Unlike the deterministic optimization, the formulation of robust design optimization & DFSS is somewhat complicated.
Minimize
Subject to 
where, 
are the standard deviation of 
and 
. The value of 
and 
are user defined parameters. If users
define 
and 
, the design objective is a minimization of
the variance of 
. Also, if
users define 
, the inequality
constraints are DFSS constraints.
Reference
1. Fletcher, R., Practical method of optimization, John Wiley & Sons, Chichester, 1987.
2. Vanderplaats, G.N., Numerical optimization techniques for engineering design, McGraw-Hill, 1984.
3. Osyczka, A., Multicriterion optimization in engineering, Ellis Horwood Limited, 1984.