PRO-CHAIN - Statistical Analysis and Robust Design of Process Chains

Products are often manufactured by means of a sequential chain of processing steps. As a minimum, the most important process steps and corresponding variations should be analyzed in order to obtain realistic information about relevant parameter dependencies and properties of the overall process and resulting products.

The patented PRO-CHAIN methodology helps to

  • quantify influences of scatter from the entire history of a process up to the ultimate result, giving valuable insight into local behavior,
  • considerably improve the forecasting quality of simulations and, with a subsequent robust optimization, the quality of the resulting product,
  • answer and visualize »what-if« scenarios, without additional time-consuming simulation runs.

PRO-CHAIN can be applied, for example, to the following process chains:

  • from metal forming / casting  to component tests / crash analysis
  • from semiconductor process over device to circuit simulation


PRO-CHAIN on a Glance

PRO-CHAIN includes an efficient local analysis of variations on highly resolved meshes allowing a design-parameter space reduction for each process step.

It comes with a fast and nevertheless accurate prediction of new designs, incorporating distributions of eg thicknesses, strains or damages by means of an approximation model (metamodel).

In addition, PRO-CHAIN enables an accurate transformation of local scatter from one step to the next one, minimizing the necessary number of simulation runs.Due to that, the influences of scatter are quantified and considered over the entire history of a process up to the ultimate result. Thus, the forecasting quality of simulations and, with following robust optimization, the quality of the resulting product can be considerably improved. The new design will be definitely more robust.

PRO-CHAIN offers a fast visualization of new designs including their statistical information, additionally.

Altogether, it leads to an intensive reduction of required memory and computational time compared with standard Monte Carlo methods.

© Fraunhofer SCAI
PRO-CHAIN strategy exemplary for the process chain forming to crash: simulation types (orange), typical variations / scatter (blue), software tools (green).

Exemplified by the forming to crash analysis process chain shown above, the strategy consists of the following main steps and software tools:

Analysis of the first process step (forming):

  • ensemble of forming simulation runs based on a design-of-experiments with minimal number of simulation runs
  • parameter sensitivity analysis and iterative construction of the data base (DesParO)
  • optional application of a multi-objective robust design-parameter optimization (DesParO)

Transformation of the data base, including distributions of functionals on the simulation mesh and their local variations, so that the output of forming serves as an input for crash analysis:

  • compression of the data base
  • mapping of the ensemble of relevant functionals to the next processing step (with SCAI’s MpCCI MetalMapper) and setup of a new data base

Analysis of the second process step (crash):

  • ensemble of crash simulation runs based on an extended design-of-experiments
  • sensitivity analysis and iterative construction of the data base (DesParO)
  • multi-objective robust optimization of the whole process chain (DesParO)


Steffes-lai, Daniela: Approximation methods for high dimensional simulation results - Parameter sensitivity analysis and propagation of variations for process chains. Logos-Verlag, Berlin, 2014. ISBN 978-3-8325-3696-1. Dissertation, Universität zu Köln.


Steffes-lai, D., Nikitina, L., Clees, T.: Vorrichtung und Verfahren zum Bearbeiten einer Prozesssimulationsdatenbasis eines Prozesses. Int. Patent PCT/EP2010/061450. Veröffentlichung 09.02.2012. EU-Patent EP000002433185, US-Patent US9002684 .