Quantified Relations: A Class of Predicate Logic Design Constraints Among Sets of Manufacturing, Operating, and Other Variations

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Abstract
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 modeling, and possibly computing effort. It seems to subsume Ward’s prior work on the Label Interval Calculus, extending the approach to a wider range of engineering design problems.

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