Defining assembly specifications from product functional requirements using inertial tolerancing in precision assembly

Production yield is usually defined as a function of the variability and tolerance interval of processes, and off-centering (bias) is often neglected. When working in precision assembly, where tolerance intervals are specified in the range of some micrometers, off-centering effects can no longer be neglected. Indeed, the smaller the interval, the more sensitive the yield becomes, inertial tolerancing is a methodology derived from Taguchi loss function, to specify part dimensions and assemblies so that off-centerings are taken into account. We discuss different inertia allocation methods proposed by Pillet and propose a new method where inertia are simply allocated according to possible process performances. Concerning production indicators, due to this methodology, we suggest to abandon traditional capability indices and use sigmadelta-tolerancing with square error. We benefit from sigmadelta-graphs to monitor processes and to help to visually quantify the lack of production and assembly processes. Finally, we describe an entire design procedure, that leads from product functional requirements to production specification, and apply it to an industrial case study. A key element that we provide in this procedure is a novel formulation of assembly yield in the presence of off-centering. The procedure is not "single-shot" but rather iterative, starting from both opposite ends : customer needs and break-even production costs