Extreme Vertex Designs: Example

The data set used in this example is available in the example database installed with the software (called "Weibull20_DOE_Examples.rsgz20"). To access this database file, choose File > Help, click Open Examples Folder, then browse for the file in the Weibull sub-folder.

The name of the example project is "Mixture Design - Extreme Vertex Design."

Four components, A, B, C and D, are used to make a polymer material. Their proportions are restricted by lower and upper bounds, and two linear constraints:

Bounds:

Linear constraints:

The objective of the experiment is to find the best settings of each component in order to maximize the strength of the material. An experiment within the feasible region defined by the above constraints should be conducted. The experimenters want some experiment runs to be placed at the boundary of the feasible region and some to be inside the region.

Designing the Experiment

The experimenters create an extreme vertex design folio, perform the experiment according to the design, and then enter the response values into the folio for analysis. The design matrix and the response data are given in the "Extreme Vertex Design" folio. The following steps describe how to create this folio on your own.

After you click OK, the constraints are displayed in the folio as shown next.

    • To determine whether you have entered any incompatible or unnecessary linear constraints, click the Validate Constraints icon next to the Linear Constraints heading.

 

No constraints are marked as problematic, so you can proceed.

Analysis and Results

The data set for this example is given in the "Extreme Vertex Design" folio of the example project. After you enter the data from the folio, you can perform the analysis by doing the following:

Note: To minimize the effect of unknown nuisance factors, the run order is randomly generated when you create the design. Therefore, if you followed these steps to create your own folio, the order of runs on the Data tab may be different from that of the folio in the example file. This can lead to different results. To ensure that you get the very same results described next, show the Standard Order column in your folio, then click a cell in that column and choose Sheet > Sheet Actions > Sort > Sort Ascending. This will make the order of runs in your folio the same as that of the example file. Then copy the response data from the example file and paste it into the Data tab of your folio.

In the window that appears, select the Linear and Quadratic check boxes. Then click OK.

In the ANOVA table, you can see that effects AD, BD and CD are significant. The p value for effect BC is also relatively close to the risk level of 0.1. Therefore, you decide to include it in the final model.

Optimization

The reduced model includes only the terms that were found to be significant. The following steps describe how to obtain this model on your own.

The optimum settings are shown next.

Conclusions

The optimal solution is found to be A = 0.2, B = 0.35, C = 0.2 and D = 0.25. Under this setting, the expected strength of the material is 3.75. Keep in mind that it is necessary to conduct an experiment using this setting to confirm this conclusion.

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