  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, we
can gain knowledge 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, we propose an
improved upper bound. We then discuss how the stack chain geometry impacts the
bound definition. Finally, we show an application of the proposed approach in
tolerance design of an aircraft sub-assembly. 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.
