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

5.5.3.1.5.

Single response: Effect of sampling error on optimal solution

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.