Subproject A7

Mathematical methods to derive laws for uncertainty scaling were derived, based on dimensional analysis. This also lead to laws of growth for product properties under the influence of uncertainty. Different kinds of uncertainty can be modelled with the uncertainty scaling models, such as dynamic systems, aging and wear. The models can describe incertitude (scenario laws of growth) as well as stochastic uncertainty (probabilistic uncertainty).

These scaling models can be used to describe technical systems with high complexity, that can not be fully described by axiomatic models, as long as measured data or a physical model of the technical system is available.

Based on these scaling models the size range development methodology of Pahl and Beitz was updated and restructured to control scaling uncertainty. Scaling uncertainty is a newly defined concept which classifies uncertainty into model related uncertainty (scaling under uncertainty) and uncertainty caused by known variance (scaling of uncertainty), both of which can cause issues in the scaling process.

To control scaling uncertainty a strong focus was laid onto process analysis to identify the scaling relevant uncertainty. This is done by creating an enhanced process model for scaled technical processes, which allows identification and in conjunction with the scaling models mentioned above the evaluation of scaling uncertainty.

With this improved information basis the integration of the uncertainty mode and effects analysis UMEA (from subproject A1 in the first period of SFB 805) is possible; enabling the designer to define measures to control scaling uncertainty. This can be done by ensuring the compatibility of partial solutions of a technical concept under the aspect of scaling. One important result is also the structured analysis of scaling limitations.

The general result is a frontloading centred methodology for size range development, which targets the synthesis of well-scalable solutions by using deep process analysis, similitude theory and the principles of robust design.