SGER: An Axiomatic Approach to Probabilistic Tolerancing

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The objective of this Small Grant for Exploratory Research (SGER) project is to analyze the possibilities for probabilistic dimensioning and tolerancing, in which products are specified by probabilities on their physical dimensions rather than deterministic ranges to take account of inevitable small manufacturing inaccuracies. The approach will be to formulate a rigorous fundamental theory of probabilistic tolerances based on appropriate axioms. Instead of tolerances specified by deterministic intervals, in this approach tolerances will be defined by probability distributions. Axioms will be proposed to delineate the sets of probabilities that can logically be tolerances. Probabilistic tolerances will permit consideration of relations among the various tolerances for a single part. Moreover, consideration will be given to the elucidation of rules for accepting or rejecting entire lots or batches of parts based on measurements for a small random sample. Throughout the research, measurement errors and measurement costs will be considered rigorously. In later stages of this project, applications to nanomanufacturing will be explored.If successful, this research will provide a foundation for probabilistic tolerances; it will be the first rigorous analysis of probabilistic dimensioning and tolerancing systems. This could potentially revolutionize the way that geometric parts are formally specified. Probabilistic tolerancing can improve the competitiveness of US manufacturing because it permits more cost-effective part fabrication and assembly. Faster and cheaper production is possible when the requirement that every part satisfy a list of fixed deterministic tolerances is replaced by appropriate less rigid but equally functional probabilistic requirements. The costs of rework and discard - and associated environmental effects - will be reduced. Higher product quality will be possible without increased costs. In addition, this project will foster rigorous interdisciplinary research, integrate research and education, and encourage the participation of underrepresented groups in science and engineering.