Methods for incorporating imprecision in engineering design decision-making are briefly reviewed and compared. A tutorial is presented on the Method of Imprecision (MoI), a formal method, based on the mathematics of fuzzy sets, for representing and manipulating imprecision in engineering design. The results of a design cost estimation example, utilizing a new informal cost specification, are presented. The MoI can provide formal information upon which to base decisions during preliminary engineering design and can facilitate set-based concurrent design.

Negotiations are common in engineering design, especially on large projects, and are typically conducted informally. Often, negotiation is used to handle the imprecision or uncertainty that is inherent in the design process. Performance targets, initially specified as hard numerical constraints, are adjusted throughout the design process in negotiations between engineers and managers. Crucial unmeasured or unmeasurable aspects of performances, such as aesthetic concerns, are commonly negotiated. Negotiations settle conflicts between engineering groups over values of shared design variables and distribution of limited design resources. In this thesis, a formal description of negotiation in engineering design is presented. This formal model builds on earlier work at Caltech in the modelling of imprecision in engineering design. Negotiation is modelled mathematically as the aggregation of preferences. A complete characterization of the aggregation problem and of the aggregation operators...

iii This document and the work it represents was impossible without the support of my wife Ginger. Often one needs non-technical advice to make clear what one is contemplating. Also one always needs a financial supporter. My thesis advisor Erik Antonsson helped focus many of my thoughts. In addition to providing me with technical assistance, he as well provided instruction on the process of conducting academic research, the communication of ideas both orally and written, and the approach to a developing field. I also owe much to my colleagues in the Engineering and Applied Science Division at Caltech. Their comments and advice maintained my comprehension and rigor. Andrew Lewis in particular provided me with invaluable support. Many of the technical proofs were impossible without him. This material and the work it represented were made possible, in part, by a fellowship from the AT&T-Bell Laboratories Ph.D. scholar program, sponsored by the AT&T foundation. Also, the National Science Foundation provided funding under a Presidential Young

The Method of Imprecision, or M o I, is a formal method for incorporating imprecise information into a design process. This methodology has been exercised on a problem in preliminary vehicle structure design in collaboration with VW Wolfsburg. Results show that the method is useful in trading off multiple conflicting attributes, including styling preferences and engineering requirements. Keywords: Industrial Applications of DTM; Vehicle Structure Design; Design Methods and Models; Design Representations; Computational Methods of Design; Fuzzy Sets INTRODUCTION Preliminary design is inherently imprecise (Becker, 1973; Blockley, 1980; Gavin, 1994; Yao and Furuta, 1986), and many preliminary design decisions are made informally. Preliminary design has enormous economic importance, as much of the cost of a design is determined by these (often informal) preliminary decisions (Whitney, 1988). A further complication is the difficulty of communicating imprecise information between different...

A platform is the set of elements and interfaces that are common to a family of products. We have previously presented a method for designing product families based on platforms that quantifies performance and cost metrics. That approach allows a team of engineers to design and evaluate candidate platforms, given perfect understanding of the designs and requirements. In this paper we present a model to account for uncertainty present during the development of those product families. Real options concepts are introduced to model the risks and delayed decision benefits present under uncertainty in technologies, funding, etc. We develop a quantitative measure of the value to the company for different family designs, and apply it to select the most appropriate design from the possible alternatives. An application to the design of platform-based families of spacecraft is shown. Results from the models indicated the platforms that were most valuable to the company under different scenarios, ...

The method of imprecision is a design method whereby a multi-objective design problem is resolved by maximizing the overall degree of designer preference: values are iteratively selected based on combining the degree of preference placed on them. Consider, however, design problems that exhibit multiple uncertainty forms (noise). In addition to degrees of preference (imprecision) there are probabilistic uncertainties caused by, for example, measuring and fabrication limitations. There are also parameters that can take on any value possible within a specified range, such as a manufacturing or tuning adjustment. Finally, there may be parameters which must necessarily satisfy all values within the range over which they vary, such as a horsepower requirement over a motor’s different speeds. This paper defines a “best ” set of design parameters for design problems with such multiple uncertainty forms and requirements. 1

This paper addresses a class of engineering design problems in which multiple sources of variations affect a product's design, manufacture, and performance. Examples of these sources include uncertainty in nominal dimensions, variations in manufacture, changing environmental or operating conditions, and operator adjustments. Quantified relations (QR's) are defined as a class of predicate logic expressions representing constraints between sets of design variations. Within QR's, each variable's quantifier and the order of quantification express a physical system's causal relationships. This paper also presents an algorithm which propagates intervals through QR's involving continuous, monotonic equations. Causal relationships between variables in engineering systems are discussed, and a tabular representation for them is presented. This work aims to broaden the application of automated constraint satisfaction algorithms, shortening design cycles for this class of problem by reducing model...

iii Frederick Douglass once said “If there is no struggle, there is no progress. ” I think this statement describes my PhD experience here at Caltech well. In ways the past four and half years have been more challenging than I expected yet also more rewarding than I anticipated. This journey would not have been possible without the financial and emotional support of my family and the guidance of my advisors present and past: Professors Fred Culick (Caltech), Victoria Coverstone (University of Illinois at Urbana–Champaign), and Alec Gallimore (University of Michigan). Their support of my education transformed a possibility of a PhD from a dream, to a hope, and now to a reality. I want to thank my Ph. D. advising committee: Professors Erik Antonsson, Jim Beck, and John Ledyard. All three provided invaluable insight and knowledge, especially Professor Beck who assisted with the subset simulation work. Along with Professor Culick, my advising committee gave me the liberty to pursue research ideas and shielded me from many bureaucratic and financial issues a PhD requires. I also thank Dr. Joel Sercel who provided the initial impetus and research ideas that this thesis became and Melinda Kirk for administrative support. This thesis builds upon work by a variety of researchers including Professor Ivan Au

Uncertainty plays a critical role in the analysis for a wide and diverse set of fields from economics to engineering. The term ‘uncertainty ’ has come to encompass a multiplicity of concepts. This paper begins with a literature survey of uncertainty definitions and classifications from various fields. A classification of uncertainty for the design and development of complex systems follows. The various classifications are more practical than theoretical: to make distinct the techniques used to address each type of uncertainty and to demonstrate the effects of each type of uncertainty in each field. The classification for the design and development of complex systems delineates ambiguity, epistemic, aleatory, and interaction uncertainty. Epistemic uncertainty is further subdivided into modelform, phenomenological, and behavioral uncertainty, each of which is described in detail. The uncertainty taxonomy presented is an integral part of ongoing research into propagating and mitigating the effect of all types of uncertainty in the design and development of complex multidisciplinary engineering systems.

There is an increased awareness of the benefits of modeling imprecision in engineering problems, but success is limited by two problems associated with the calculus of imprecision: (1) Solving equations for a parameter is difficult because the common operators of addition and multiplication lack true inverses. (2) The multiple occurrence of imprecise quantities in engineering functions can lead to incorrectly very imprecise results because each occurrence of the parameter is treated as a separate parameter with the same range rather than multiple occurrences of the same parameter. Results obtained in the area of interval analysis are extended to the area of the calculus of imprecision. New operators are defined for functions of imprecise quantities that alleviate these two obstacles, and thus provide a general framework for including imprecision directly in engineering calculations. Keywords: Fuzzy arithmetic fuzzy equations, fuzzy numbers, intervals, manufacturability. 1. INTRODUCTIO...