Dante Development Corporation is considering bidding on a contract for a new office building complex. Figure 4.17 shows the decision tree prepared by one of Dante’s analysts. At node 1,….
Use the Custom Designer to create a response surface design for the four responses and three factors.
The sample data table Tiretread.jmp contains the results of a three-factor response surface experiment. The factors are Silica, Silane, and Sulfur. The experiment was conducted to optimize four responses: Abrasion, Modulus, Elongation, and Hardness. The goals for the four responses have been added as column properties. (Note: Click on the asterisk next to each response in the Columns panel, and select Response Limits to view the goals).
(a) Use the Distribution platform to explore the factor settings. How many settings were used for each factor?
(b) Use Graph > Graph Builder to explore the relationship between the factors and the responses. Note: Drag a factor to the X zone and a response to the Y zone. To explore more than one factor at a time, drag a second factor to the X zone next to the first, and release. To explore more than one response at a time, drag a second response to the Y zone above the first, and release. The smooth lines (splines) describe the general relationship between the factors and each response.
(c) Run the RSM for 4 Responses script in the Tables panel to fit a response surface model for all four responses. Scroll to the bottom of the Fit Least Squares window to see the Prediction Profiler. Note the prediction traces for each factor for the four responses. For example, the prediction traces for Sulfur are different for the four responses. An increase in sulfur results in an increase in abrasion, but causes a decrease in elongation. Also note the response goals in the last column of the profiler. The goals are maximized for the first two responses, and they match the target for the last two.
(d) Select Optimization and Desirability > Maximize Desirability from the red triangle menu next to Prediction Profiler to simultaneously optimize all four responses. What are the optimal settings for the three factors? Were the response goals met (and met equally well) for all four responses?
(e) Return to the data table. This experiment was a 20-run Central Composite response surface design. Use the Custom Designer to create a response surface design for the four responses and three factors. What is the minimum number of runs required? What is the default number of runs?