5.
Process Improvement
5.5. Advanced topics


How do you determine the optimal region to run a process?  
Often the primary DOE goal is to find the operating conditions that maximize (or minimize) the system responses  The optimal region to run a process is usually determined after a sequence of experiments has been conducted and a series of empirical models obtained. In many engineering and science applications, experiments are conducted and empirical models are developed with the objective of improving the responses of interest. From a mathematical point of view, the objective is to find the operating conditions (or factor levels) X_{1}, X_{2}, ..., X_{k} that maximize or minimize the r system response variables Y_{1}, Y_{2}, ..., Y_{r}. In experimental optimization, different optimization techniques are applied to the fitted response equations \( \hat{Y}_{1}, \hat{Y}_{2}, \ldots , \hat{Y}_{r} \). Provided that the fitted equations approximate adequately the true (unknown) system responses, the optimal operating conditions of the model will be "close" to the optimal operating conditions of the true system.  
The DOE approach to optimization  The experimental optimization of response surface models differs from classical optimization techniques in at least three ways:  
Find approximate (good) models and iteratively search for (near) optimal operating conditions 


Randomness (sampling variability) affects the final answers and should be taken into account 
In contrast, in classical optimization techniques the functions are deterministic and given. 

Optimization process requires input of the experimenter 
