The Projected Variance method

The Projected Variance (PV) method describes robustness as the variance of the response induced by the variance in the independent variable(s) propagated through the response surface. This method was first described by Box [17]. Vuchkov et al. [18] has used this method in case of second 

In case of setting b the amount of propagated error is reduced by a smaller gradient compared to setting a. In the general case the following assumptions are valid a response depends on p independent variables, so y = f x, X2,. Xp)or y = x bif linearity is assumed, when x is the vector 

The factors are set precisely during the investigation period, so function/(xi,X2.Xp)is calculated without errors in the x s. During mass 

The response is not only affected by the tolerances of x, but also the measurement error (or pure error) in the response disturbs the response, of which the following assumptions are made  

If it is assumed for simplicity that the response surface can locally be approximated using a linear function (this is plausible when the function f(x X2, Xp) describes a smooth surface and/or when s is relative small), then the propagated variance can be calculated by (see reference [19] for a complete derivation)  

---