DOE (Design of Experiment) is a powerful tool for solving optimalisation tasks, that takes full advantage of statistical approach.
The target of DOE is finding such combinations of controllable factors (influences) that the feedback (result) is the most advantageous.
Failure modes and effects analysis is another strong tool, that helps to identify possbile failures and insufficiencies in designs and processes.
In case the method is used for evaluationg a design it is referred as DFMEA. Its meaning is based in fact, that it significantly contributes to limitation of risks realted to implementing designs into real world.