SGER: An Axiomatic Approach to Probabilistic Tolerancing

这个探索性研究小资助金(SGER)项目的目标是分析概率尺寸和公差的可能性，在概率尺寸和公差中，产品通过其物理尺寸上的概率而不是确定性范围来指定，以考虑不可避免的小制造误差。其方法将是根据适当的公理，制定一套严格的概率公差基本理论。在这种方法中，容差将由概率分布来定义，而不是由确定性区间指定的容差。将提出公理来描述在逻辑上可以是公差的概率集。概率公差将允许考虑单个零件的各种公差之间的关系。此外，将考虑阐明根据小随机样本的测量来接受或拒绝整批或批次零件的规则。在整个研究过程中，将严格考虑测量误差和测量成本。在该项目的后期阶段，将探索纳米制造的应用。如果成功，这项研究将为概率公差奠定基础；这将是对概率尺寸和公差系统的第一次严格分析。这可能会彻底改变几何零件被正式指定的方式。概率公差可以提高美国制造业的竞争力，因为它允许更具成本效益的部件制造和组装。当每个零件满足一系列固定确定性公差的要求被适当的、不那么严格但功能相同的概率要求取代时，生产速度更快、成本更低。返工和报废的成本以及相关的环境影响将会降低。在不增加成本的情况下，更高的产品质量是可能的。此外，该项目将促进严格的跨学科研究，整合研究和教育，并鼓励代表性不足的群体参与科学和工程。

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.