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

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.
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