5.5. Advanced topics
5.5.9. An EDA approach to experimental design
The ordered data plot answers the following two questions:
Settings may be declared as "best" in three different ways:
The ordered data plot will yield best settings based on the first criteria (data). That is, this technique yields those settings that correspond to the best response value, with the best value dependent upon the project goals:
The output from the ordered data plot is:
An ordered data plot is formed by:
|Motivation||To determine the best setting, an obvious place to start is the best response value. What constitutes "best"? Are we trying to maximize the response, minimize the response, or hit a specific target value? This non-statistical question must be addressed and answered by the analyst. For example, if the project goal is ultimately to achieve a large response, then the desired experimental goal is maximization. In such a case, the analyst would note from the plot the largest response value and the corresponding combination of the k-factor settings that yielded that best response.|
|Plot for defective springs data||Applying the ordered response plot for the defective springs data set yields the following plot.|
|How to interpret||
From the ordered data plot, we look for the following:
Best Settings (Based on the Data):
At the best (highest or lowest or target) response value, what are the corresponding settings for each of the k factors? This defines the best setting based on the raw data.
Most Important Factor:
For the best response point and for the nearby neighborhood of near-best response points, which (if any) of the k factors has consistent settings? That is, for the subset of response values that is best or near-best, do all of these values emanate from an identical level of some factor?
Alternatively, for the best half of the data, does this half happen to result from some factor with a common setting? If yes, then the factor that displays such consistency is an excellent candidate for being declared the "most important factor". For a balanced experimental design, when all of the best/near-best response values come from one setting, it follows that all of the worst/near-worst response values will come from the other setting of that factor. Hence that factor becomes "most important".
At the bottom of the plot, step though each of the k factors and determine which factor, if any, exhibits such behavior. This defines the "most important" factor.
|Conclusions for the defective springs data||
The application of the ordered data plot to the defective
springs data set results in the following conclusions: