Box-Behnken 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 "Response Surface Method - Box-Behnken Design."

Consider a UV-light system that is used to inactivate fungal spores of Aspergillus niger in corn meal.* Fungal contamination of grains during the post-harvest period has been a recurring health hazard.

The response is the log10 reduction of the fungal spores. Therefore, the goal is to maximize the reduction (response).

Three process parameters in the UV-light system will affect the inactivation results. They are: A) treatment time (number of pulses), B) the distance from the UV strobe and C) input voltage for the UV lamp.

A 15 run Box-Behnken design with three center points is conducted. A full quadratic model is fitted to the data. Using this model, the optimal setting that gives the largest reduction of fungal spores is found.

Designing the Experiment

The experimenters create a Box-Behnken design folio, perform the experiment according to the design, and then enter the response values in the folio for further analysis. The design matrix and the data are given in the "UV-light Treatment" folio. The following steps describe how to create this folio on your own.

Analysis and Results

The data set for this example is given in the "UV-light Treatment" folio of the example project. After you enter the data from the folio, you can specify the settings for 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 All Terms check box. Then click OK.

The results in the Analysis Summary area on the control panel show that time (A) and voltage (C) have significant effects on the reduction of the fungal spores, as well as AA (the quadratic effect of A) and the interaction of AC.

In the ANOVA table, you can see that effects A, C, AC and AA are significant. The p value for factor B is 0.1481, which is close to the risk level of 0.1. Therefore, you decide to include it in the final model.

Optimization

The results for the reduced model (which only includes the terms that were found to be significant) are given in the "Reduced Model" folio. The following steps describe how to create this folio on your own.

The coefficients for the model will appear in the Regression Table, as shown next.

The optimum settings for factors A and B are shown next.

Conclusions

The optimal solution is found to be A = 100 s, B = 3 cm and C = 3800 v. Under this setting, the expected logarithmic transformation of the reduction is 4.9. Keep in mind that it is necessary to conduct an experiment using this setting to confirm this conclusion.

* S. Jun, J. Irudayaraj, A. Demirci and D. Geiser, "Pulsed UV-light treatment of corn meal for inactivation of Aspergillus niger spores," International Journal of Food Science and Technology, 2003, 38, 883-888.

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