Research Interests: Uncertainty in Engineering Design Decisions

The focus of my research is on the value of representing imprecise information in engineering design.

My research interests arise from my work experience and my undergraduate degree in operations research.  At a high level, I am interested in modeling and decision making in engineering design.  The focus of my Ph.D. research is the representation of uncertainty during engineering and systems design.  This work focuses on imprecise numbers and different representations of variability, ambiguity, and lack of knowledge.  The abstract of my dissertation follows.

Dissertation abstract

The engineering design community recognizes that an essential part of the design process is decision making. Each decision consists of two main phases—problem formulation and problem solution. Because decisions generally are made under uncertainty, engineers need appropriate methods for modeling and managing uncertainty. Existing literature focuses on modeling uncertainty using precisely known probabilities. The objective of this thesis is to investigate and develop alternative methods for managing uncertainty during the formulation phase of engineering design decisions, focusing on situations in which probabilities are not known precisely. 

Two important characteristics of uncertainty in the context of engineering design are imprecision and irreducible uncertainty. In order to model both of these characteristics, it is valuable to use probabilities that are most generally imprecise and subjective. These imprecise probabilities generalize traditional, precise probabilities; when the available information is extensive, imprecise probabilities reduce to precise probabilities. However, when information is scarce, they more accurately represent a
decision-maker’s uncertainty. 

An approach for comparing the practical value of different uncertainty models is developed. The approach examines the value of a model using the principles of information economics: value equals benefits minus costs. The benefits of a model are measured in terms of the quality of the product that results from the design process.  Costs are measured not only in terms of direct design costs, but also the costs of creating and using the model.

Using this approach, the practical value of using an uncertainty model that explicitly recognizes both imprecision and irreducible uncertainty is demonstrated in the context of a high-risk engineering design example in which the decision-maker has few statistical samples to support the decision. It is also shown that a particular imprecise
probability model called probability bounds analysis generalizes sensitivity analysis, a process of identifying whether a particular decision is robust given the decision-maker’s lack of information. An approach for bounding the value of future statistical data samples while collecting information to support design decisions is developed, and specific policies for making decisions in the presence of imprecise information are examined in the context of engineering.

This work so far focuses on imprecise numbers and different representations of variability, ambiguity, and lack of knowledge.  I am particularly interested in making a distinction between probabilistic characterizations of uncertainy (related to the concepts of variability, randomness, and aleatory uncertainty) and the imprecision that results from lack of evidence or incomplete characterizations of evidence and beliefs, concepts related to ambiguity  or epistemic uncertainty.  Engineers frequently mix these two aspects of uncertainty, in ways that can lead to the impression that more information is known than the engineers actually do know.

Development of ideas

Note that this section has not been updated since late 2005.

I started my work with a focus on aleatory and epistemic uncertainty.  I now try to avoid the terms aleatory and epistemic because they have been used primarily in an attempt to different inherent natures of uncertainty, rather than focusing on how human decision-makers should manage uncertainty in engineering design.  I now prefer to think of inherent variability and imprecision.  The actual existence of inherent variability is a philosophical issue about which many people disagree.  However, most authors, including some skeptics of a fundamental distinction between types of uncertainty, are willing to admit that it is useful in practice to accept that some uncertainties, such as machining errors, are the result of truly random processes.  Even if the process is not random at the level of fundamental physics, engineers may choose to assume it is for practical reasons, much as they make other assumptions and simplifications when modeling real systems.

To capture both inherent variability and imprecision, the theory of imprecise probabilities, as introduced by Peter Walley (1991), is adopted. Imprecise probabilities express both variability and imprecision by allowing for intervals of probabilities.  These imprecise probabilities are a direct extension of traditional probability theory: they can be interpreted as subjective probabilities—an expression of a DM’s beliefs in terms of their willingness to bet.  The use of lower and upper probabilities (rather than just a single precise probability as in traditional probability theory) also reflects a DM’s confidence in his or her beliefs: the larger the confidence, the smaller the difference between the lower and upper probabilities, i.e., the smaller the imprecision.  Walley has axiomatically defined imprecise probabilities and has shown that they are rational in terms of avoiding a sure loss.

Unfortunately, imprecise probabilities as defined by Walley pose significant computational challenges that remain to be resolved.  For engineering applications, it is crucial to adopt a mathematical formalism that is convenient and inexpensive for computation and decision making.  Ferson and Donald (1998) have developed such a formalism, called probability bounds analysis (PBA) by imposing some additional restrictions on imprecise probabilities.  Although PBA is not quite as expressive as imprecise probabilities, it can still represent both variability and imprecision and has been shown to be useful in engineering design (Aughenbaugh, Ling et al. 2005; Aughenbaugh and Paredis 2005).  

My research also focuses on information economics.  Economics is the study of choice under conditions of scarcity.  Extending this definition, information economics is the study of choice in information collection and management when resources to expend on information are scarce.  Because designers face a scarcity of resources, such as time and money, in the design process, the principles of information economics should be applied to the information collection process in engineering design.  But how  can they be applied?  A challenge is that the benefits of collecting information are not known until the information is collected. When paying to acquire information, it is as if the decision-maker is purchasing a sealed envelope; he or she does not know what is inside until he or she buys and opens the envelope.

I have also explored the role of modeling and simulation in systems design as part of my masters' degree.  My main focus was on the application of executable specifications—a software and systems engineering tool—in mechanical engineering design.  These tools provide a means for moving from the requirements to a function structure in a way that directly results in a simulation model of the system at some level of abstraction.  I believe that such a tool is valuable in engineering design, especially if it could be coupled with physics based models as design decisions are explored and taken.