disparate engineering disciplines as well as economics, marketing, business, operations research, probability theory, optimization and others. The decision-based view of engineering design is that design is inherently a multi-disciplinary process. Even more, it is an omni- disciplinary process—it encompasses all disciplines.

Today's students are taught problem solving; they are not taught decision making.'^ When students are given a problem to solve, they are taught to go to the appropriate equation, plug in the data, and crank out an answer. But, when they are given a decision to make, out of the normal classroom context, they typically disconnect from their education, throw out all knowl- edge of modeling, and guess." They rarely understand that there

' ' For example, the mathematic of uncertainty is probability theory. Only about half the undergraduate engineering curricula require probability theory. Only a handful of cumcula even offer a course in decision theory. I know of no under- graduate curriculum that uses a rigorous decision theory approach in its capstone design course.

" Over the pa.st 10 years, I have played a decision-making game with over two dozen groups of engineering students from a wide range of engineering institu- tions, both in the U.S. and abroad. The groups included both undergraduates and graduates, and some professional engineers and faculty. The game poses a decision that is easily modeled in about one minute and the model yields considerable information. Yet only a few percent of the people who have participated in this game developed a model, and they were predominantly professional design engineers and a few faculty. When questioned about their failure to model, the students profess to see no connection between the principles they have been taught and the situation to which 1 subject them. Yet the connection is obvious and trivial,

is any connection between problem solving and decision making or that the models that they use in problem solving can be useful in gathering information for decision making. And they are largely unprepared to deal with uncertainty. This needs to change. Decision making is the way of design, and uncertainty pervades all design.

The current approach to engineering education is to teach modeling as a problem solving approach. Models are taught in the context of science. This context is a look at the past. The models that we teach have been developed to gain an under- standing of the results of scientific experiments. For example, we measure force, mass, and acceleration over many experi- ments, and validate the equation F = ma, which we see unifies and explains the behavior of many physical systems. But, in engineering design, we are not concerned with the results of previous experiments. We want to predict the future. We want to know. If I design the system thus, where will it go? How will it behave? And, since we are trying to predict the future, we do not have the luxury of measured values of F and m. Instead, we can only estimate them—they are random variables, and thus we can predict a only as a random variable. Failure to properly account for uncertainty in the forecast of such variables leails to erroneous results (Hazelrigg, 1994, 1996a).

The approach to decision-based design outlined here advo- cates an entirely new approach to engineering education. It is an approach that uses our knowledge of nature to predict the future performance of proposed systems designs, and to quantify and understand the uncertainty inherent in this prediction. It would emphasize modeling and analysis as a means of obtaining improved information for design decision making. The deci- sion-based design curriculum would focus on predictive capa- bilities for design with structures, design with fluids, design with heat, design with digital circuits, design for closed-loop control, etc., and on the skills needed to express, communicate, quantify, and analyze potential designs.

Unless a student has some ability to address every box in the framework for decision-based engineering design, he or she has a seriously deficient ability to make rational design decisions.

Concluding Remarlis This paper takes as its starting point the notion that engi-

neering design is a decision-making process. This notion is compatible with the definition of decision as used by the deci- sion sciences, and its use lends applicability to the results of

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some 250 years of research in the field. An approach to engi- neering design is then built upon this notion. It is called deci- sion-based design.

Decision-based design can be implemented according to the framework established in Fig. 2 and discussed above. This framework is based on vN-M utility as an index, a metric or measure of worth against which design alternatives can be com- pared and optimal designs sought, and it recognizes the limita- tions imposed by Arrow's Impossibility Theorem. The validity of the method depends upon acceptance of the six axioms of vN-M utility, however, I argue that these axioms are key to the conduct of engineering design as a rational process. Indeed, if we do not aspire to engineering design as a rational process, I would question the purpose of any engineering curriculum. The framework presented is rather rigid. The acceptance of vN-M utility as the measure of worth against which designs will be compared leaves very little freedom for alterations to this frame- work. And the acceptance of the vN-M axioms leaves one and only one valid measure of worth for a design for comparison to other designs and choice. Further, this measure of worth can be determined only by viewing each element of a design in the total systems context as provided by Fig. 2. Finally, one cannot denounce this conclusion unless they also denounce one or more of the vN-M axioms.

The approach and framework outlined is rooted to mathemat- ics through the vN-M axioms, which deal with the assessment of human values for comparison of choice under risk. There is, in this method, an explicit recognition that designs are created to provide value to humans, and design decisions are made in some attempt to maximize that value. Decision-based design recognizes the need for human intervention in the design pro- cess in four areas: determination of human values, determination of the relationships to be included in analytical models, assess- ment of probabilities for random events, and creativity through the creation of design options coupled with judgement on which options should be given consideration for implementation. Deci- sion-based design, implemented through the framework out- lined above provides a rigorous foundation for design, but de- nies altogether that this rigor will ever eliminate humans from the design process.

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658 / Vol. 120, DECEMBER 1998 Transactions of the ASME

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