Numerical Optimization Tips
A response cannot be assigned criteria unless it has a model.
Check the design evaluation, ANOVA statistics, and diagnostics graphs. These tools are used to make sure the models provide a good estimate of the true response surface.
There are two symbols that can appear on the criteria list for factors.
An asterisk (*) before a factor indicates that factor is not in any model. Numeric factors will be given a goal of equal to their mid-point. Categoric factors will be given a goal of equal to the first level.
A hash (#) before a factor indicates that factor is a discrete numeric factor. When this factor is selected, an option to restrict the search to its discrete levels is presented at the bottom of the list.
The default goals are in range for factors and none for responses. The default goal limits are in the range tested for factors, and the minimum and maximum observed values for responses.
Click on a response or factor to set more meaningful goals. .
Goals that apply to both factors and responses
In Range - Specify a range for acceptable results. Responses can have one-sided In Range goals. Select and delete the lower or upper limit to set one-sided goals. Factors must have both limits.
Maximize - The lower limit is the lowest acceptable outcome. The upper limit is desired best result.
Minimize - The lower limit is the desired best result. The upper limit is the highest acceptable outcome.
Target - The best result is somewhere in between acceptable limits and there is a “best” outcome.
Goals that apply to responses only
None - Do not use this response model for optimization. This is treated as “In Range” with infinite limits. Check the “Hide on Report” box to keep it off the solutions tab.
Cpk - The process capability index (Cpk) brings specifications into the optimization. It calculates the number of standard errors the predicted response is within the specification limits. The default settings for the Lower Spec Limit (LSL) and Upper Spec Limit (USL) are the minimum and maximum observed values. The Cpk Low is 0 (exactly on the specification) and the Cpk high is 1.5 (six sigma capable). Leave one of the specification limits blank for one-sided specifications.
Goals that apply to factors only
Equal to - Set the factor equal to a single value to restrict the optimization search.
Additional Tools
Use Interval - Modifies the goal by including uncertainty estimates. It will only appear once a goal is selected for a response. The three types of interval set the type of adjustment (Confidence, Prediction, or Tolerance). A larger acceptable alpha risk will result in a narrower interval therefore a smaller adjustment. The tolerance interval also requires the proportion of the population contained in the interval.
Weight - This value can range from 0.10 to 10. It fine-tunes how the optimization process searches for the best solution. A low weight (near 0.10) will allow more solutions that don’t quite meet the optimal goal. A high weight (close to 10) will cause the optimization to seek a solution close to or beyond the stated goal. From a practical standpoint, leaving the weights at 1.0 is a good place to start.
Importance - Specify the relative importance of one goal versus another. Some goals may be critical (assign them +++++), while some may be of medium importance (assign them +++) and some are of lowest importance (+). Default is to have all goals set to +++.
Options Button - Under the options button are several tools to fine tune the trade off between speed and completeness. The default settings work for the majority of problems. For more details see the optimization options help.
Include Standard Error Models is often enabled to limit how far the algorithm will extrapolate if the factor goals are widened. One response is added for each existing response. The goal for the Std Err response is set to in range, with the lower limit deleted. This will limit the extrapolated predictions to be no worse than the worst actual data point.