Modeling Imprecision in Product Design

A method for representing and manipulating imprecise and vague information in engineering design is described. Designers and customers preferences are captured with Fuzzy sets. Formal methods for including noise, trade-o strategies and design iteration are included. Introduction Imprecision and vagueness are intrinsic aspects of engineering design. If (at the start of a design process) a proposed solution were neither imprecise nor vague, its description would be precise and it would therefore be a completed design. While (stochastic) uncertainty typically remains in a completed design description (e.g., dimensional tolerances), the nominal desired dimensions are precise. However, much of the early description of a design concept (physical dimensions, material properties, etc.) is vague and imprecise. Engineering design is essentially the process of reducing the imprecision in the description of solution concepts. Imprecision occurs throughout the product design process. It is most easily, and naturally, observed in the early stages when a designer (or group of designers) is articulating a potential solution concept. The \back of the envelope" sketch will not include precise dimensions or other attributes, but is almost universally described imprecisely (e.g., \This diameter will be about 2 cm."). This imprecision can be represented by designers preference and customers preference. Our approach is to ask the designers and customers their preferences for various aspects of the design. They indicate their preference (ranked from 0 to 1) for each value of each parameter describing the design. We describe the customers' needs using Performance Parameters, which de ne the desired performance of the design. We denote each performance parameter as pj, and the associated preference function is denoted (pj). This collection of Performance Parameters spans the Performance Parameter Space (PPS). We describe the designers' preferences as Design Parameters, which include the designers' experience and expertise, as well as availability, manufacturability, and other attributes of the design. Similarly we denote each design parameter as di, and the associated preference function is denoted (di). This collection of Design Parameters spans the Design Parameter Space (DPS). The preference information is usually (but not always) a convex Fuzzy Number. Thus, we use the mathematics of Fuzzy Calculus to operate on these imprecise descriptions of the design, but we do not treat this information as Fuzzy membership, nor do we perform fuzzifying or de-fuzzifying operations, or logical operators on fuzzy sets. Rather, we use this imprecise preference data to perform the usual engineering computations encountered in design to map the preferences of the designers onto the Performance Parameter Space, and also to map the preferences of the customers onto the Design Parameter Space. This provides the designer with the ability to trade-o the many (and typically incommensurate) aspects of a design in an understandable way. As mentioned above, stochastic uncertainty (noise) also is typically present in engineering design, and can be characterized by Noise Parameters. A noise parameter nk might be the possible positioning of an operator switch, and so the alternatives may be nite. Alternatively, nk might be a value of a manufacturing error on a design parameter, and so the Noise Parameter Space (NPS) may have a continuum of possibilities. The approach we describe here can also include these e ects, and can show how the level of noise present in a design a ects the customers and designers preferences, and the trade-o s made in design decision-making. Published in Proceedings of the Third IEEE International Conference on Fuzzy Systems (FUZZ-IEEE '94), volume 1, pages 346{351. IEEE