Status: Resolved (Dave Doehlert)
STRATEGY for Windows comes with a large library of designs. Why would I want to spend money to get an optimal design when I already have more designs in STRATEGY than I'll ever use and there are more designs in books and journals?
Why should I buy an optimal design? To do better research and troubleshooting in fewer runs at lower cost using a design that is uniquely appropriate to my application.
If there is a design in a book which is good enough for your project, use it. There is a set of 57 excellent designs in Dave's book, Experiment Strategies. All of those designs are also contained in STRATEGY for Windows.
These are good designs for most purpose, but there are many situations in which you can do better. If you want to save time and money, you can buy an optimal design which will require fewer runs and deliver information that is as good or better than a standard design. Here are a few specific examples.
Example 1
The five factor central composite design available in STRATEGY for Windows contains 16 cube corners, 10 star points, and 3 replicates of the center (29 runs in all) which will fit for the quadratic model in 21 terms. The Optimal (I) design will fit the same model in fewer runs: 21.
Note that if you want still greater precision of prediction, then choose an Optimal (I) design in 22, 23, or 24 runs (etc.), and get greater precision from each increase in number of runs.
When runs are expensive, use an Optimal (I) design to keep costs down and to finish the research sooner.
Example 2
The four factor factorial design which is all corners of the cube is suitable for fitting the model with main effects and two-factor interactions. There are eleven terms in that model.
There is in books an irregular fraction of these 16 runs in 12 runs which does pretty well. (the ½ fraction in 8 runs will not separate the 2-factor interactions.)
With an Optimal (I) design, you can do better in 12 runs; you can even do very well in 11 runs (minimal).
When runs are expensive and precision is desired, buy an Optimal (I) design.
Summary
Optimal (I) designs can save runs and give you a fitted model that has greater precision in predicting the trials that you did not run.
See also: Are the D-Optimal designs just as good as I-Optimal designs?
03-FEB-97