2. An experiment was run in a semiconductor manufacturing facility involving five factors. The response is the rate of fault production {smaller-the-better]. After performing central composite design and experiments, following response surface model was developed with error pooling process. y = 3'13 lyltg 4. Ex; + 2 .7113 2.31:; + 2.23:; + 2.63;} + 2.; I22 4' 2.9.!"C2 0.31:1} + .9x;x; + 2.61:1}; 4' 2min Lam + 1.6m; where :t: and x2 are control factors and x3. xx. and Is are noise factors. All variables in this model are coded variables and the noise factors are varied with N'ID (ID, 12}. In this regression, MSE = 1 is achieved. (a) 1What is the most e'ective factor to the response? Why? {b} Find the mean and variance models for the robust design optimization using the second order reliability method {SORM}. (c) An engineer formulates an objective function of the above robust design optimization by equallyr weighting at the achieved mean and variance. 1What command in MATLAB would he or she use to find the robust optimum and Why