User manual SAS DESIGN OF EXPERIMENTS RELEASE 9

[. . . ] Design of Experiments Guide Get the Most from JMP® Whether you are a first-time or a long-time user, there is always something to learn about JMP. Visit JMP. com and to find the following: · · · · · · live and recorded Webcasts about how to get started with JMP video demos and Webcasts of new features and advanced techniques schedules for seminars being held in your area success stories showing how others use JMP a blog with tips, tricks, and stories from JMP staff a forum to discuss JMP with other users http://www. jmp. com/getstarted/ Release 9 Design of Experiments Guide "The real voyage of discovery consists not in seeking new landscapes, but in having new eyes. " Marcel Proust JMP, A Business Unit of SAS SAS Campus Drive Cary, NC 27513 The correct bibliographic citation for this manual is as follows: SAS Institute Inc. JMP® 9 Design of Experiments Guide, Second Edition. JMP® 9 Design of Experiments Guide, Second Edition Copyright © 2010, SAS Institute Inc. , Cary, NC, USA ISBN 978-1-60764-597-9 All rights reserved. [. . . ] To adjust the prediction traces of the factors and find a Stretch value that is closer to the target, click the red triangle on the Prediction Profiler title bar and select Maximize Desirability. This command adjusts the profile traces to produce the response value closest to the specified target (the target given by the desirability function). The range of acceptable values is determined by the positions of the upper and lower handles. Figure 5. 8 shows the result of the most desirable settings. Changing the settings of Silica from 1. 2 to 1. 7, Silane from 50 to 54, and Sulfur from 2. 3 to 2. 8 raised the predicted response from 396 to the target value of 450. Finding maximum desirability is an iterative process so your results may differ slightly from those shown below. 134 Response Surface Designs A Box-Behnken Design: The Tennis Ball Example Chapter 5 Figure 5. 8 Prediction Profiler with Maximum Desirability Set for a Response Surface Analysis See Modeling and Multivariate Methods for further discussion of the Prediction Profiler. A Response Surface Plot (Contour Profiler) Another way to look at the response surface is to use the Contour Profiler. Click the red triangle on the Response Stretch title bar and select Factor Profiling > Contour Profiler to display the interactive contour profiler, as shown in Figure 5. 9. The contour profiler is useful for viewing response surfaces graphically, especially when there are multiple responses. This example shows the profile to Silica and Sulfur for a fixed value of Silane. Options on the Contour Profiler title bar can be used to set the grid density, request a surface plot (mesh plot), and add contours at specified intervals, like those shown in the contour plot in Figure 5. 9. The sliders for each factor set values for Current X and Current Y. Chapter 5 Response Surface Designs A Box-Behnken Design: The Tennis Ball Example 135 Figure 5. 9 Contour Profiler for a Response Surface Analysis Enter the Lo limit and Hi limit values to shade the unacceptable regions in the contour plot Figure 5. 10 Contour Profiler with High and Low Limits The Prediction Profiler and the Contour Profiler are discussed in more detail in Modeling and Multivariate Methods. 136 Response Surface Designs Creating a Response Surface Design Chapter 5 Geometry of a Box-Behnken Design The geometric structure of a design with three effects is seen by using the Scatterplot 3D platform. The plot shown in Figure 5. 11 illustrates the three Box-Behnken design columns. You can clearly see the center points and the 12 points midway between the vertices. For details on how to use the Scatterplot 3D platform, see Basic Analysis and Graphing. Figure 5. 11 Scatterplot 3D Rendition of a Box-Behnken Design for Three Effects Creating a Response Surface Design Response Surface Methodology (RSM) is an experimental technique invented to find the optimal response within specified ranges of the factors. These designs are capable of fitting a second-order prediction equation for the response. The quadratic terms in these equations model the curvature in the true response function. If a maximum or minimum exists inside the factor region, RSM can estimate it. In industrial applications, RSM designs usually involve a small number of factors. This is because the required number of runs increases dramatically with the number of factors. Using the response surface designer, you choose to use well-known RSM designs for two to eight continuous factors. Some of these designs also allow blocking. Response surface designs are useful for modeling and analyzing curved surfaces. [. . . ] Meyer, R. D. , Steinberg, D. M. , and Box, G. (1996), Follow-up Designs to Resolve Confounding in Multifactor Experiments, Technometrics, 38:4, p307. (1974), "An algorithm for the Construction of D-Optimal Experimental Designs, " Technometrics, 16:2, pp. 203-210. (2009), Design and Analysis of Experiments, Seventh Edition, Hoboken: John Wiley & Sons, Inc. Morris, M. D. , Mitchell, T. J. , and Ylvisaker, D. [. . . ]