5.
Process Improvement
5.5. Advanced topics 5.5.9. An EDA approach to experimental design 5.5.9.9. Cumulative residual standard deviation plot
|
|||||||||||||||||||
Augment via center point | For the usual continuous factor case, the best (most efficient and highest leverage) additional model-validation point that may be added to a 2k or 2k-p design is at the center point. This center point augmentation "costs" the experimentalist only one additional run. | ||||||||||||||||||
Example |
For example, for the k = 2 factor (Temperature
(300 to 350), and time (20 to 30)) experiment discussed in the
previous sections, the usual 4-run
22 full factorial design may be replaced by the
following 5-run 22 full factorial design with a center point.
|
||||||||||||||||||
Predicted value for the center point |
Since "-" stands for -1 and "+" stands for +1, it is natural to code
the center point as (0,0). Using the recommended model
|
||||||||||||||||||
Importance of the confirmatory run | The importance of the confirmatory run cannot be overstated. If the confirmatory run at the center point yields a data value of, say, Y = 5.1, since the predicted value at the center is 5 and we know the model is perfect at the corner points, that would give the analyst a greater confidence that the quality of the fitted model may extend over the entire interior (interpolation) domain. On the other hand, if the confirmatory run yielded a center point data value quite different (e.g., Y = 7.5) from the center point predicted value of 5, then that would prompt the analyst to not trust the fitted model even for interpolation purposes. Hence when our factors are continuous, a single confirmatory run at the center point helps immensely in assessing the range of trust for our model. | ||||||||||||||||||
Replicated center points | In practice, this center point value frequently has two, or even three or more, replications. This not only provides a reference point for assessing the interpolative power of the model at the center, but it also allows us to compute model-free estimates of the natural error in the data. This in turn allows us a more rigorous method for computing the uncertainty for individual coefficients in the model and for rigorously carrying out a lack-of-fit test for assessing general model adequacy. |