DFSS vs BoToch-MVaR for design under uncertainty

[abdsharaf]

I have a general question, what would be the difference between doing robust optimization using Design for Sex Sigma (DFSS) method, and Botroch-based (MVaR) method?
As far as DFSS is concerned, it is used for manufacturing/design-oriented methodology that minimize both mean and standard deviation of the objectives and constraints.
i can imagine that DFSS focus on the reliability aspects ( for exampme tolerance-based optimization tasks) whereas MVaR maximize the robust hypervolume (paretor dominance), but without taking the manufactoring-tolerance and reliability aspects into account.

Even that we consider the noise and variation in input (design variables as example) and Monte Carlo in both approaches, i am still wondering which approach should i go for when it comes to design under uncertainty for electrical machine (my study case), DFSS or MVaR or even combining both?

[eytan]

Hi @abdsharaf, as you mention, SS aims to minimize both the mean and variance, so it will be minimizing all forms of deviation, whereas MVaR with a given \alpha will ensure that all objectives exceed some nominal value with some probability alpha, under whatever noise distribution. From my understanding of the literature, MVaR is a more interpretable measure of six-sigma type goals (you are guaranteed to have a value at least as good as the target \alpha% of the time), while also making less assumptions (typically six-sigma indices assume gaussian errors). What risk measure makes the most sense for your application is application specific though—do you care most about achieving at least some objective value, or do you care about minimizing the variance in your system?

[abdsharaf]

@eytan, Well, actually i care most about considering the input variance influence ( which are geometric entities of the motor design) on the optimization task. So the idea is to imagine, when we considere this input tolerance caused by manufacturing process ( which is not matching the simulation-based design), how the results of the multi-objective optimization will be. So for me it is clear that DFSS takes robustified mean/std within the optimization indicating more relevance for manufactoring-oriented quality measure, while MVaR takes a quantile instead, indicating a risk-aware measure. But still the question, whether DFSS can be enough procedure for my task or it makes sense to have MVaR frontier and for what reason.