A Chernov bound for robust tolerance design and application

Abstract

Within an industrial manufacturing process, tolerancing is a key player. The dimensions uncertainties management starts during the design phase, with an assessment on variability of parts not yet produced. For one assembly step, knowledge can be gained from the tolerance range required for the parts involved. In order to assess output uncertainty of this assembly in a reliable way, this paper presents an approach based on the deviation of the sum of uniform distributions. As traditional approaches based on Hoeffding inequalities do not give accurate results when the deviation considered is small, an improved upper bound is proposed. Then, the impact of the stack chain geometry on the bound definition is discussed. Finally, an application of the proposed approach in tolerance design of an aircraft sub-assembly is detailed. The main interest of the technique compared to existing methodologies is the management of the confidence level and the emphasis of the explicit role of the balance within the stack chain.