5.
Process Improvement
5.5. Advanced topics 5.5.3. How do you optimize a process? 5.5.3.1. Single response case


Experimental error means all derived optimal operating conditions are just estimates  confidence regions that are likely to contain the optimal points can be derived  Process engineers should be aware that the estimated optimal operating conditions x^{*} represent a single estimate of the true (unknown) system optimal point. That is, due to sampling (experimental) error, if the experiment is repeated, a different quadratic function will be fitted which will yield a different stationary point x^{*}. Some authors (Box and Hunter, 1954; Myers and Montgomery, 1995) provide a procedure that allows one to compute a region in the factor space that, with a specified probability, contains the system stationary point. This region is useful information for a process engineer in that it provides a measure of how "good" the point estimate x^{*} is. In general, the larger this region is, the less reliable the point estimate x^{*} is. When the number of factors, k, is greater than 3, these confidence regions are difficult to visualize.  
Confirmation runs are very important  Awareness of experimental error should make a process engineer realize the importance of performing confirmation runs at x^{*}, the estimated optimal operating conditions. 